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प्रश्न
Obtain Einstein’s photoelectric equation with the necessary explanation.
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उत्तर
Einstein’s explanation of photoelectric equation:
1. When a photon of energy hv is incident on a metal surface, it is completely absorbed by a single electron and the electron is ejected.
2. In this process, a part of the photon energy is used for the ejection of the electrons from the metal surface (photoelectric work function Φ0) and the remaining energy as the kinetic energy of the ejected electron. From the law of conservation of energy,
hv = Φ0 + `1/2` mv2 ..........(1)
where m is the mass of the electron and u its velocity
Emission of photoelectrons
3. If we reduce the frequency of the incident light, the speed or kinetic energy of photoelectrons is also reduced. At some frequency V0 of incident radiation, the photoelectrons are ejected with almost zero kinetic energy.
Then the equation (1) becomes
hv0 = Φ0
where v0 is the threshold frequency. By rewriting the equation (1), we get
hv = hv0 + `1/2` mv2 ……(2)
The equation (2) is known as Einstein’s Photoelectric equation.
If the electron does not lose energy by internal collisions, then it is emitted with maximum kinetic energy Kmax. Then
Kmax = `1/2 "mv"_"max"^2`
where vmax is the maximum velocity of the electron ejected.
The equation (1) is rearranged as follows:
Kmax = hv – Φ0
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