1

Quantum MechanicsExperiments

1

Photoelectric effect

Photoelectric effect

.h k e

.h k e

Lenard 1902: Studied energy of the photoelectrons with intensity of light.He could increase the intensity thousand fold.

1. Noticed a well defined minimum voltage Vstop to stop the current in the circuit. Vstop was independent of the intensity of light.

Current vs Voltage

Cut-off voltage

Different intensities: Ib > Ia

2. Increasing the intensity of light would increase the current

3. He performed the experiment withvarious coloured lights and found themaximum energy of the electrons diddepend on the frequency of light.Qualitatively he obtained more thefrequency more the energy.

Objections with wave theory

1. Kinetic energy (K) of the photo-electron should increasewith intensity of the beam.

But Kmax was found to beindependent of the intensityof the falling light.

2. Effect should occur for any frequency of light providedonly that light is intense enough to eject the electron.

But a cut-off frequency was observed below which photoelectrons were not ejected (no matter howintense was beam).

3. Energy in the classical theoryis uniformly distributed over the wave front. If light is feeble,there should be a time lag betweenthe light striking the plate andejection of photoelectrons. Ejection is instant, t < 10 sec- 9

Einstein equation

Light is wave : Interference, Diffraction, polarisationLight is a stream of photons/wave packets (particles) So wave behaves like particle

Compton effect

Collision between photon and electron

Arthur Holly Compton(1892-1962)

Compton Effectin 1920

Partial transfer of photon energy

m = m(v) is the relativistic mass

Conservation of momentum along initial photon direction

Conservation of momentum along perpendicular to initial photon direction

Square and add the above two expressions

Energy conservation

Compton wavelength

Compton shift

= 2.4 pm

~

Compton Experiment

Franck and Hertz experiment (1914)(James Franck and Gustav Hertz)

Confirmation of discrete energy levels in atom

Vo

100

200

300

I in mA

Accelerating Voltage in Volts5 10 15

Peaks at 4.9 V and its multiples

Groundstate

1st excitedstate

2nd excitedstate

4.9 eV6.7 eV

Continuum

E=0

E= -10.4eV

Particles behaving as waves

Electron diffractionDavisson –Germer (USA)and Thompson (UK) (1927)

Experiments

Diffraction?

Apply Bragg’s lawFrom X-ray diffraction

KE=54 eV is non relativistic

mEp

ph

2

de Broglie wavelength of electron

mEp

ph

2

“In a situation where the wave aspect of a system is revealed, its particle aspect is concealed; and,in a situation where the particle aspect is revealed, its wave aspect is concealed. Revealing both simultaneously is impossible; the wave and particle aspects are complementary.”

Bohr’s Complementarity Principle