Chapter 33 Early Quantum Theory and Models of the Atom
Chapter 33
Early Quantum Theory
and Models of the Atom
1,Planck’s Quantum Hypothesis
2,The Photoelectric Effect
3,Compton Effect
4,Wave Nature of Matter
Chapter 33 Early Quantum Theory and Models of the Atom
New words and expressions
quantum hypothesis 量子假设
black-body 黑体
radiation 辐射
Planck’s quantum hypothesis 普朗克假设
quantized 量子化
The photoelectric effect 光电效应
stopping potential 遏止电压
Chapter 33 Early Quantum Theory and Models of the Atom
cutoff frequency 红限频率
Einstein’s Photoelectric Equation 爱因斯光电方程
work function 逸出功
compton effect 康普顿效应
matter wave (de Broglie wave) 物质波
Wave-Particle Duality 波粒二象性
Complementarity 互补性
Chapter 33 Early Quantum Theory and Models of the Atom
量子物理引言到十九世纪末期,物理学各个分支的发展都已日臻完善,并不断取得新的成就 。 首先在牛顿力学基础上,
哈密顿和拉格朗日等人建立起来的分析力学,几乎达到无懈可击的地步,特别是十九世纪中期,海王星的发现充分表明了牛顿力学是完美无缺的 。 其次,通过克劳修斯,玻耳兹曼和吉布斯等人的巨大努力,建立了体系完整而又严密的热力学和统计力学,并且应用越来越广泛 。
由安培,法拉第和麦克斯韦等人对电磁现象进行的深入而系统的研究,为电动力学奠定了坚实的基础,特别是由麦克斯韦的电磁场方程组预言了电磁波的存在,
Chapter 33 Early Quantum Theory and Models of the Atom
随即被赫兹的实验所证实 。 后来又把牛顿,惠更斯和菲涅耳所建立的光学也纳入了电动力学的范畴,更是一项 辉煌的成就 。 因此当时许多著名的物理学家都认为物理学的基本规律都已被发现,就连当时赫赫有名的权威人物开耳文勋爵在一篇于 1900年发表的瞻望二十世纪物理学发展的文章中也说：,在已经基本建成的科学大厦中,后辈物理学家只需要做一些零星的修补工作就行了,,不过他还不愧为一名确有远见卓识的物理学家,因为他接着又指出：,但是在物理晴朗天空的远处,还有两朵小小令人不安的乌云,,即运用当时的物理学理论所无法正确解释的两个实验现象,
一个是热辐射现象中的紫外灾难,另一个是否定绝对时空观的迈克尔逊 --莫雷实验,正是这两朵小小的乌云,
冲破了经典物理学的束缚,打消了当时绝大多数物理学家的盲目乐观情绪,为后来建立近代物理学的理论基础
Chapter 33 Early Quantum Theory and Models of the Atom
作 出了贡献 。 事实上还有第三朵小小的乌云,这就是放射性现象的发现,它有力地表明了原子不是构成物质的基本单元,原子也是可以分割的 。
所有这些实验结果都是经典物理学无法解释的,
它们使经典物理处于十分困难境地,为摆脱这种困境,
有一些思想敏锐而又不受旧观念束缚的物理学家纷纷重新思考研究,在二十世纪初期,建立起了近代物理的两大支柱 ------量子论和相对论,并在这个基础上又建立起以研究原子的结构,性质及其运动规律为目的的原子物理学,后来又进一步发展,相继建立起原子核物理学和基本粒子物理学,这些内容统称为量子物理学 。
Chapter 33 Early Quantum Theory and Models of the Atom
N.玻尔,M.玻恩,W.L.布拉格,L.V.德布罗意,A.H.康普顿,M.居里,P.A.M 狄喇克,A.爱因斯坦,W.K.海森堡,郞 之万,W.泡利、普朗克、薛定谔 等第五次索尔维会议与会者合影 (1927年 )
Chapter 33 Early Quantum Theory and Models of the Atom
量子概念是 1900 年普朗克首先提出的，距今已有一百多年的历史,其间，经过爱因斯坦、玻尔、德布罗意、玻恩、海森伯、薛定谔、狄拉克等许多物理大师的创新努力，到 20 世纪 30 年代，就建立了一套完整的量子力学理论,
量子力学 宏观领域 经典力学现代物理的理论基础量子力学相 对 论量子力学 微观世界的理论起源于对波粒二相性的认识
Chapter 33 Early Quantum Theory and Models of the Atom
§ 33-1 Planck’s Quantum Hypothesis (P763－ 764)
1,Black-body Radiation (黑体辐射 )
One of the observations that was unexplained at
the end of the 19th century was the spectrum of
light emitted by hot objects.
1) 热辐射 实验证明不同温度下物体能发出不同的电磁波,这种能量按频率的分布随温度而不同的电磁辐射叫做热辐射,
A we known that all objects emit radiation whose
total intensity is proportional to the fourth power
of the Kelvin temperature.
4TI?
Chapter 33 Early Quantum Theory and Models of the Atom
２ )辐射出射度 (辐出度 )
单位时间,单位面积上所辐射出的各种频率 （ 或各种波长 ）
的电磁波的能量总和,
0 d)()( TMTM
0 2 4 6 8 10 12
Hz10/ 14?
钨丝和太阳的单色辐出度曲线
2
12
10
4
6
8
))HzW / ( m10)(( 28TM?太阳可见光区钨丝
（ 5800K）
太阳
（ 5800K）
))HzW / ( m10)(( 29TM?钨丝
0 d)()( TMTM
Chapter 33 Early Quantum Theory and Models of the Atom
2,Blackbody (黑体 )
能完全吸收照射到它上面的各种频率的电磁辐射的物体称为黑体,A blackbody is a body that would
absorb all the radiation falling on it.
Chapter 33 Early Quantum Theory and Models of the Atom
任何物体 （ 气,液,固 ） 在任何温度下,都会有热辐射,只是在不同的温度下所发出的各种电磁波的能量按波长 （ 频率 ） 有不同的分布,所以才表现出各种颜色 。 低温物体发出的是红外光,炽热物体发出的是可见光,极高温物体发出的是紫外光 。
All objects emit electromagnetic radiation at any
temperature,As the temperature increases,the
electromagnetic radiation emitted by bodies is
most intense at higher and higher frequencies.
实验表明 辐射能力越强的物体，其吸收能力也越强,
A good absorber is also a good emitter.
Chapter 33 Early Quantum Theory and Models of the Atom
1400K800K 1000K 1200K
Shorter wavelength
Any heated solid or liquid,and even by dense
gases,can continuously radiate electromagnetic
wave which contains a continuous range of
wavelength,
例如：加热铁块,温度?,铁块颜色由看不出发光? 暗红? 橙色? 黄白色? 蓝白 色 。
Chapter 33 Early Quantum Theory and Models of the Atom
红外照相机拍摄的人的头部的 热图热的地方显白色，冷的地方显黑色
Chapter 33 Early Quantum Theory and Models of the Atom
一个黑白花盘子的两张照片室温下，反射光 1100K，自身辐射光
Chapter 33 Early Quantum Theory and Models of the Atom
１ ) Stefan-Boltzman equation斯特藩 —玻尔兹曼定律
4
0 d)()( TTMTM
428 KmW106 70.5
斯特藩 —玻尔兹曼常量
The rate at which an object emits energy via
electromagnetic radiation depends on the
object’s surface area A and the temperature T of
that area in Kelvins and is given by
This is called the Stefan-Boltzman equation,and
is a universal (Stefan-Boltzman) constant
3,黑体辐射规律
Chapter 33 Early Quantum Theory and Models of the Atom
Two important theoretical curves on blackbody
based on classical ideas were those proposed by
W.Wien (in 1896),
2) Wien’s 维恩位移定律维恩位移定律
bT?m?
Km10898.2 3b常量峰值波长
Chapter 33 Early Quantum Theory and Models of the Atom
K60 00K
1048 3
1089 8.2
9
3
m
bT
例 太阳的单色辐出度的峰值波长,
试由此估算太阳表面的温度,
nm4 8 3m
解 由维恩位移定律对宇宙中其他发光星体的表面温度也可用这种方法进行推测,
Examples 33-1 and 33-2 on page 764
Chapter 33 Early Quantum Theory and Models of the Atom
3) Rayleigh-Jeans theory 瑞利 —金斯公式
))HzW / ( m10)(( 29TM?
0 1 2 3
6
Hz10/ 14?
1
2
3
4
5
瑞利 - 金斯公式实验曲线
k2 0 0 0?T
*
*
*
*
*
* *
*
*
**
*
*
* * *
kT
c
TM 2
2π2
)(
瑞利 - 金斯公式紫外灾难
Chapter 33 Early Quantum Theory and Models of the Atom
Neither Wien’s nor Rayleigh -Jeans formulations
were in accord with experiment.
Wien’s was accurate at short wavelenths but
deviated from exp,At longer ones,whereas the
reverse was true for the Rayleigh-Jeans theory.
A cloud covered in fair skies of physics !
物理学晴朗天空中的一朵乌云 !
Chapter 33 Early Quantum Theory and Models of the Atom
1900年德国物理学家普朗克为了得到与实验曲线相一致的公式，
提出了一个与经典物理学概念截然不同的“能量子”假设：能量是分立的，不是连续的。
普朗克 （ 德国 ） （ 1858--
1947）,量子论的奠基人,1900
年 12月 14日他在德国物理学会上,
宣读了以,关于正常光谱中能量分布定律的理论,为题的论文，提出了黑体能量的量子化假设，并导出了黑体辐射的能量分布公式，劳厄称这一天是“量子论的诞生日”,
4,Planck’s Quantum Hypothesis 普朗克假设 (P765)
The break came in late 1900.
Chapter 33 Early Quantum Theory and Models of the Atom
sJ106 2 6 0 7 5 5.6 34h
Planck constant 普朗克常量
h?能量子 为单元来吸收或发射能量,
普朗克认为：金属空腔壁中电子的振动可视为一维谐振子，它吸收或者发射电磁辐射能量时，不是过去经典物理认为的那样可以连续的吸收或发射能量，
而是以与振子的频率成正比的
h1
h2
h3
h4
h5
h6
),3,2,1( nnh
空腔壁上的带电谐振子吸收或发射能量应为
Chapter 33 Early Quantum Theory and Models of the Atom
1e
dπ2d)(
/
3
2 kThc
hTM
普朗克黑体辐射公式
Max Planck (1858-1947) proposed an empirical
formula (经验式 ) that nicely fit the date:
The energy of any molecular vibration 振子的能量
could be only some whole number multiple of hf.
