Question

The ground state energy of an atom is $-13.6 \,eV$. The photon emitted during the transition of electron from $n = 3$ to $n = 1$ state, is incident on a photosensitive material of unknown work function. The photoelectrons are emitted from the materials with a maximum kinetic energy of $9 \,eV$. The threshold wavelength of the material used is

• A. $0.9\times 10^{-7}\, m$
• B. $4\times 10^{-7} \,m$
• C. $0.47\times 10^{-7} \,m$
• D. $9\times 10^{-7} \,m$

Answer 1

Answer: (B)

a transition from $n = 3$ to $n = 1$ state, the energy of the emitted photon,
$h\upsilon = E_{2} - E_{1}$
$= 13.6 \left[\frac{1}{1^{2}} -\frac{1}{3^{2}}\right]eV$
$ = 12.1 \,eV $
From Einstein's photoelectric equation,
$h\upsilon = K_{max} + W_{0}$
$\therefore W_{0} = h\upsilon -K_{max}$
$ = 12.1 -9 $
$ = 3.1 \,eV$
Threshold wavelength,
$\lambda_{0} = \frac{hc}{W_{0}} $
$ = \frac{6.62\times10^{-34} \times 3 \times 10^{8}}{3.1\times 1.6\times 10^{-19}} $
$ = 4\times10^{-7} m$