equipment 2. photoelectric effect. einstein’s photon theory (...

equipment

2. Photoelectric Effect. Einstein’s Photon Theory ( 光电效应、爱因斯坦光子理论 )

R

K1

K2

E

G

V

les, called photons.

Einstein assumed that the energy in a light beam travelsthrough space in concentratedbund pi

The energy E of a single photon is given by E = hv . Applying the photon concept to the photoelectric effect, Einstein wrote

SI

Si

光电管K

A

)10(2

10

2max Amvh

Equation above says that a photoncarries an energy hv into the surface. Part of this energy A0 is used in causing the electron to pass through the metal surface. The excess energy (hv-A0) is given to the electron in the form of kinetic energy.

In 1916, Milikan, experimentsverified Einstein’s ideas in every detail. Einstein succeed in explainingthe photoelectric effect.

h

-

-

金属

electron

-

--A

v

The dual nature of light, particle and wave

光的波粒二象性

particle wave（ energy ）（ frequency ）

（ momentum ）（ wavelength ）E

P

h

These two natures are connected by h.

)1( hE

)2(/

h

C

hCEP

220

2 )( cPEE

3. The Compton effect ( 康普顿效应 )

Compelling confirmation of theconcept of the photon as a concen-trated bundle of energy was providedin 1923 by A.H.Compton who earned a Noble prize for this work in 1927. Compton allowed a beam of X-raysof sharply defined wavelengthλto fall on a graphite block. He measured, for various angles of scattering, the intensity of the scattered X-raysas a function of their wavelength.

1) Equipment

Compton allowed a beam of X-rays of sharply defined wavelengthλto fall on a graphite block. He measured, for various angles of scattering, theintensity of the scattered X-rays as a function of their wavelength.

0

X 光光栏

石墨

0.70Å

X 射线分析仪

1) Equipment

0

2) Experimental results :

X 光光栏

石墨

0.70Å

X 射线分析仪2

3

4

1 =00

=450

=900

=1350

0.70 0.75 (Å)

强度

The scattered X-rays have intensity peaks at two wavelengths: one of the them is the same as the incident wavelength, 0, the other, , being

larger by an amount △.

应用程序

2

3

4

1 =00

=450

=900

=1350

0.70 0.75 (Å)

强度

This so-called Compton shift △ varies with the angle at which the scattered X-rays are observed.

Compton shift △ for collisions with tightly bound electrons is immeasurably small.

3) Explain Compton Effect 对康普顿效应的解释 Compton was able to explain his experimental

results by postulation that the incoming X-ray beam was not a wave but an assembly of photons

of energy E (= hv) and that these photons expe- rienced billiard-ball-like collisions with the free

electrons in the scattering block.

h0

0n̂m0

e X

Before After

h0

0n̂e

mV

h

X

Analyze quantitatively

m0

eh0

0n̂

20Cm

m0

e

n̂Before After

Before After

Electron Photon Electron Photon

energy

momentum

2mC0h h

0 00 n̂C

h nC

hˆ

Vm

Let us assume this is an elastic scattering collision.

=+ +

= +

h0

0n̂e

mV

h


Before After

)1(2200 mChCmh

)2(ˆˆ00

n

C

hVmn

C

h

)4(cos2)()()( 02202 C

h

C

h

C

h

C

hmV

{

nC

hˆ

Vm 0

0 n̂C

h

From （ 1 ） )3()( 200

2 CmhmC From the low of cosine

Xm0

eh0

0n̂

m0

en̂h0

0n̂e

mV

h


)4(cos2)()()( 02202 C

h

C

h

C

h

C

hmV

)3()( 200

2 CmhmC

)5()cos1(2 0222

02222 hhhCVm

（ 3 ） 2- （ 5 ）

Before After

nC

hˆ

Vm 0

0 n̂C

hXm0

eh0

0n̂

m0

en̂h0

0n̂e

mV

h

)6()(2 02

0 hCm

)cos1(2)1( 0242

02

242 hCm

C

VCm

)3()( 200

2 CmhmC )5()cos1(2 0

2220

2222 hhhCVm（ 3 ） 2- （ 5 ）：

)cos1(2 0242

042

0 hCmCm

nC

hˆ

Vm 0

0 n̂C

h

)7()(2 02

0 hCm

)8()cos1()(

00

0

Cm

hC

or

or

2

2

0

1CV

mm

)9()cos1(00

Cm

hCC

)cos1(0

Cm

h0

2sin

2 2

0

Cm

h

（ m ）

mCm

h 12

0

1043.2

2sin0243.02 2

0

（ Å ）

….(10)

….(11)

nC

hˆ

Vm 0

0 n̂C

h

)8()cos1()(

00

0

Cm

hC

Compton wavelength

2sin0243.02 2

0

（ Å ）

)cos1(0

Cm

h0

2sin

2 2

0

Cm

h

（ m ）

….(10)

….(11)

Discuss ，Equation (11) predicts within experimental error the experimentally observed Compton shifts. The peak for 0 can be understood as resulting

nC

hˆ

Vm 0

0 n̂C

h

Discuss ， The peak for 0 can be understood as resulting from a collision between a photon and electrons bound in an ionic core. The electron’s effective mass is much greater.

ionic core 铅球Photon乒乓球

The Compton effect for longer wavelength is hardly observed. quantum results reduces to classical results. For example, 0 = 10 cm, △/ 0 = 2.43×10-11,

the Compton effect is hardly observed.

nC

hˆ

Vm 0

0 n̂C

h

4 ） SignificanceA ） Compelling confirmation of the concept of the photon as a concentrated bundle of energywas provided. The photon hasmass, energy and momentum.B) In microscopic field, the law of conservation of momentum and the law of conservation of energy are still strictly observed. Exp. An X-ray with E = 0.60MeV are scattered from a carbon block. Its wavelength changed 20% in the collision. What kinetic energy is

imparted to the recoiling electron?

nC

hˆ

Vm 0

0 n̂C

h

例：能量为 0.60MeV 的 X 射线在碳块上散射后，波长变化了 20%，求反冲电子动能。

Known, E0=h0=0.6MeV, =0.20,

Find, Ee=?

Solve,0

00 C

hhE

)(1048.22.12.0 12000 m

)(1007.21060.11060.0

1031063.6/ 12

196

834

00 mEhC

kinetic energy of the recoiling electron,

hhEEEe 00

eEm0

e

n̂h0

0n̂e

mV

h

)(1048.22.12.0 12000 m

kinetic energy of the recoiling electron,

hhEEEe 00

0

0

0

hCCh

Ch

012

0834

1048.2

2.01031063.6

)(1060.1 14 J

MeVEe 10.0 The kinetic energy 0.10Mev imparted to the recoiling electron.

eE

n̂h0

0n̂e

mV

h

equipment 2. photoelectric effect. einstein’s photon theory (...

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