Dual Nature of Radiation and Matter

Basic facts

𝒆

𝒎is 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

Work functionMinimum 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

Example Most difficult to remove electrons from : Caesium

Easiest to remove electron from : Platinum

Alkali Metals have low work functions

Ways of removing electron :

Heat : Thermionic

Light : Photoelectric

Electric field

Whatever be the process energy equal to work function is required

PHOTOELECTRIC EFFECTParameters :

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

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

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 .

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

Effect of frequencyA minimum frequency is required to cause photoelectric effect called Threshholdfrequency 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

Effect of collector potentialCollector 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

Saturation current will be same for all frequencies > Threshold

Various plotsPlot 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

Photons1 . 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)

De Broglie WavelengthEverything 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

𝑽Amstrong

Heisenberg UncertaintyPosition and momentum can not be measured accurately simultaneously

Davison and germer verified wave nature of electrons by measuring the wavelength

Joule to ev1 ev = (charge on electron ) X 1Volt

Plank formula for calculating energy in ev

E (in ev ) = 𝟏𝟐𝟒𝟎

λwhere 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