Chapter 33 Early Quantum Theory and Models of the Atom
---quantum of energy 能量子
Energy would not be a continuous quantity as
had been believed for centuries; rather it is
quantized (量子化 ) — it exists only in discrete
amount.
E=n? n=1,2,3...
= h f
“Quantum” means,discrete amount” as
opposed to,continuous”.
Chapter 33 Early Quantum Theory and Models of the Atom
Ramp versus stair analogy,On a ramp a box
can have continuous values of energy but on
stairs the box can have only discrete values of
energy.
Chapter 33 Early Quantum Theory and Models of the Atom
0 1 2 3
6
Hz10/ 14?
))HzW / ( m10)(( 29TM?
瑞利 - 金斯公式
1
2
3
4
5
k2 0 0 0?T
普朗克公式的理论曲线实验值
*
*
*
*
*
* *
*
*
**
*
*
* * *
Chapter 33 Early Quantum Theory and Models of the Atom
这个公式不仅与实验结果相符合,而且也解决了在经典热力学中固体比热与实验不符的问题 。
普朗克在 1900年 10月 19日德国物理学会说,即使这个辐射公式能证明是绝对精确的,但是如果仅仅是一个侥幸猜测出来的内插公式,那么它的价值也是有限的,。
他在 1907年给爱因斯坦的信中写到：,我为基本量子
（ 光量子 ） 所寻找的不是它在真空中的意义,而是它在吸收和发射地方的意义,并且我认为真空中过程已由麦克斯韦方程作了精辟的描述,。 直到 1913年他还对光子持否定态度 。
由于提出能量子假设,获 1918年诺贝尔物理学奖 。
Chapter 33 Early Quantum Theory and Models of the Atom
This is the first time that the quantum concept
was proposed in physics’ history,Later,the day
of December 14,1900 was called the birthday of
quantum theory.
Planck got the first Nobel Physics Prize in 1918
for his radical innovation (根本的改革,创新 ).
普朗克量子假设与经典理论不相容，是一个革命性的概念，打破几百年来人们奉行的自然界连续变化的看法，圆满地解释了热辐射现象，并成为现代量子理论的开端，带来物理学的一次巨大变革。
Chapter 33 Early Quantum Theory and Models of the Atom
普朗克的量子假说当时并未引起人们的广泛重视,
人们把他的黑体辐射公式只看成一个与实验符合最好的经验或半经验公式,但是爱因斯坦却看到了量子假说的重要性 。 1887年赫兹发现了光电效应,1905年爱因斯坦用光量子理论解释了光电效应 。 光电效应用经典的光的波动论是没办法解释的,只有用量子论才能解释 。
Chapter 33 Early Quantum Theory and Models of the Atom
§ 33-2 The Photoelectric Effect 光电效应 (P765-767)
1,The Photoelectric Effect
Photoelectric effect is the phenomenon that when
light shines on a metal surface,electrons are
emitted from the surface.
光照射某些金属时能从表面释放出电子的效应,这时逸出的电子称为 光电子 。
Chapter 33 Early Quantum Theory and Models of the Atom
V A
1) Experimental Apparatus
A metal plate and a electrode are placed inside
an evacuated glass tube,When the photocell is in
the dark the ammeter reads
zero.
When light of sufficiently
high frequency illuminates
the plate,the ammeter
indicates a current flowing in
the circuit.
Chapter 33 Early Quantum Theory and Models of the Atom
(1) The numbers of electrons in unit time emitted
from electrode is proportional to the intensity of
incident light (饱和光电流与入射光强成正比 ).
2) Experimental Results
电流饱和值
mi
（光强）
Ii?m
1I
2I
i
m1i
m2i
o0U? U
12 II?
Chapter 33 Early Quantum Theory and Models of the Atom
(2) Adjusting the V,—— there exists a stopping
potential Vstop
遏止电压
0U
遏止电势差与入射光频率具有线性关系,
m a xk0 EeU?
0U
0
Cs K Cu
Ekmax,光电子的最大初动能
Chapter 33 Early Quantum Theory and Models of the Atom
Then Ekmax,the maximum kinetic energy of the
emitted electrons can be determined using
conservation of energy:
s to peVmvK
2
m a xm a x 2
1
Measurements show that,The maximum
kinetic energy of these electrons Ekmax is
linearly increased with the frequency of
incident light;For light of a given frequency,
Ekmax does not depend on the
intensity of the light source 与入射光强无关,
Chapter 33 Early Quantum Theory and Models of the Atom
(3) Varying the frequency f of the incident light
and measure the associated stopping potential Vstop,
The cutoff wavelength:
There exist cutoff frequency f0 红限频率,below
which no photoelectric effect occur no matter
how intense the incident light is.
0 = c/f0
Chapter 33 Early Quantum Theory and Models of the Atom
(4) The electrons are ejected instantaneously
瞬时性当光照射到金属表面上时，几乎立即就有光电子逸出,
仅当 才发生光电效应，截止频率与 材料有关 与 光强无关,
几种纯金属的 截止 频率
0ff?
金属截止频率
Hz10/ 140f
4.545 5.50 8.065 11.53
铯 钠 锌 铱 铂
19.29
Chapter 33 Early Quantum Theory and Models of the Atom
按经典理论，电子逸出金属所需的能量，需要有一定的时间来积累，一直积累到足以使电子逸出金属表面为止,与实验结果不符,
经典理论遇到的困难红限问题瞬时性问题按经典理论,无论何种频率的入射光,只要其强度足够大，就能使电子具有足够的能量逸出金属,与实验结果不符,
Chapter 33 Early Quantum Theory and Models of the Atom
2 The Einstein’s Photoelectric Equation
If the electron is to escape from the target,it must
pick up energy at least equal to W0,Any additional
energy (hf - W0) that the electron acquires from the
photon appears as kinetic energy Ek of the electron.
Einstein summed up the experimental results as:
0m a x WEhf k
where W0 is the work function (逸出功,与材料有关 ).
电子吸收一个光子的能量 = 电子的最大初动能 + 逸出功
（ 1）,光量子”假设 h?光子的能量为
Chapter 33 Early Quantum Theory and Models of the Atom
In 1913-14,carefully experiments were carried
out by R.A.Millikan,The results were fully in
agreement with Einstein’s particle theory,
If the frequency f is less than the cutoff
frequency f0,where hf0 = W0,no electrons will be
ejected at all,no matter how great the intensity.
几种金属的逸出功金属 钠 铝 锌 铜 银 铂
2.28 4.08 4.31 4.70 4.73 6.35eV/W
对同一种金属,一定，,与光强无关kEW
Chapter 33 Early Quantum Theory and Models of the Atom
逸出功
0?hW?
爱因斯坦方程
Wmh 2
2
1 v?
hW 0
产生光电效应条件条件 （截止频率）
光强越大，光子数目越多，即单位时间内产生光电子数目越多，光电流越大,（ 时）
0
光子射至金属表面，一个光子携带的能量 将一次性被一个电子吸收，若,电子立即逸出，
无需时间积累（ 瞬时 性）,
h
0
Chapter 33 Early Quantum Theory and Models of the Atom
Applications of the Photoelectric Effect,P768
Besides playing an important historical role in
confirming the photo theory of light,it also has
many practical applications.
光电控制的路灯系统
Optical sound track on movie film; automatic
door opener making use of the photocell circuit
Chapter 33 Early Quantum Theory and Models of the Atom
§ 33-3 Photons and Compton Effect (P769-771)
1920年，美国物理学家康普顿在观察 X射线被物质散射时，发现 散射 线中含有 波长 发生 变化 了的成分,
1 实验装置
Chapter 33 Early Quantum Theory and Models of the Atom
在散射 X射线中除有与入射波长相同的射线外，还有波长比入射波长更长的射线,这种现象称为 康普顿效应,
The scattered light
had a slightly longer?' than did the incident light
by an amount D?,which is increase as the
scattering angle increase —— Compton shift.
Compton scattered short wavelength? light (X-
rays) from various materials.
Chapter 33 Early Quantum Theory and Models of the Atom
2 Experimental Results:
Three features of
scattering curve:
1.除原波长?0外出现了移向长波方面的新的散射波长?。
2.新波长?随散射角的增大而增大。
3.当散射角增大时，原波长的谱线强度降低，而新波长的谱线强度升高。
0
45
90
135
（相对强度）
（波长）?
I
0?
0?
Chapter 33 Early Quantum Theory and Models of the Atom
3,Contradict to the Classical Theory:
When light pass through materials,the electrons
in it will be forced vibration,The frequency of
vibration should be same with incident light,and
radiate electromagnetic wave with the same
frequency to all directions.
经典电磁理论预言,散射辐射具有和入射辐射一样的频率,经典理论无法解释波长变化,
经典理论的困难
Chapter 33 Early Quantum Theory and Models of the Atom
4,Compton’s explanation to scattering of x ray
Incident photons in x ray elastic colliding with
stationary electrons of the material (X射线光子与
,静止,的,自由电子,弹性碰撞 ).
0?
00?v
x
y光子电子
（ 1） 物理模型
x
y
电子光子
Chapter 33 Early Quantum Theory and Models of the Atom
电子反冲速度很大，需用 相对论力学 来处理,
入射光子（ X 射线或 射线）能量大,?
固体表面电子束缚较弱，可视为 近自由电子,
电子热运动能量,可近似为 静止电子,?h
eV10~10 54?hE? 范围为：
Chapter 33 Early Quantum Theory and Models of the Atom
During colliding,the energy and momentum are
conserved.
c o s2 2 0
2
2
22
2
2
0
2
22
c
h
c
h
c
hmv
x
y
0
0 e
c
h
ech
v?m
e?
0e
2200 mchcmhv
能量守恒
v me
c
he
c
h
0
0
动量守恒
)(2)c o s1(2)1( 020024202
2
42 hcmhcm
c
cm v
Chapter 33 Early Quantum Theory and Models of the Atom
康普顿波长
Compton wavelength
nm1043.2m1043.2 312
0
C
cm
h?
)co s1(
00
cm
hcc
)(2)c o s1(2)1( 020024202
2
42 hcmhcm
c
cm v
2/122
0 )/1(
cmm v
2
s i n2)co s1( 2
00
cm
h
cm
hDCompton shift
D 0
Chapter 33 Early Quantum Theory and Models of the Atom
散射光波长的改变量 仅与 有关?D?
