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Origin of Quantum Theory
Quantum theory is a theory needed to describe physics on a
microscopic scale, such as on the scale of atoms, molecules,
electrons, protons, etc.
Classical theories:
Newton – Mechanical motion of objects (F = ma)
Maxwell – Light treated as a wave
NEITHER OF THESE THEORIES QUITE WORK FOR ATOMS,
MOLECULES, ETC.
Quantum
Any of the very small increments or parcels into which many
forms of energy are subdivided.
Light is a form of energy is a quantum of EM energy
Shortest wavelengths
(Most energetic photons)
E = hn = hc/l
h = 6.6x10-34 [J*sec]
(Planck’s constant)
Longest wavelengths
(Least energetic photons)
OR
Until about 1900, the classical wave theory of light described
most observed phenomenon.
Light waves:
Characterized by:
 Amplitude (A)
 Frequency (n)
 Wavelength (l)
Energy of wave a A2
In the early 20th century, several effects were observed which
could not be understood using the wave theory of light.
Two of the more influential observations were:
1) The Photo-Electric Effect
2) The Compton Effect


The phenomenon of ejection of electrons from a
metal surface when illuminated by light or any
other radiation of suitable wavelength (or
frequency)
The electrons ejected from the metal surface are
called “photoelectrons”


An adjustable
voltage is applied.
Voltage can be
forward or reverse
biased (which slows
down the electrons)
Photoelectrons
return to cathode
through an
ammeter which
records the current


Effect of frequency:
The minimum frequency required for the
photoelectric emission to commence is called
Threshold frequency.
It depends on material and nature of surface of
material.
Effect of intensity of light:
Photoelectric current is directly proportional to the
intensity of light, provided frequency is more than
threshold frequency.
High intensity (bright)
Stopping potential
Low intensity (dim)
Reverse bias
Forward bias
frequency
The stopping potential α Frequency of incident light






For each emitter surface, there is a certain minimum
frequency called threshold frequency below which the
emission does not take place.
For frequency greater than threshold frequency, the
magnitude of photoelectric current is proportional to the
intensity of incident light
The rate of emission of photo electrons is independent of its
temperature
The stopping potential is proportional to frequency but
independent of intensity of light
The photo electric emission is instantaneous. Time lag < 10-9
second
The maximum K.E. increases with increase in frequency of
incident light but independent of intensity.




Einstein suggested that light consisted of discrete units
of energy
E = hυ
Electrons could either get hit with and absorb a whole
photon, or they could not. There was no in-between
(getting part of a photon).
If the energy of the unit of light (photon) was not large
enough to let the electron escape from the metal, no
electrons would be ejected. (Hence, the existence of
cutoff.)
If the photon energy were large enough to eject the
electron from the metal (here, W is the energy
necessary to eject the electron), then energy of the
photon absorbed (hυ) goes into ejecting the electron
(W) plus any extra energy left over which would show
up as kinetic energy (KE).

hυ = W + ½ mv2

hυ = W + eV




where υ is the frequency of the light
W is the “WORK FUNCTION”, or the amount of
energy needed to get the electron out of the metal
V is the stopping potential
When Vs = 0, υ= υcutoff , and hυcutoff = W.
 Photons can be treated as “packets of light” which behave as a
particle.
 To describe interactions of light with matter, one generally has to
appeal to the particle (quantum) description of light.
 A single photon has an energy given by
E =hv= hc/l,
where
h = Planck’s constant = 6.6x10-34 [J s] and,
c = speed of light
= 3x108 [m/s]
l = wavelength of the light (in [m])
 Photons also carry momentum. The momentum is related to the
energy by:
p = E / c = h/l
Shortest wavelengths
(Most energetic photons)
E = hn = hc/l
h = 6.6x10-34 [J*sec]
(Planck’s constant)
Longest wavelengths
(Least energetic photons)
In 1924, A. H. Compton performed an experiment
where X-rays impinged on matter, and he measured
the scattered radiation.
Incident X-ray
wavelength
l1
M
A
T
T
E
R
Scattered X-ray
wavelength
l2
Compton
l2 > l1
e
Electron comes flying out
Problem: According to the wave picture of light, the incident X-ray
should give up some of its energy to the electron, and emerge with a
lower energy (i.e., the amplitude is lower), but should have l2=l1.
Classical picture: oscillating electromagnetic field causes oscillations in
positions of charged particles, which re-radiate in all directions at same
frequency and wavelength as incident radiation.
Change in wavelength of scattered light is completely unexpected
classically
Incident light wave
Oscillating electron
Before
Emitted light wave
After
pn 
scattered photon
Incoming photon
pn
θ
Electron
pe
scattered electron
Before
After
pn 
scattered photon
Incoming photon
pn
θ
Electron
pe
Conservation of energy
hn  me c = hn    p c  m c
2
Conservation of momentum
hˆ
pn = i = pn   p e

2 4 1/ 2
e
2 2
e
scattered electron
l
From this Compton derived the change in wavelength
l  l =
h
1  cos 
me c
= lc 1  cos   0
lc = Compton wavelength =
h
= 2.4 1012 m
me c
Compton (1923) measured intensity of scattered X-rays from solid
target, as function of wavelength for different angles. He won the 1927
Nobel prize.
X-ray source
Collimator
(selects angle)
θ
Target
Detector
Crystal
(selects
wavelength)
At all angles there is also an
unshifted peak.
This comes from a collision
between the X-ray photon and
the nucleus of the atom
Result: peak in scattered
radiation shifts to longer
wavelength than source.
Amount depends on θ (but not
on the target material).