Question

Derived Einstein's Photoelectric equation. Explain photoelectric effect with help of this equation.

Answer 1

Einstein's Photoelectric equation:
By conservation of energy
The energy of incident photon=maximum K.E of $e^{-}+$ work function
$hv=\frac{1}{2}m{V}_{max}^2+W_0$
$(W_0=\frac{h{v}_0}{Thresholdfrequency})$
$K_{max}=hv-h{v}_0$
$K_{max}=h(v-v_0)$
(1) Explanation of the effect of intensity: The increase of intensity means the increase the number of photons striking the metal surface at a unit time. As each photon ejects only one $e^{-}$ so the number if ejection electron increases.
(2) Explanation of threshold frequency: If $v\propto v_0$ That is the frequency of incident radiation is less than the threshold frequency, the kinetic energy of photoelectrons becomes negative. This is no physical meaning.
(3) Explanation of kinetic energy: If $v>V_0$ then the maximum kinetic energy of $e^{-}$ increases linearly with frequency v.
(4) Explanation of time lag: Photoelectric is the result of elastic collision b/w photon & $e^{-}$. The transfer of energy of a photon to $e^{-}$ is one lump, not continuous absorption.