0,0?D
Cm a x 2)(,πD?
散射光子能量减小
00,
（ 3） 结论
x
y
0
0 e
c
h
ech
v?m
e?
0e
Chapter 33 Early Quantum Theory and Models of the Atom
(1) The peak centered about the incident wave-
length arises from interactions between x rays
and the electrons that are tightly bound to the
carbon atoms making up the target 波长不变的散射光来自光子与整个原子 （ 内层电子 ） 的 碰撞,
4,Explanations
0
2
s i n2' 2D
Mc
h
Chapter 33 Early Quantum Theory and Models of the Atom
(2) The peak centered about the longer wave-
length arises from interactions between x rays
and the very loosely bound electrons in the target
(波长变长的散射光来自光子与原子外层电子的 碰撞 ).
(3) Compton effect is pronounced enough to be
observed if? and?c are comparable,so does x
ray (只有当入射波长?与?c可比拟时,康普顿效应才显著 。 因此要用 X射线才能观察到 ).
so0,t he n),(w he n
0
c?D cm
h
Chapter 33 Early Quantum Theory and Models of the Atom
5,The Physical Meaning of Compton Effect:
p = E/c = h f / c = h/?
= h f
It supported the theory of photon,光量子”,
and further proved:
It proved firstly the postulate by exp,that
photon has momentum proposed by Einstein.
It proved that both conservation law of
energy and momentum are hold during the
interaction between microscopic particles.
Chapter 33 Early Quantum Theory and Models of the Atom
Example,Assume that photon in x ray of
wavelength?=1.00?10-10 m collide elastically with
free electron,The scattering angle of x ray?=90?.
Find,what is (a) the compton shift D?=? (b) the
kinetic energy got by recoiling electron 反冲电子得到多少动能?
m1043.22s i n2 122D c
Solution,(a)
)()
11('
D?
D?
D
hchchfhfK
(b) The kinetic energy gotten by electron K is
what photon losses,so
=4.71?10-17 J
=295 eV
Chapter 33 Early Quantum Theory and Models of the Atom
§ 33-5 & 33-6 Wave-Particle Duality (波粒二象性 );
the principle of Complementarity; Wave Nature
of Matter 实物粒子的波动性 (p772-774)
1,Wave-particle Duality
Some experiments indicate that light behaves
like a wave,others indicate that it behaves like a
stream of particles.
We cannot picture a combination of wave and
particle,Instead,we must recognize that the two
aspects of light are different,faces” that light
shows to experiments.
Chapter 33 Early Quantum Theory and Models of the Atom
It states that to understand any given
experiment,we must use either the wave or
photon theory,but not both.
2,The Principle of Complementarity（互补性 P772)
The great Danish physicist Niels Bohr (1885-
1962) proposed his famous Principle of
Complementarity.
These two aspects of light complement one
another.
微观粒子在某些条件下表现出粒子性,在另一些条件下表现出波动性,而两种性质虽寓于同一体中,
却不能同时表现出来 。
Chapter 33 Early Quantum Theory and Models of the Atom
少女？
老妇？
两种图象不会同时出现在你的视觉中。
Chapter 33 Early Quantum Theory and Models of the Atom
思想方法 自然界在许多方面都是明显地对称的，他采用类比的方法提出物质波的假设,
,整个世纪以来,在辐射理论上,比起波动的研究方法来,是过于忽略了粒子的研究方法； 在实物理论上,
是否发生了相反的错误呢？ 是不是我们关于 ‘ 粒子 ’ 的图象想得太多,而过分地忽略了波的图象呢？,
法国物理学家德布罗意
（ Louis Victor de Broglie 1892 – 1987 )
3.Wave Nature of Matter 实物粒子的波动性 (p772-774)
Chapter 33 Early Quantum Theory and Models of the Atom
Chapter 33 Early Quantum Theory and Models of the Atom
法国物理学家,1929年诺贝尔物理学奖获得者,波动力学的创始人,量子力学的奠基人之一 。 德布罗意之前,人们对自然界的认识,
只局限于两种基本的物质类型：实物和场 。 前者由原子,电子等粒子构成,光则属于后者 。
但是,许多实验结果出现了难以解释的矛盾 。
物理学家们相信,这些表面上的矛盾,势必有其深刻的根源 。 1923年,德布罗意最早想到了这个问题,并且大胆地设想,人们对于光子的波粒二象性会不会也适用于实物粒子 。 如果成立的话,实物粒子也同样具有波动性 。 为了证
Chapter 33 Early Quantum Theory and Models of the Atom
实这一设想,1923年,德布罗意又提出了做电子衍射实验的设想 。 1924年,又提出用电子在晶体上作衍射实验的想法 。 1927年,戴维孙和革末用实验证实了电子具有波动性,不久,G.P.
汤姆孙与戴维孙完成了电子在晶体上的衍射实验 。 此后,人们相继证实了原子,分子,中子等都具有波动性 。 德布罗意的设想最终都得到了完全的证实 。 这些实物所具有的波动称为德布罗意波,即物质波 。
Chapter 33 Early Quantum Theory and Models of the Atom
德布罗意原来学习历史,随着作用量子 h
越来越深入到物质结构的各个领域,在求知欲的趋势下,他改学理论物理学 。 他善于用历史的观点,用对比的方法分析问题 。 1923
年,他就试图把粒子性和波动性统一起来 。
德布罗意是他在 1924年博士论文,关于量子理论的研究,中提出的,5年后,他因为这篇论文获得了诺贝尔物理学奖金 。 这时德布罗意关于物质波的假设已经被实验证实 。
Chapter 33 Early Quantum Theory and Models of the Atom
Why can't we think of a moving electron—or
any other particle,for that matter—as a matter
wave that transfers energy and momentum to
other matter at points?
In 1924 French physicist Louis de Broglie
(1892-1986 extended the idea of the wave-
particle duality of light and made following
appeal to symmetry:
Light-wave have particle nature,then does
matter has wave nature?
Chapter 33 Early Quantum Theory and Models of the Atom
He suggested that a particle of matter with E and p
has wave nature.
matter wave (de Broglie wave)
─ de Broglie wavelength
1 Hypothesis of De Broglie (德布罗意假设 )
德布罗意假设：实物粒子具有波粒二象性 (wave-
particle duality).
hE?
hp?
Chapter 33 Early Quantum Theory and Models of the Atom
例 在一束电子中，电子的动能为,
求此电子的德布罗意波长,Wavelength of an
electron？
eV200
解 2
0k 2
1,vv mEc
0
k2
m
E?v
1-61
31
19
sm104.8sm
101.9
106.12002
v
nm1067.8 2
nm
104.8101.9
1063.6
631
34
0
vm
h?cv?
此波长的数量级与 X 射线波长的数量级相当,
Chapter 33 Early Quantum Theory and Models of the Atom
Comparing with a bullet of m=0.01kg,v=300m/s:
m
m
h
p
h 341021.2
30001.0
341063.6
Macroscopic particles has larger m,so 0，
the wave-nature can not be shown 表现不出波动性,
,宏观物体只表现出粒子性
”
Chapter 33 Early Quantum Theory and Models of the Atom
2 德布罗意波的实验证明
1) 戴维孙 (Davisson) — 革末 (Germer)电子衍射实验
(electron scatter)
I
35 54 75 V/U
50
当散射角 时电流与加速电压曲线
50
检测器电子束散射线
电子被镍晶体衍射实验
M
U
K
G
电子枪
Chapter 33 Early Quantum Theory and Models of the Atom
kd?2co s2s i n2
kd?s in.,,,,,,,
.,,,,,,,
.,,,,,,,
d 2?
2?
2?
2sin
d
50,1k
m1015.2 10d
镍晶体
m1065.1si n 10 d
m1067.1
2
10
kee
Em
h
m
h
v
电子波的波长两相邻晶面电子束反射射线干涉加强条件
Chapter 33 Early Quantum Theory and Models of the Atom
2) G,P,汤姆孙 (Thomson电子衍射实验 ( 1927年 )
e m Ukhd 2
1si n
e m Ud
kh
2
1si n
k7 7 7.0s i n
当 时,与实验结果相近,?51777.0a r c s i n1k
U M
D P
电子束透过多晶铝箔的衍射
K
双缝衍射图
Chapter 33 Early Quantum Theory and Models of the Atom
§ 33-8,33-9,33-10 The Hydrogen Atom (P753-784)
The idea that matter is made up of atoms was
accepted by most scientists by 1900,With the
discovery of the electron in the 1890s,scientists
began to think of the atom itself as having a
structure and electrons as part of that structure.
1 Early Models of the Atom
Chapter 33 Early Quantum Theory and Models of the Atom
J,J,Thomson,soon after his discovery of
electrons in 1897,visualized a typical model of the
atom in 1903 as a homogeneous sphere of positive
charge inside of which there were tiny negative
charged electrons,1903年,汤姆孙提出原子的,葡萄干蛋糕模型,,
Thomson’s apparatus for
measuring the ratio of mass
to charge for the electron.
Chapter 33 Early Quantum Theory and Models of the Atom
Around 1911,E,Rutherford (1871-1937) and his
colleagues performed experiments whose results
contradicted Thomson’s model of the atom,
α 粒子实验存在大角散射
Chapter 33 Early Quantum Theory and Models of the Atom
The results based on the Rutherford’s,planetary”
model is accord well with the one from scattering
of? particle.卢瑟福的原子有核模型 （ 行星模型 ） 原子的中心有一带正电的原子核,它几乎集中了原子的全部质量,电子围绕这个核旋转,核的尺寸与整个原子相比是很小的,
1911年卢瑟福提出的原子的核模型电子原子核
Chapter 33 Early Quantum Theory and Models of the Atom
2 Two main difficulties of R’s,planetary”model
(1) It predicts that atoms are unstable —
electrons should quickly spiral into the
nucleus —but we know that atoms in general are
stable,since the matter around us is stable;
由于原子总能量减小，电子将逐渐的接近原子核而后相遇，
原子不稳定,e?
+e?
Chapter 33 Early Quantum Theory and Models of the Atom
(2) It predicts that light of a continuous range of
frequencies will be emitted,whereas experiment
shows line spectra 原子光谱的谱线,
根据经典电磁理论，电子绕核作匀速圆周运动，作加速运动的电子将不断向外辐射电磁波,v?F?
r e?
e?
