This document discusses the dual nature of radiation and matter. It explains the photoelectric effect and defines key parameters like work function, threshold frequency, stopping potential, and kinetic energy. The photoelectric effect can be explained using Einstein's equation that energy supplied must equal the work function plus maximum kinetic energy. Stopping potential and kinetic energy are shown to depend on frequency but not intensity. Plots of various variables are described and the wave-particle duality of light and matter is discussed.

1. Dual Nature of
Radiation and Matter

2. Basic facts

𝒆
𝒎
is constant , independent of nature of material used
e = charge on electron m = mass of electron
We know that Energy = q V
One electron volt is the energy gained by electron when it is accelerated by
1 Volt of potential difference
1 ev = 1.602 ×10–19 J

3. Work function
Minimum Energy required by an electron to escape
from metal surface .
An electron may not come out even after having
energy greater than work function due to internal
collision

4. Example
Most difficult to remove electrons from : Caesium
Easiest to remove electron from : Platinum
Alkali Metals have low work functions

5. Ways of removing electron :
Heat : Thermionic
Light : Photoelectric
Electric field
Whatever be the process energy equal to work function is required

6. PHOTOELECTRIC EFFECT
Parameters :
Frequency : Frequency is related to energy of incident
light .
Intensity : Intensity is related to amount of light . Higher
Intensity means more number of photons .
Collector potential : Used to collect emitted electrons . It is kept positive so that
electrons can be collected

7. Einstein Equation
Based on particle nature (photon) of light
Energy supplied = work function + KE max
h v = W0 + KE max
Tightly bound electrons will emerge with kinetic energies less than KE max
Kemax does not depend on Intensity . It only depends only on Frequency and Work
function

8. Stopping potential
Collector potential is generally kept positive to collect electrons , But if we keep it
negative , it will repel electrons . At some potential, all electrons will get repelled .
At this potential , Photocurrent will be zero .This is called stopping potential
If we can stop electron having maximum KE we can stop every other electron .
To stop fastest electron : eVstopping = KEmax
KE max = hv – W0 eVstopping = hv – W0
Vstopping = (hv – Wo)/ e
So stopping potential depends on frequency and work function .

9. Effect of Intensity on Photocurrent
 Current is number of electrons passing through a cross section in unit time .
 Intensity  No. of photons/second  No of electron emitted  Current
 Photocurrent ∝ Intensity
 Intensity has no effect on Stopping Potential because it does not
change KE max

10. Effect of frequency
A minimum frequency is required to cause photoelectric effect called Threshhold
frequency Work function = h vthreshold = h c /λthreshold
Kemax depends on frequency , So Stopping potential will also depend
Vstopping = (hv – Wo)/ e
Stopping potential = y
Frequency = x
Y = (h/e) x – (Wo/e)
At x axis : Stopping = 0

11. Effect of collector potential
Collector potential is meant for collecting emitted electrons .
So current will first increase with increase in collector potential , after which it will saturate . It
will saturate (become constant ) when emitted electrons = collected electrons .
This maximum current is called saturated current .
Saturated current is independent of frequency , but depends on intensity . Higher the
intensity , greater the current

12. Saturation current will be same for all frequencies > Threshold

13. Various plots
Plot Relation Nature of Graph
KEmax vs Frequency KE = hv – W0 Linear
KEmax vs Intensity No relation
KEmax vs Collector Potential No relation
Stopping potential vs Frequecy Vstopping = ( hv-wo ) / e Linear
Stopping potential vs Intensity No relation
Stopping potential vs Collector No relation
Photocurrent vs Intensity Directly proportional Linear
Photocurrent vs Collector First increase then constant (saturate)
Photocurrent vs frequency Saturation current is same for all
frequencies

14. Photons
1 . Electrically neutral , No effect of Electric field or magnetic field
2 . Massless
3 . Energy = Momentum =
Energy and Momentum depends only on Frequency (or wavelength)
When photon collides with particle  Total momentum will remain conserved like any other
normal collision . But some photos may die in collision (Number of photon may change after
Collison)

15. De Broglie Wavelength
Everything has a wave nature .
Ohh , then what is the wavelength
For charged Species : K = q V ( V = accerelating Potential )
For electron Charge = e  K = eV 
For Electrons only or √
𝟏𝟓𝟎
𝑽
Amstrong

16. Heisenberg Uncertainty
Position and momentum can not be measured accurately simultaneously
Davison and germer verified wave nature of electrons by measuring the wavelength

17. Joule to ev
1 ev = (charge on electron ) X 1Volt
Plank formula for calculating energy in ev
E (in ev ) =
𝟏𝟐𝟒𝟎
λ
where λ is in nanometer
To convert meter to nanometer : divide meter by 109
Light of 620 nm  (1240/620)ev of energy = 2 ev of energy