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Dual Nature Of Radiation And Matter

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Energy and momentum of photoelectrons



In photoelectric effect, the momentum of incident photon of energy is : 

Variation of photocurrent with potential for different intensity of incident light

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The graph shows variation of stopping potential versus frequency of incident radiation for two photosensitive metals A and B. Which of the two metals has higher threshold frequency and why?

Einstein's photoelectric equation

Einstein's photoelectric equation :

The kinetic energy of the photoelectron coming out may be anything between zero and where is the energy supplied to the individual electrons.

How does one explain the emission of electrons from a photosensitive surface with the help of Einstein's photoelectric equation?

Stopping potential

The smallest magnitude of the anode potential which just stops the photocurrent is called the stopping potential.
This potential should stop even the ost energitic photoelectron. Hence 
Tha value of maximum kinetic energy should be equal to
We know
(a) Describe briefly three experimentally observed features in the phenomenon of photoelectric effect.
(b) Discuss briefly how wave theory of light cannot explain these features
(a) Write the important properties of photons which are used to establish Einstein's photoelectric equation.
(b) Use this equation to explain the concept of (i) threshold frequency of (ii) stopping potential

De-broglie wavelength

De Broglie's wavelength is the wavelength associated with a massive particle,hypothesized by De Broglie that explains Bohr's quantised orbits by bringing in the wave-particle duality.  It is written as
(de broglie wavelength)

An electron microscope uses electrons accelerated by a voltage of 50 kV. Determine the de-Broglie wavelength associated with the electrons. Taking other factors, such as numerical aperture etc. to be same, how does the resolving power of an electron microscope compare with what of an optical microscope which uses yellow light?

Davisson and Germer experiment

Davison and Germer observed the diffraction of electrons by crystals. The setup consists of an electron gun firing electron beam onto a nickel target inside a vaccum chamber. The diffracted electrons are observed by the galvanometer.The experiment was performed by varying the voltage from 44V to 68V. It was observed that a strong peak appeared when the voltage was 54V at a scattering angle of due to constructive interference effects of the electrons. The wavelength of the matter waves was found to be 0.168 nm from diffraction measurements which matches that of de-Broglie wavelength at 54 V thus verifying the wave nature of electrons. 
If a strong diffraction peak is observed when electrons are incident at an angle 'i' from the normal to the crystal planes with distance 'd' between them (see figure). de-Broglie wavelength of electrons can be calculated by the relationship (n is an integer)