+原子不断地向外辐射能量，
能量逐渐减小，电子绕核旋转的频率也逐渐改变，发射光谱应是连续谱；
Chapter 33 Early Quantum Theory and Models of the Atom
3 Atomic Spectra,Key to the Structure of Atom
Heated solids,liquids and dense gases emit light,
due to oscillations of atoms and molecules.
6562.8? 4340.5?4861.3?
A,J,Angstrom (Swedish瑞典人 ) observed the red
line of hydrogen line spectrum in the visible region
in 1853.
A is from him.。
The emission spectrum (发射光谱 ) is characteristic
of the material and can serve as a type of
“fingerprint” for identification of the gas.
Chapter 33 Early Quantum Theory and Models of the Atom
In 1885,J,J,Balmer showed that the four visible
lines in hydrogen spectrum fit following formula:
,5,4,3,)121(1 22 nnR?
R = 1.0974?107 m-1 ——
Rydberg constant 里德伯常量
The radiation from excited gases showed that the
spectrum was not continuous,but discrete.
Chapter 33 Early Quantum Theory and Models of the Atom
Later experiments on hydrogen showed that
there were similar series of lines (谱线系 ) which
had a pattern just like the Balmer series,but at
different wavelength.
,...3,2,1
1
11
22
i
i
n
n
R
Lyman series 莱曼系
,...5,4,1
3
11
22
i
i
n
n
R
Paschen series
帕邢系
(in the UV region)
(in the IR region))11( 22 nnh c Rhchf
Chapter 33 Early Quantum Theory and Models of the Atom
莱曼系?,3,2,)1
1
1(1
22 nnR
紫外
,4,3,)121(1 22 nnR巴尔末系可见光
,5,4,)131(1 22 nnR帕邢系
,6,5,)141(1 22 nnR布拉开系
,7,6,)151(1 22 nnR普丰德系
,8,7,)161(1 22 nnR汉弗莱系红外
Chapter 33 Early Quantum Theory and Models of the Atom
4 Bohr’s Theory of the Hydrogen Atom (P778):
Electrons move about the nucleus in circular
orbits,but only certain orbits (stationary state )
are allowed,An electron in each orbit would have
a definite energy and would move in the orbit
without radiating energy.
定态假设,1.
假设一 电子在原子中，可以在一些 特定 的轨道上运动而 不 辐射电磁波，这时原子处于 稳定 状态（ 定态 ），
并具有一定的能量,
Chapter 33 Early Quantum Theory and Models of the Atom
In heated solids,the energy of oscillating electric
charges must change discontinuously—from one
discrete energy state to another,with the emission
of a quantum of light,原子能量的量子化 。
频率定则,2.
fi EEh
频率条件假设 二 当原子从高能量 的定态跃迁到低能量
iE
fE
的定态时，要发射频率为 的光子,
当原子从能量较高（ Ei）的稳定状态跃迁到能量较低（ Ef ）的稳定状态时，原子发射出单色光,
Ei
Ef
●
f
Chapter 33 Early Quantum Theory and Models of the Atom
●+e
● -e
rn
vn
En
m
mp
The electron’s angular momentum L is quantized
and equal to an integer n times h/2?.
n,quantum number of orbit.
,3,2,1
2
nnhnL
3,Bohr’s quantum condition:
π2
hnrmL v量子化条件假设 三 电子以速度 在半径为 的圆周上绕核运动时，只有电子的 角动量 等于 的 整数倍 的那些轨道是 稳定 的,,（ 角动量量子化 ）π2h
v r
L
主 量子数
,3,2,1?n
Chapter 33 Early Quantum Theory and Models of the Atom
2
1
2
2
2
0
π
nrn
me
hr
n
),3,2,1(n
π2
hnrm
nn?v
由假设 2 量子化条件
n
n
n r
m
r
e 2
2
0
2
π4
v?
由牛顿定律
,玻尔半径
m1029.5
π
11
2
2
0
1
me
hr?1?n
氢原子能级公式
n
n
nn r
emE
0
2
2
π42
1
v
第 轨道电子总能量
Chapter 33 Early Quantum Theory and Models of the Atom
2
1
222
0
4 1
8 n
E
nh
meE
n
n
nn r
emE
0
2
2
π42
1
v
（电离能）
基态 能量
22
0
4
1 8 h
meE
eV6.13
)1(?n
21 nEE n?
激发态 能量 )1(?n
eV/E
氢原子能级图
1?n基态 6.13?
2?n
3?n
4?n激发态
4.3?
51.1?
85.0?
n 0
自由态
Chapter 33 Early Quantum Theory and Models of the Atom
玻尔理论对氢原子光谱的解释
fi EEh
fi
if
nn
nnch
me
c
,)11(
8
1
2232
0
4
氢原子能级跃迁与光谱系
1?n
2?n
3?n
4?n
n 0E
E
莱曼系巴耳末系帕邢系
222
0
4 1
8 nh
meE
n
布拉开系
17 m10097.1 （里德伯常量）R?
ch
me
32
0
4
8?
Chapter 33 Early Quantum Theory and Models of the Atom
Bohr’s model of atom gave us a first picture of
what an atom is like,It proposed an explanation
for why there should be emission and absorption
of light by atoms at discrete wavelength.
The electron in a hydrogen atom tends to be in
the lowest energy level — in its ground state.
We see that not only are the orbit radii quantized,
but so is the energy,The quantum number n that
labels the orbit radii also labels the energy levels.
For n = 1,
- 1 3,6 e VJ1017.2
8
18
22
0
4
1
h
meE
Chapter 33 Early Quantum Theory and Models of the Atom
由能级算出的光谱线频率和实验结果完全一致
Bohr theory predicts well ionization energy 13.6eV
for hydrogen,but was not so successful for others.
Chapter 33 Early Quantum Theory and Models of the Atom
（ 1） 正确地指出 原子能级 的存在（原子能量量子化）；
（ 2） 正确地指出 定态 和 角动量量子化 的概念；
（ 3） 正确的解释了氢原子及类氢离子光谱；
氢原子玻尔理论的意义和困难
（ 4） 无法解释 比氢原子更复杂的原子；
（ 5） 把微观粒子的运动视为有确定的 轨道 是不正确的；
（ 6） 是 半 经典 半 量子 理论，存在逻辑上的缺点，即把微观粒子看成是遵守经典力学的质点，同时，又赋予它们量子化的特征,
Chapter 33 Early Quantum Theory and Models of the Atom
1914 年弗兰克 — 赫兹从实验上证实了 原子存在分立的能级,1925 年他们因此而获物理学 诺贝尔奖,
pI
V9.4
V9.4
0 5 10 15 V/
0U
板极电流和加速电压之间的关系
0U rU
pI
栅极灯丝 板极弗兰克 — 赫兹实验装置低压水银蒸汽
V5.0r?U
A
G P
+ ++
+
- -
-
-
Chapter 33 Early Quantum Theory and Models of the Atom
§ 33-11 de Broglie’s Hypothesis Applied to Atom
According to de Broglie,a particle of mass m
moving with a nonrelativistic speed v would have
He proposed,Each electron orbit in
an atom is a standing wave,To form
constructive interference,persist,the
circumference of a Bohr orbit of
radius rn should be 2? rn as Fig.,so
mv
h
nr n?2
Chapter 33 Early Quantum Theory and Models of the Atom
2
,or nhmv r n?
This is the quantum condition ( 量子化条件 )
proposed by Bohr,This implies that the wave-
particle duality is at the root of atomic structure.
Bohr’s theory worked well for one-electron ions,
but didn’t prove as successful for multielectron
atoms,A new theory was needed and was indeed
developed in 1920s,
This new and radical theory is called quantum
mechanics —— unifies the wave-particle duality
into a single consistent theory.
Chapter 33 Early Quantum Theory and Models of the Atom
1 Statistical Meaning of De Broglie’s Wave:
Particle,Energy? ; Momentum p; Quantities N
Wave,wavelength? ; Frequency f ; Amplitude E0
The numbers of particles N? I? E02
The intensity of De Broglie’s wave
somewhere is proportional to the
probability that the particle appears
near there（ 在某处德布罗意波的强度与粒子在该处邻近出现的概率成正比 ）,
Their Relation:
Chapter 33 Early Quantum Theory and Models of the Atom
The De Broglie’s wave is different from classical
wave,Mechanical wave is the propagation of the
mechanical oscillation; De Broglie’s wave is the
statistical description for the motion of
microscopic particle.
不是经典的波,不代表实在的物理量的波动,
The particle and wave are united in the
probability-wave theory (统一于 概率波 理论 ).
Chapter 33 Early Quantum Theory and Models of the Atom
2 对物质波的理解，概率波的概念怎样理解物质波（德布罗意波）?
