dual nature of matter
TRANSCRIPT
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