Using Bohr’s atomic model, derive the expression for the radius of n th orbit of the revolving electron in a hydrogen atom.
(a) Write two main observations of photoelectric effect experiment which could only be explained by Einstein’s photoelectric equation.
b) Draw a graph showing variation of photocurrent with the anode potential of a photocell.

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Detailed Solution

$\begin{array}{l} F_{c} = F_{E} \\ \frac{m_{e} v_{n}^{2}}{r_{n}} = \frac{{Kze}^{2}}{r_{n}^{2}} \\ m_{e} v_{n}^{2} r_{n} = {Kze}^{2} \end{array}$
By Bohr's second postulate
$\begin{array}{l} L = m_{e} v_{n} r_{n} = \frac{nh}{2 π} \\ r_{n} = \frac{n^{2} h^{2}}{4 π^{2} m_{e} {ke}^{2} Z} \\ r_{n} = \frac{n^{2} h^{2}}{4 π^{2} m_{e} {ke}^{2}} (∵ Z = 1) \end{array}$
OR
(i) There exists a threshold frequency below which no photoelectron is ejected.
(ii) KE of electron depends linearly on frequency and is independent of intensity of radiation.

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