薛定谔,波是基本的，电子是,波包”。 但波包要扩散,而电子是稳定的。
德布罗意,物质波是引导粒子运动的,导波”。
—— 本质是什么，不明确。
另一种理解,粒子是基本的，电子的物质波是大量电子 相互作用 形成的。
—— 被以下实验否定
Chapter 33 Early Quantum Theory and Models of the Atom
电子双缝的衍射实验减弱入射电子束的强度，让一个一个电子依次通过双缝，则随着电子树的积累，衍射图样依次如图。
7个电子 100个电子底片上出现一个个的点子?电子具有 粒子性。
Chapter 33 Early Quantum Theory and Models of the Atom
70000
3000 20000
随着电子增多，逐渐形成衍射图样。
来源于,一个电子”所具有的波动性,而不是电子间相互作用的结果。
Chapter 33 Early Quantum Theory and Models of the Atom
电子数 N=7100300020000电子数 70000
单个粒子在哪一处出现是偶然事件；
大量粒子的分布有确定的统计规律。
出现概率小 出现概率大电子双缝干涉图样
Chapter 33 Early Quantum Theory and Models of the Atom
玻恩 （ M.Born）,尽管单个电子的去向是概率性的,但其概率在一定条件下 （ 如双缝 ）,还是有确定的规律的 。
德布罗意波 并不是经典的波那样是代表实在物理量的波动 。 在双缝实验中 。 不管入射 波强度如何小,
经典的波在缝后的屏幕上都,应该,显示出强弱连续分布的衍射条纹,只是亮度微弱而已 。 但图中明确地显示物质波的主体仍是粒子,而且该种粒子的运动并不具有经典的振动形式 。
Chapter 33
Early Quantum Theory
and Models of the Atom
1,Planck’s Quantum Hypothesis
2,The Photoelectric Effect
3,Compton Effect
4,Wave Nature of Matter
Chapter 33 Early Quantum Theory and Models of the Atom
New words and expressions
quantum hypothesis 量子假设
black-body 黑体
radiation 辐射
Planck’s quantum hypothesis 普朗克假设
quantized 量子化
The photoelectric effect 光电效应
stopping potential 遏止电压
Chapter 33 Early Quantum Theory and Models of the Atom
cutoff frequency 红限频率
Einstein’s Photoelectric Equation 爱因斯光电方程
work function 逸出功
compton effect 康普顿效应
matter wave (de Broglie wave) 物质波
Wave-Particle Duality 波粒二象性
Complementarity 互补性
Chapter 33 Early Quantum Theory and Models of the Atom
量子物理引言到十九世纪末期,物理学各个分支的发展都已日臻完善,并不断取得新的成就 。 首先在牛顿力学基础上,
哈密顿和拉格朗日等人建立起来的分析力学,几乎达到无懈可击的地步,特别是十九世纪中期,海王星的发现充分表明了牛顿力学是完美无缺的 。 其次,通过克劳修斯,玻耳兹曼和吉布斯等人的巨大努力,建立了体系完整而又严密的热力学和统计力学,并且应用越来越广泛 。
由安培,法拉第和麦克斯韦等人对电磁现象进行的深入而系统的研究,为电动力学奠定了坚实的基础,特别是由麦克斯韦的电磁场方程组预言了电磁波的存在,
Chapter 33 Early Quantum Theory and Models of the Atom
随即被赫兹的实验所证实 。 后来又把牛顿,惠更斯和菲涅耳所建立的光学也纳入了电动力学的范畴,更是一项 辉煌的成就 。 因此当时许多著名的物理学家都认为物理学的基本规律都已被发现,就连当时赫赫有名的权威人物开耳文勋爵在一篇于 1900年发表的瞻望二十世纪物理学发展的文章中也说：,在已经基本建成的科学大厦中,后辈物理学家只需要做一些零星的修补工作就行了,,不过他还不愧为一名确有远见卓识的物理学家,因为他接着又指出：,但是在物理晴朗天空的远处,还有两朵小小令人不安的乌云,,即运用当时的物理学理论所无法正确解释的两个实验现象,
一个是热辐射现象中的紫外灾难,另一个是否定绝对时空观的迈克尔逊 --莫雷实验,正是这两朵小小的乌云,
冲破了经典物理学的束缚,打消了当时绝大多数物理学家的盲目乐观情绪,为后来建立近代物理学的理论基础
Chapter 33 Early Quantum Theory and Models of the Atom
作 出了贡献 。 事实上还有第三朵小小的乌云,这就是放射性现象的发现,它有力地表明了原子不是构成物质的基本单元,原子也是可以分割的 。
所有这些实验结果都是经典物理学无法解释的,
它们使经典物理处于十分困难境地,为摆脱这种困境,
有一些思想敏锐而又不受旧观念束缚的物理学家纷纷重新思考研究,在二十世纪初期,建立起了近代物理的两大支柱 ------量子论和相对论,并在这个基础上又建立起以研究原子的结构,性质及其运动规律为目的的原子物理学,后来又进一步发展,相继建立起原子核物理学和基本粒子物理学,这些内容统称为量子物理学 。
Chapter 33 Early Quantum Theory and Models of the Atom
N.玻尔,M.玻恩,W.L.布拉格,L.V.德布罗意,A.H.康普顿,M.居里,P.A.M 狄喇克,A.爱因斯坦,W.K.海森堡,郞 之万,W.泡利、普朗克、薛定谔 等第五次索尔维会议与会者合影 (1927年 )
Chapter 33 Early Quantum Theory and Models of the Atom
量子概念是 1900 年普朗克首先提出的，距今已有一百多年的历史,其间，经过爱因斯坦、玻尔、德布罗意、玻恩、海森伯、薛定谔、狄拉克等许多物理大师的创新努力，到 20 世纪 30 年代，就建立了一套完整的量子力学理论,
量子力学 宏观领域 经典力学现代物理的理论基础量子力学相 对 论量子力学 微观世界的理论起源于对波粒二相性的认识
Chapter 33 Early Quantum Theory and Models of the Atom
§ 33-1 Planck’s Quantum Hypothesis (P763－ 764)
1,Black-body Radiation (黑体辐射 )
One of the observations that was unexplained at
the end of the 19th century was the spectrum of
light emitted by hot objects.
1) 热辐射 实验证明不同温度下物体能发出不同的电磁波,这种能量按频率的分布随温度而不同的电磁辐射叫做热辐射,
A we known that all objects emit radiation whose
total intensity is proportional to the fourth power
of the Kelvin temperature.
4TI?
Chapter 33 Early Quantum Theory and Models of the Atom
２ )辐射出射度 (辐出度 )
单位时间,单位面积上所辐射出的各种频率 （ 或各种波长 ）
的电磁波的能量总和,
0 d)()( TMTM
0 2 4 6 8 10 12
Hz10/ 14?
钨丝和太阳的单色辐出度曲线
2
12
10
4
6
8
))HzW / ( m10)(( 28TM?太阳可见光区钨丝
（ 5800K）
太阳
（ 5800K）
))HzW / ( m10)(( 29TM?钨丝
0 d)()( TMTM
Chapter 33 Early Quantum Theory and Models of the Atom
2,Blackbody (黑体 )
能完全吸收照射到它上面的各种频率的电磁辐射的物体称为黑体,A blackbody is a body that would
absorb all the radiation falling on it.
Chapter 33 Early Quantum Theory and Models of the Atom
任何物体 （ 气,液,固 ） 在任何温度下,都会有热辐射,只是在不同的温度下所发出的各种电磁波的能量按波长 （ 频率 ） 有不同的分布,所以才表现出各种颜色 。 低温物体发出的是红外光,炽热物体发出的是可见光,极高温物体发出的是紫外光 。
All objects emit electromagnetic radiation at any
temperature,As the temperature increases,the
electromagnetic radiation emitted by bodies is
most intense at higher and higher frequencies.
实验表明 辐射能力越强的物体，其吸收能力也越强,
A good absorber is also a good emitter.
Chapter 33 Early Quantum Theory and Models of the Atom
1400K800K 1000K 1200K
Shorter wavelength
Any heated solid or liquid,and even by dense
gases,can continuously radiate electromagnetic
wave which contains a continuous range of
wavelength,
例如：加热铁块,温度?,铁块颜色由看不出发光? 暗红? 橙色? 黄白色? 蓝白 色 。
Chapter 33 Early Quantum Theory and Models of the Atom
红外照相机拍摄的人的头部的 热图热的地方显白色，冷的地方显黑色
Chapter 33 Early Quantum Theory and Models of the Atom
一个黑白花盘子的两张照片室温下，反射光 1100K，自身辐射光
Chapter 33 Early Quantum Theory and Models of the Atom
１ ) Stefan-Boltzman equation斯特藩 —玻尔兹曼定律
4
0 d)()( TTMTM
428 KmW106 70.5
斯特藩 —玻尔兹曼常量
The rate at which an object emits energy via
electromagnetic radiation depends on the
object’s surface area A and the temperature T of
that area in Kelvins and is given by
This is called the Stefan-Boltzman equation,and
is a universal (Stefan-Boltzman) constant
3,黑体辐射规律
Chapter 33 Early Quantum Theory and Models of the Atom
Two important theoretical curves on blackbody
based on classical ideas were those proposed by
W.Wien (in 1896),
2) Wien’s 维恩位移定律维恩位移定律
bT?m?
Km10898.2 3b常量峰值波长
Chapter 33 Early Quantum Theory and Models of the Atom
K60 00K
1048 3
1089 8.2
9
3
m
bT
例 太阳的单色辐出度的峰值波长,
试由此估算太阳表面的温度,
nm4 8 3m
解 由维恩位移定律对宇宙中其他发光星体的表面温度也可用这种方法进行推测,
Examples 33-1 and 33-2 on page 764
Chapter 33 Early Quantum Theory and Models of the Atom
3) Rayleigh-Jeans theory 瑞利 —金斯公式
))HzW / ( m10)(( 29TM?
0 1 2 3
6
Hz10/ 14?
1
2
3
4
5
瑞利 - 金斯公式实验曲线
k2 0 0 0?T
*
*
*
*
*
* *
*
*
**
*
*
* * *
kT
c
TM 2
2π2
)(
瑞利 - 金斯公式紫外灾难
Chapter 33 Early Quantum Theory and Models of the Atom
Neither Wien’s nor Rayleigh -Jeans formulations
were in accord with experiment.
Wien’s was accurate at short wavelenths but
deviated from exp,At longer ones,whereas the
reverse was true for the Rayleigh-Jeans theory.
A cloud covered in fair skies of physics !
物理学晴朗天空中的一朵乌云 !
Chapter 33 Early Quantum Theory and Models of the Atom
1900年德国物理学家普朗克为了得到与实验曲线相一致的公式，
提出了一个与经典物理学概念截然不同的“能量子”假设：能量是分立的，不是连续的。
普朗克 （ 德国 ） （ 1858--
1947）,量子论的奠基人,1900
年 12月 14日他在德国物理学会上,
宣读了以,关于正常光谱中能量分布定律的理论,为题的论文，提出了黑体能量的量子化假设，并导出了黑体辐射的能量分布公式，劳厄称这一天是“量子论的诞生日”,
4,Planck’s Quantum Hypothesis 普朗克假设 (P765)
The break came in late 1900.
Chapter 33 Early Quantum Theory and Models of the Atom
sJ106 2 6 0 7 5 5.6 34h
Planck constant 普朗克常量
h?能量子 为单元来吸收或发射能量,
普朗克认为：金属空腔壁中电子的振动可视为一维谐振子，它吸收或者发射电磁辐射能量时，不是过去经典物理认为的那样可以连续的吸收或发射能量，
而是以与振子的频率成正比的
h1
h2
h3
h4
h5
h6
),3,2,1( nnh
空腔壁上的带电谐振子吸收或发射能量应为
Chapter 33 Early Quantum Theory and Models of the Atom
1e
dπ2d)(
/
3
2 kThc
hTM
普朗克黑体辐射公式
Max Planck (1858-1947) proposed an empirical
formula (经验式 ) that nicely fit the date:
The energy of any molecular vibration 振子的能量
could be only some whole number multiple of hf.
