Unit 7 Dual nature of matter and radiation (4 Marks)
Course Content: Dual nature of radiation. Hertz and Lenard’s observations; Einstein
photo-electric equation – particle nature of light,
Matter waves – wave nature of particles, De-broglie relation, Davisson-Germer
experiment.
Atom, literally means "uncuttable". Till the time it was so, there was no problem. There
were laws in Chemistry (like Dalton's theory), which satisfactorily explained behaviour
of these basic building blocks, when they reacted with other basic building blocks.
The problem came when the electron was discovered (ever wondered why all
Modern Physics portions start with the discharge tube - after all if we start all
electrostatics portion with Coulomb's law then we do keep using it later on, but we do not
talk about the discharge tube later on). The last portion of section on discharge tube says
that at a very low pressure - ~0.01 mm Hg, whole space is filled with Crooke's dark
space. At this stage, a stream of invisible particles is emitted from the cathode, and the
portion of the tube opposite to the cathode starts glowing.
On passing these radiation through a magnetic and electric field (something like
Thomson's experiment), it is found out that they are negatively charged "particles"
(waves would have formed wavefronts making these radiation available everywhere).
The charge is found to be (by Millikan's oil drop expt) in multiples of 'e' = 1.6x10-19 C,
and the specific charge (charge to mass ratio) to be 1.759x1011 C/Kg.
Wave particle duality :Few Terms which are common to both electrons and photons, but have quite
different meaning –
Frequency (predominantly related to waves) –
For electrons, it is 1/T where T is the time
period of revolution around the nucleus.
1
v
1
f=
=
 3
T
2 r
n
Wavelength (predominantly wave term)–
For free electrons, it is the de-Broglie
Wavelength given by
h
h
h
1.227 nm
 


p
2mK
2m(eV )
V
For bound electron,
h
h
hr
hr 2 2 0.53n 2
 




p mv mvr
nh
n
Z
For photons, it is the frequency of photon
emitted when electron jumps from higher
orbit to lower orbit, given by the equation1 1
h  RhcZ 2 [ 2  2 ]
n1 n2
For photons, it is the wavelength of photon
emitted when electron jumps from higher
orbit to lower orbit, given by –
hc
1 1
 RhcZ 2 [ 2  2 ]

n1 n2
n
Z
Energy –
For electron, it is
p2
1
K = mv 2 =
2
2m
For photon it is
hc
1 1
E
 RhcZ 2 [ 2  2 ]

n1 n2
Momentum (predominantly related to particles) –
For electron, it is
For photon it is
E h 1 hc h
1 1
p = mv = 2mK = 2m(qV )
p 

  RhZ 2 [ 2  2 ]
c
c c  
n1 n2
Q. In a H-like atom, an electron jumps from n = 5 to n = 3. Find the recoil KE of the
atom.
Photo-electric effect
Accidentally Heinrich Hertz discovered the effect in 1887. Wilhelm Hallwachs and Philipp
Lenard investigated the phenomenon of photoelectric emission in detail during 1886-1902. It was
gradually established that
- the medium was not getting ionised (on evacuating),
- the cathode was not losing negative ions (Pt anode, Na-amalgam cathode, No
Na was found on anode)
Discovery of electron suggested that photo-electric effect is due to the liberation of
electrons. (confirmed by Lenard by e/m deflection)
Problems with wave theory:
- There is actually no time lag whereas wave theory predicts time lag,
- effect is independent of intensity (even if intensity is high, there is no effect
for  > o)
- cut-off / threshold frequency - For a given substance, no electrons were
emitted below a certain frequency. Above the cutoff frequency, electrons were
emitted with an energy in proportion to the frequency of the light,
- The energy of the emitted electron is independent of the intensity of the light.
Einstein explained the effect by regarding light as a rain of corpuscles or photons of
energy h and assuming that whole photon can be absorbed by an electron.
h
hc/ 
=
=
o
hc/ 
+
+
Kmax
eVS
1 2
=
h0
+
mvmax
2
Ex. If h = 5 eV, o = 2eV, then KE of emitted electrons range from 0 to 3eV
Plot the graphs –
a) VS - 

h
VS   - 0
e
e
b) Photo current vs Intensity of light - the number of
photoelectrons emitted per second is directly proportional
to the intensity of incident radiation.
c) Effect of potential of plate on photo
current for different intensity of light
The minimum negative (retarding) potential V0
given to Anode for which photocurrent becomes
zero is called the cut-off or stopping potential.
For a given frequency of the incident radiation, the
stopping potential is independent of its intensity
d) Effect of potential of
plate on photo current
for diff. frequency of
light
Davisson and Germer Experiment –
The experiment was performed by varying the
accelerating voltage from 44 V to 68 V. It was
noticed that a strong peak appeared in the intensity
(I ) of the scattered electron for an accelerating
voltage of 54V at a scattering angle θ = 50º
The appearance of the peak in a particular
direction is due to the constructive interference of
electrons scattered from different layers of the
regularly spaced atoms of the crystals. From the
electron diffraction measurements,
2d sinθ = nλ where θ is the grazing angle.
For Ni crystal, d = 0.91Ao, θ = 65o (see fig),
putting n=1 (for 1st order), the wavelength of matter waves is found to be 0.165 nm.
1.227nm
The de Broglie λ associated with e-s, using  
for V = 54 V is = 0.167 nm.
V
Thus, there is an excellent agreement between the theoretical value and the
experimentally obtained value of de Broglie wavelength. Davisson-Germer experiment
thus strikingly confirms the wave nature of electrons and the de Broglie relation.