Chapter 33 Early Quantum Theory and Models of the Atom
---quantum of energy 能量子
Energy would not be a continuous quantity as
had been believed for centuries; rather it is
quantized (量子化 ) — it exists only in discrete
amount.
E=n? n=1,2,3...
= h f
“Quantum” means,discrete amount” as
opposed to,continuous”.
Chapter 33 Early Quantum Theory and Models of the Atom
Ramp versus stair analogy,On a ramp a box
can have continuous values of energy but on
stairs the box can have only discrete values of
energy.
Chapter 33 Early Quantum Theory and Models of the Atom
0 1 2 3
6
Hz10/ 14?
))HzW / ( m10)(( 29TM?
瑞利 - 金斯公式
1
2
3
4
5
k2 0 0 0?T
普朗克公式的理论曲线实验值
*
*
*
*
*
* *
*
*
**
*
*
* * *
Chapter 33 Early Quantum Theory and Models of the Atom
这个公式不仅与实验结果相符合,而且也解决了在经典热力学中固体比热与实验不符的问题 。
普朗克在 1900年 10月 19日德国物理学会说,即使这个辐射公式能证明是绝对精确的,但是如果仅仅是一个侥幸猜测出来的内插公式,那么它的价值也是有限的,。
他在 1907年给爱因斯坦的信中写到：,我为基本量子
（ 光量子 ） 所寻找的不是它在真空中的意义,而是它在吸收和发射地方的意义,并且我认为真空中过程已由麦克斯韦方程作了精辟的描述,。 直到 1913年他还对光子持否定态度 。
由于提出能量子假设,获 1918年诺贝尔物理学奖 。
Chapter 33 Early Quantum Theory and Models of the Atom
This is the first time that the quantum concept
was proposed in physics’ history,Later,the day
of December 14,1900 was called the birthday of
quantum theory.
Planck got the first Nobel Physics Prize in 1918
for his radical innovation (根本的改革,创新 ).
普朗克量子假设与经典理论不相容，是一个革命性的概念，打破几百年来人们奉行的自然界连续变化的看法，圆满地解释了热辐射现象，并成为现代量子理论的开端，带来物理学的一次巨大变革。
Chapter 33 Early Quantum Theory and Models of the Atom
普朗克的量子假说当时并未引起人们的广泛重视,
人们把他的黑体辐射公式只看成一个与实验符合最好的经验或半经验公式,但是爱因斯坦却看到了量子假说的重要性 。 1887年赫兹发现了光电效应,1905年爱因斯坦用光量子理论解释了光电效应 。 光电效应用经典的光的波动论是没办法解释的,只有用量子论才能解释 。
Chapter 33 Early Quantum Theory and Models of the Atom
§ 33-2 The Photoelectric Effect 光电效应 (P765-767)
1,The Photoelectric Effect
Photoelectric effect is the phenomenon that when
light shines on a metal surface,electrons are
emitted from the surface.
光照射某些金属时能从表面释放出电子的效应,这时逸出的电子称为 光电子 。
Chapter 33 Early Quantum Theory and Models of the Atom
V A
1) Experimental Apparatus
A metal plate and a electrode are placed inside
an evacuated glass tube,When the photocell is in
the dark the ammeter reads
zero.
When light of sufficiently
high frequency illuminates
the plate,the ammeter
indicates a current flowing in
the circuit.
Chapter 33 Early Quantum Theory and Models of the Atom
(1) The numbers of electrons in unit time emitted
from electrode is proportional to the intensity of
incident light (饱和光电流与入射光强成正比 ).
2) Experimental Results
电流饱和值
mi
（光强）
Ii?m
1I
2I
i
m1i
m2i
o0U? U
12 II?
Chapter 33 Early Quantum Theory and Models of the Atom
(2) Adjusting the V,—— there exists a stopping
potential Vstop
遏止电压
0U
遏止电势差与入射光频率具有线性关系,
m a xk0 EeU?
0U
0
Cs K Cu
Ekmax,光电子的最大初动能
Chapter 33 Early Quantum Theory and Models of the Atom
Then Ekmax,the maximum kinetic energy of the
emitted electrons can be determined using
conservation of energy:
s to peVmvK
2
m a xm a x 2
1
Measurements show that,The maximum
kinetic energy of these electrons Ekmax is
linearly increased with the frequency of
incident light;For light of a given frequency,
Ekmax does not depend on the
intensity of the light source 与入射光强无关,
Chapter 33 Early Quantum Theory and Models of the Atom
(3) Varying the frequency f of the incident light
and measure the associated stopping potential Vstop,
The cutoff wavelength:
There exist cutoff frequency f0 红限频率,below
which no photoelectric effect occur no matter
how intense the incident light is.
0 = c/f0
Chapter 33 Early Quantum Theory and Models of the Atom
(4) The electrons are ejected instantaneously
瞬时性当光照射到金属表面上时，几乎立即就有光电子逸出,
仅当 才发生光电效应，截止频率与 材料有关 与 光强无关,
几种纯金属的 截止 频率
0ff?
金属截止频率
Hz10/ 140f
4.545 5.50 8.065 11.53
铯 钠 锌 铱 铂
19.29
Chapter 33 Early Quantum Theory and Models of the Atom
按经典理论，电子逸出金属所需的能量，需要有一定的时间来积累，一直积累到足以使电子逸出金属表面为止,与实验结果不符,
经典理论遇到的困难红限问题瞬时性问题按经典理论,无论何种频率的入射光,只要其强度足够大，就能使电子具有足够的能量逸出金属,与实验结果不符,
Chapter 33 Early Quantum Theory and Models of the Atom
2 The Einstein’s Photoelectric Equation
If the electron is to escape from the target,it must
pick up energy at least equal to W0,Any additional
energy (hf - W0) that the electron acquires from the
photon appears as kinetic energy Ek of the electron.
Einstein summed up the experimental results as:
0m a x WEhf k
where W0 is the work function (逸出功,与材料有关 ).
电子吸收一个光子的能量 = 电子的最大初动能 + 逸出功
（ 1）,光量子”假设 h?光子的能量为
Chapter 33 Early Quantum Theory and Models of the Atom
In 1913-14,carefully experiments were carried
out by R.A.Millikan,The results were fully in
agreement with Einstein’s particle theory,
If the frequency f is less than the cutoff
frequency f0,where hf0 = W0,no electrons will be
ejected at all,no matter how great the intensity.
几种金属的逸出功金属 钠 铝 锌 铜 银 铂
2.28 4.08 4.31 4.70 4.73 6.35eV/W
对同一种金属,一定，,与光强无关kEW
Chapter 33 Early Quantum Theory and Models of the Atom
逸出功
0?hW?
爱因斯坦方程
Wmh 2
2
1 v?
hW 0
产生光电效应条件条件 （截止频率）
光强越大，光子数目越多，即单位时间内产生光电子数目越多，光电流越大,（ 时）
0
光子射至金属表面，一个光子携带的能量 将一次性被一个电子吸收，若,电子立即逸出，
无需时间积累（ 瞬时 性）,
h
0
Chapter 33 Early Quantum Theory and Models of the Atom
Applications of the Photoelectric Effect,P768
Besides playing an important historical role in
confirming the photo theory of light,it also has
many practical applications.
光电控制的路灯系统
Optical sound track on movie film; automatic
door opener making use of the photocell circuit
Chapter 33 Early Quantum Theory and Models of the Atom
§ 33-3 Photons and Compton Effect (P769-771)
1920年，美国物理学家康普顿在观察 X射线被物质散射时，发现 散射 线中含有 波长 发生 变化 了的成分,
1 实验装置
Chapter 33 Early Quantum Theory and Models of the Atom
在散射 X射线中除有与入射波长相同的射线外，还有波长比入射波长更长的射线,这种现象称为 康普顿效应,
The scattered light
had a slightly longer?' than did the incident light
by an amount D?,which is increase as the
scattering angle increase —— Compton shift.
Compton scattered short wavelength? light (X-
rays) from various materials.
Chapter 33 Early Quantum Theory and Models of the Atom
2 Experimental Results:
Three features of
scattering curve:
1.除原波长?0外出现了移向长波方面的新的散射波长?。
2.新波长?随散射角的增大而增大。
3.当散射角增大时，原波长的谱线强度降低，而新波长的谱线强度升高。
0
45
90
135
（相对强度）
（波长）?
I
0?
0?
Chapter 33 Early Quantum Theory and Models of the Atom
3,Contradict to the Classical Theory:
When light pass through materials,the electrons
in it will be forced vibration,The frequency of
vibration should be same with incident light,and
radiate electromagnetic wave with the same
frequency to all directions.
经典电磁理论预言,散射辐射具有和入射辐射一样的频率,经典理论无法解释波长变化,
经典理论的困难
Chapter 33 Early Quantum Theory and Models of the Atom
4,Compton’s explanation to scattering of x ray
Incident photons in x ray elastic colliding with
stationary electrons of the material (X射线光子与
,静止,的,自由电子,弹性碰撞 ).
0?
00?v
x
y光子电子
（ 1） 物理模型
x
y
电子光子
Chapter 33 Early Quantum Theory and Models of the Atom
电子反冲速度很大，需用 相对论力学 来处理,
入射光子（ X 射线或 射线）能量大,?
固体表面电子束缚较弱，可视为 近自由电子,
电子热运动能量,可近似为 静止电子,?h
eV10~10 54?hE? 范围为：
Chapter 33 Early Quantum Theory and Models of the Atom
During colliding,the energy and momentum are
conserved.
c o s2 2 0
2
2
22
2
2
0
2
22
c
h
c
h
c
hmv
x
y
0
0 e
c
h
ech
v?m
e?
0e
2200 mchcmhv
能量守恒
v me
c
he
c
h
0
0
动量守恒
)(2)c o s1(2)1( 020024202
2
42 hcmhcm
c
cm v
Chapter 33 Early Quantum Theory and Models of the Atom
康普顿波长
Compton wavelength
nm1043.2m1043.2 312
0
C
cm
h?
)co s1(
00
cm
hcc
)(2)c o s1(2)1( 020024202
2
42 hcmhcm
c
cm v
2/122
0 )/1(
cmm v
2
s i n2)co s1( 2
00
cm
h
cm
hDCompton shift
D 0
Chapter 33 Early Quantum Theory and Models of the Atom
散射光波长的改变量 仅与 有关?D?
0,0?D
Cm a x 2)(,πD?
散射光子能量减小
00,
（ 3） 结论
x
y
0
0 e
c
h
ech
v?m
e?
0e
Chapter 33 Early Quantum Theory and Models of the Atom
(1) The peak centered about the incident wave-
length arises from interactions between x rays
and the electrons that are tightly bound to the
carbon atoms making up the target 波长不变的散射光来自光子与整个原子 （ 内层电子 ） 的 碰撞,
4,Explanations
0
2
s i n2' 2D
Mc
h
Chapter 33 Early Quantum Theory and Models of the Atom
(2) The peak centered about the longer wave-
length arises from interactions between x rays
and the very loosely bound electrons in the target
(波长变长的散射光来自光子与原子外层电子的 碰撞 ).
(3) Compton effect is pronounced enough to be
observed if? and?c are comparable,so does x
ray (只有当入射波长?与?c可比拟时,康普顿效应才显著 。 因此要用 X射线才能观察到 ).
so0,t he n),(w he n
0
c?D cm
h
Chapter 33 Early Quantum Theory and Models of the Atom
5,The Physical Meaning of Compton Effect:
p = E/c = h f / c = h/?
= h f
It supported the theory of photon,光量子”,
and further proved:
It proved firstly the postulate by exp,that
photon has momentum proposed by Einstein.
It proved that both conservation law of
energy and momentum are hold during the
interaction between microscopic particles.
Chapter 33 Early Quantum Theory and Models of the Atom
Example,Assume that photon in x ray of
wavelength?=1.00?10-10 m collide elastically with
free electron,The scattering angle of x ray?=90?.
Find,what is (a) the compton shift D?=? (b) the
kinetic energy got by recoiling electron 反冲电子得到多少动能?
m1043.22s i n2 122D c
Solution,(a)
)()
11('
D?
D?
D
hchchfhfK
(b) The kinetic energy gotten by electron K is
what photon losses,so
=4.71?10-17 J
=295 eV
Chapter 33 Early Quantum Theory and Models of the Atom
§ 33-5 & 33-6 Wave-Particle Duality (波粒二象性 );
the principle of Complementarity; Wave Nature
of Matter 实物粒子的波动性 (p772-774)
1,Wave-particle Duality
Some experiments indicate that light behaves
like a wave,others indicate that it behaves like a
stream of particles.
We cannot picture a combination of wave and
particle,Instead,we must recognize that the two
aspects of light are different,faces” that light
shows to experiments.
Chapter 33 Early Quantum Theory and Models of the Atom
It states that to understand any given
experiment,we must use either the wave or
photon theory,but not both.
2,The Principle of Complementarity（互补性 P772)
The great Danish physicist Niels Bohr (1885-
1962) proposed his famous Principle of
Complementarity.
These two aspects of light complement one
another.
微观粒子在某些条件下表现出粒子性,在另一些条件下表现出波动性,而两种性质虽寓于同一体中,
却不能同时表现出来 。
Chapter 33 Early Quantum Theory and Models of the Atom
少女？
老妇？
两种图象不会同时出现在你的视觉中。
Chapter 33 Early Quantum Theory and Models of the Atom
思想方法 自然界在许多方面都是明显地对称的，他采用类比的方法提出物质波的假设,
,整个世纪以来,在辐射理论上,比起波动的研究方法来,是过于忽略了粒子的研究方法； 在实物理论上,
是否发生了相反的错误呢？ 是不是我们关于 ‘ 粒子 ’ 的图象想得太多,而过分地忽略了波的图象呢？,
法国物理学家德布罗意
（ Louis Victor de Broglie 1892 – 1987 )
3.Wave Nature of Matter 实物粒子的波动性 (p772-774)
Chapter 33 Early Quantum Theory and Models of the Atom
Chapter 33 Early Quantum Theory and Models of the Atom
法国物理学家,1929年诺贝尔物理学奖获得者,波动力学的创始人,量子力学的奠基人之一 。 德布罗意之前,人们对自然界的认识,
只局限于两种基本的物质类型：实物和场 。 前者由原子,电子等粒子构成,光则属于后者 。
但是,许多实验结果出现了难以解释的矛盾 。
物理学家们相信,这些表面上的矛盾,势必有其深刻的根源 。 1923年,德布罗意最早想到了这个问题,并且大胆地设想,人们对于光子的波粒二象性会不会也适用于实物粒子 。 如果成立的话,实物粒子也同样具有波动性 。 为了证
Chapter 33 Early Quantum Theory and Models of the Atom
实这一设想,1923年,德布罗意又提出了做电子衍射实验的设想 。 1924年,又提出用电子在晶体上作衍射实验的想法 。 1927年,戴维孙和革末用实验证实了电子具有波动性,不久,G.P.
汤姆孙与戴维孙完成了电子在晶体上的衍射实验 。 此后,人们相继证实了原子,分子,中子等都具有波动性 。 德布罗意的设想最终都得到了完全的证实 。 这些实物所具有的波动称为德布罗意波,即物质波 。
Chapter 33 Early Quantum Theory and Models of the Atom
德布罗意原来学习历史,随着作用量子 h
越来越深入到物质结构的各个领域,在求知欲的趋势下,他改学理论物理学 。 他善于用历史的观点,用对比的方法分析问题 。 1923
年,他就试图把粒子性和波动性统一起来 。
德布罗意是他在 1924年博士论文,关于量子理论的研究,中提出的,5年后,他因为这篇论文获得了诺贝尔物理学奖金 。 这时德布罗意关于物质波的假设已经被实验证实 。
Chapter 33 Early Quantum Theory and Models of the Atom
Why can't we think of a moving electron—or
any other particle,for that matter—as a matter
wave that transfers energy and momentum to
other matter at points?
In 1924 French physicist Louis de Broglie
(1892-1986 extended the idea of the wave-
particle duality of light and made following
appeal to symmetry:
Light-wave have particle nature,then does
matter has wave nature?
Chapter 33 Early Quantum Theory and Models of the Atom
He suggested that a particle of matter with E and p
has wave nature.
matter wave (de Broglie wave)
─ de Broglie wavelength
1 Hypothesis of De Broglie (德布罗意假设 )
德布罗意假设：实物粒子具有波粒二象性 (wave-
particle duality).
hE?
hp?
Chapter 33 Early Quantum Theory and Models of the Atom
例 在一束电子中，电子的动能为,
求此电子的德布罗意波长,Wavelength of an
electron？
eV200
解 2
0k 2
1,vv mEc
0
k2
m
E?v
1-61
31
19
sm104.8sm
101.9
106.12002
v
nm1067.8 2
nm
104.8101.9
1063.6
631
34
0
vm
h?cv?
此波长的数量级与 X 射线波长的数量级相当,
Chapter 33 Early Quantum Theory and Models of the Atom
Comparing with a bullet of m=0.01kg,v=300m/s:
m
m
h
p
h 341021.2
30001.0
341063.6
Macroscopic particles has larger m,so 0，
the wave-nature can not be shown 表现不出波动性,
,宏观物体只表现出粒子性
”
Chapter 33 Early Quantum Theory and Models of the Atom
2 德布罗意波的实验证明
1) 戴维孙 (Davisson) — 革末 (Germer)电子衍射实验
(electron scatter)
I
35 54 75 V/U
50
当散射角 时电流与加速电压曲线
50
检测器电子束散射线
电子被镍晶体衍射实验
M
U
K
G
电子枪
Chapter 33 Early Quantum Theory and Models of the Atom
kd?2co s2s i n2
kd?s in.,,,,,,,
.,,,,,,,
.,,,,,,,
d 2?
2?
2?
2sin
d
50,1k
m1015.2 10d
镍晶体
m1065.1si n 10 d
m1067.1
2
10
kee
Em
h
m
h
v
电子波的波长两相邻晶面电子束反射射线干涉加强条件
Chapter 33 Early Quantum Theory and Models of the Atom
2) G,P,汤姆孙 (Thomson电子衍射实验 ( 1927年 )
e m Ukhd 2
1si n
e m Ud
kh
2
1si n
k7 7 7.0s i n
当 时,与实验结果相近,?51777.0a r c s i n1k
U M
D P
电子束透过多晶铝箔的衍射
K
双缝衍射图
Chapter 33 Early Quantum Theory and Models of the Atom
§ 33-8,33-9,33-10 The Hydrogen Atom (P753-784)
The idea that matter is made up of atoms was
accepted by most scientists by 1900,With the
discovery of the electron in the 1890s,scientists
began to think of the atom itself as having a
structure and electrons as part of that structure.
1 Early Models of the Atom
Chapter 33 Early Quantum Theory and Models of the Atom
J,J,Thomson,soon after his discovery of
electrons in 1897,visualized a typical model of the
atom in 1903 as a homogeneous sphere of positive
charge inside of which there were tiny negative
charged electrons,1903年,汤姆孙提出原子的,葡萄干蛋糕模型,,
Thomson’s apparatus for
measuring the ratio of mass
to charge for the electron.
Chapter 33 Early Quantum Theory and Models of the Atom
Around 1911,E,Rutherford (1871-1937) and his
colleagues performed experiments whose results
contradicted Thomson’s model of the atom,
α 粒子实验存在大角散射
Chapter 33 Early Quantum Theory and Models of the Atom
The results based on the Rutherford’s,planetary”
model is accord well with the one from scattering
of? particle.卢瑟福的原子有核模型 （ 行星模型 ） 原子的中心有一带正电的原子核,它几乎集中了原子的全部质量,电子围绕这个核旋转,核的尺寸与整个原子相比是很小的,
1911年卢瑟福提出的原子的核模型电子原子核
Chapter 33 Early Quantum Theory and Models of the Atom
2 Two main difficulties of R’s,planetary”model
(1) It predicts that atoms are unstable —
electrons should quickly spiral into the
nucleus —but we know that atoms in general are
stable,since the matter around us is stable;
由于原子总能量减小，电子将逐渐的接近原子核而后相遇，
原子不稳定,e?
+e?
Chapter 33 Early Quantum Theory and Models of the Atom
(2) It predicts that light of a continuous range of
frequencies will be emitted,whereas experiment
shows line spectra 原子光谱的谱线,
根据经典电磁理论，电子绕核作匀速圆周运动，作加速运动的电子将不断向外辐射电磁波,v?F?
r e?
e?
+原子不断地向外辐射能量，
能量逐渐减小，电子绕核旋转的频率也逐渐改变，发射光谱应是连续谱；
Chapter 33 Early Quantum Theory and Models of the Atom
3 Atomic Spectra,Key to the Structure of Atom
Heated solids,liquids and dense gases emit light,
due to oscillations of atoms and molecules.
6562.8? 4340.5?4861.3?
A,J,Angstrom (Swedish瑞典人 ) observed the red
line of hydrogen line spectrum in the visible region
in 1853.
A is from him.。
The emission spectrum (发射光谱 ) is characteristic
of the material and can serve as a type of
“fingerprint” for identification of the gas.
Chapter 33 Early Quantum Theory and Models of the Atom
In 1885,J,J,Balmer showed that the four visible
lines in hydrogen spectrum fit following formula:
,5,4,3,)121(1 22 nnR?
R = 1.0974?107 m-1 ——
Rydberg constant 里德伯常量
The radiation from excited gases showed that the
spectrum was not continuous,but discrete.
Chapter 33 Early Quantum Theory and Models of the Atom
Later experiments on hydrogen showed that
there were similar series of lines (谱线系 ) which
had a pattern just like the Balmer series,but at
different wavelength.
,...3,2,1
1
11
22
i
i
n
n
R
Lyman series 莱曼系
,...5,4,1
3
11
22
i
i
n
n
R
Paschen series
帕邢系
(in the UV region)
(in the IR region))11( 22 nnh c Rhchf
Chapter 33 Early Quantum Theory and Models of the Atom
莱曼系?,3,2,)1
1
1(1
22 nnR
紫外
,4,3,)121(1 22 nnR巴尔末系可见光
,5,4,)131(1 22 nnR帕邢系
,6,5,)141(1 22 nnR布拉开系
,7,6,)151(1 22 nnR普丰德系
,8,7,)161(1 22 nnR汉弗莱系红外
Chapter 33 Early Quantum Theory and Models of the Atom
4 Bohr’s Theory of the Hydrogen Atom (P778):
Electrons move about the nucleus in circular
orbits,but only certain orbits (stationary state )
are allowed,An electron in each orbit would have
a definite energy and would move in the orbit
without radiating energy.
定态假设,1.
假设一 电子在原子中，可以在一些 特定 的轨道上运动而 不 辐射电磁波，这时原子处于 稳定 状态（ 定态 ），
并具有一定的能量,
Chapter 33 Early Quantum Theory and Models of the Atom
In heated solids,the energy of oscillating electric
charges must change discontinuously—from one
discrete energy state to another,with the emission
of a quantum of light,原子能量的量子化 。
频率定则,2.
fi EEh
频率条件假设 二 当原子从高能量 的定态跃迁到低能量
iE
fE
的定态时，要发射频率为 的光子,
当原子从能量较高（ Ei）的稳定状态跃迁到能量较低（ Ef ）的稳定状态时，原子发射出单色光,
Ei
Ef
●
f
Chapter 33 Early Quantum Theory and Models of the Atom
●+e
● -e
rn
vn
En
m
mp
The electron’s angular momentum L is quantized
and equal to an integer n times h/2?.
n,quantum number of orbit.
,3,2,1
2
nnhnL
3,Bohr’s quantum condition:
π2
hnrmL v量子化条件假设 三 电子以速度 在半径为 的圆周上绕核运动时，只有电子的 角动量 等于 的 整数倍 的那些轨道是 稳定 的,,（ 角动量量子化 ）π2h
v r
L
主 量子数
,3,2,1?n
Chapter 33 Early Quantum Theory and Models of the Atom
2
1
2
2
2
0
π
nrn
me
hr
n
),3,2,1(n
π2
hnrm
nn?v
由假设 2 量子化条件
n
n
n r
m
r
e 2
2
0
2
π4
v?
由牛顿定律
,玻尔半径
m1029.5
π
11
2
2
0
1
me
hr?1?n
氢原子能级公式
n
n
nn r
emE
0
2
2
π42
1
v
第 轨道电子总能量
Chapter 33 Early Quantum Theory and Models of the Atom
2
1
222
0
4 1
8 n
E
nh
meE
n
n
nn r
emE
0
2
2
π42
1
v
（电离能）
基态 能量
22
0
4
1 8 h
meE
eV6.13
)1(?n
21 nEE n?
激发态 能量 )1(?n
eV/E
氢原子能级图
1?n基态 6.13?
2?n
3?n
4?n激发态
4.3?
51.1?
85.0?
n 0
自由态
Chapter 33 Early Quantum Theory and Models of the Atom
玻尔理论对氢原子光谱的解释
fi EEh
fi
if
nn
nnch
me
c
,)11(
8
1
2232
0
4
氢原子能级跃迁与光谱系
1?n
2?n
3?n
4?n
n 0E
E
莱曼系巴耳末系帕邢系
222
0
4 1
8 nh
meE
n
布拉开系
17 m10097.1 （里德伯常量）R?
ch
me
32
0
4
8?
Chapter 33 Early Quantum Theory and Models of the Atom
Bohr’s model of atom gave us a first picture of
what an atom is like,It proposed an explanation
for why there should be emission and absorption
of light by atoms at discrete wavelength.
The electron in a hydrogen atom tends to be in
the lowest energy level — in its ground state.
We see that not only are the orbit radii quantized,
but so is the energy,The quantum number n that
labels the orbit radii also labels the energy levels.
For n = 1,
- 1 3,6 e VJ1017.2
8
18
22
0
4
1
h
meE
Chapter 33 Early Quantum Theory and Models of the Atom
由能级算出的光谱线频率和实验结果完全一致
Bohr theory predicts well ionization energy 13.6eV
for hydrogen,but was not so successful for others.
Chapter 33 Early Quantum Theory and Models of the Atom
（ 1） 正确地指出 原子能级 的存在（原子能量量子化）；
（ 2） 正确地指出 定态 和 角动量量子化 的概念；
（ 3） 正确的解释了氢原子及类氢离子光谱；
氢原子玻尔理论的意义和困难
（ 4） 无法解释 比氢原子更复杂的原子；
（ 5） 把微观粒子的运动视为有确定的 轨道 是不正确的；
（ 6） 是 半 经典 半 量子 理论，存在逻辑上的缺点，即把微观粒子看成是遵守经典力学的质点，同时，又赋予它们量子化的特征,
Chapter 33 Early Quantum Theory and Models of the Atom
1914 年弗兰克 — 赫兹从实验上证实了 原子存在分立的能级,1925 年他们因此而获物理学 诺贝尔奖,
pI
V9.4
V9.4
0 5 10 15 V/
0U
板极电流和加速电压之间的关系
0U rU
pI
栅极灯丝 板极弗兰克 — 赫兹实验装置低压水银蒸汽
V5.0r?U
A
G P
+ ++
+
- -
-
-
Chapter 33 Early Quantum Theory and Models of the Atom
§ 33-11 de Broglie’s Hypothesis Applied to Atom
According to de Broglie,a particle of mass m
moving with a nonrelativistic speed v would have
He proposed,Each electron orbit in
an atom is a standing wave,To form
constructive interference,persist,the
circumference of a Bohr orbit of
radius rn should be 2? rn as Fig.,so
mv
h
nr n?2
Chapter 33 Early Quantum Theory and Models of the Atom
2
,or nhmv r n?
This is the quantum condition ( 量子化条件 )
proposed by Bohr,This implies that the wave-
particle duality is at the root of atomic structure.
Bohr’s theory worked well for one-electron ions,
but didn’t prove as successful for multielectron
atoms,A new theory was needed and was indeed
developed in 1920s,
This new and radical theory is called quantum
mechanics —— unifies the wave-particle duality
into a single consistent theory.
Chapter 33 Early Quantum Theory and Models of the Atom
1 Statistical Meaning of De Broglie’s Wave:
Particle,Energy? ; Momentum p; Quantities N
Wave,wavelength? ; Frequency f ; Amplitude E0
The numbers of particles N? I? E02
The intensity of De Broglie’s wave
somewhere is proportional to the
probability that the particle appears
near there（ 在某处德布罗意波的强度与粒子在该处邻近出现的概率成正比 ）,
Their Relation:
Chapter 33 Early Quantum Theory and Models of the Atom
The De Broglie’s wave is different from classical
wave,Mechanical wave is the propagation of the
mechanical oscillation; De Broglie’s wave is the
statistical description for the motion of
microscopic particle.
不是经典的波,不代表实在的物理量的波动,
The particle and wave are united in the
probability-wave theory (统一于 概率波 理论 ).
Chapter 33 Early Quantum Theory and Models of the Atom
2 对物质波的理解，概率波的概念怎样理解物质波（德布罗意波）?
薛定谔,波是基本的，电子是,波包”。 但波包要扩散,而电子是稳定的。
德布罗意,物质波是引导粒子运动的,导波”。
—— 本质是什么，不明确。
另一种理解,粒子是基本的，电子的物质波是大量电子 相互作用 形成的。
—— 被以下实验否定
Chapter 33 Early Quantum Theory and Models of the Atom
电子双缝的衍射实验减弱入射电子束的强度，让一个一个电子依次通过双缝，则随着电子树的积累，衍射图样依次如图。
7个电子 100个电子底片上出现一个个的点子?电子具有 粒子性。
Chapter 33 Early Quantum Theory and Models of the Atom
70000
3000 20000
随着电子增多，逐渐形成衍射图样。
来源于,一个电子”所具有的波动性,而不是电子间相互作用的结果。
Chapter 33 Early Quantum Theory and Models of the Atom
电子数 N=7100300020000电子数 70000
单个粒子在哪一处出现是偶然事件；
大量粒子的分布有确定的统计规律。
出现概率小 出现概率大电子双缝干涉图样
Chapter 33 Early Quantum Theory and Models of the Atom
玻恩 （ M.Born）,尽管单个电子的去向是概率性的,但其概率在一定条件下 （ 如双缝 ）,还是有确定的规律的 。
德布罗意波 并不是经典的波那样是代表实在物理量的波动 。 在双缝实验中 。 不管入射 波强度如何小,
经典的波在缝后的屏幕上都,应该,显示出强弱连续分布的衍射条纹,只是亮度微弱而已 。 但图中明确地显示物质波的主体仍是粒子,而且该种粒子的运动并不具有经典的振动形式 。
