Question

The ground state energy of an atom is $-13.6eV$. 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 $9eV$. 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,
$h\upsilon =E_2-E_1$
$=13.6\left[\frac{1}{1^2}-\frac{1}{3^2}\right]eV$
$=12.1eV$
From Einstein's photoelectric equation,
$h\upsilon =K_{max}+W_0$
$\therefore W_0=h\upsilon -K_{max}$
$=12.1-9$
$=3.1eV$
Threshold wavelength,
${\lambda }_0=\frac{hc}{W_0}$
$=\frac{6.62\times 10^{-34}\times 3\times 10^8}{3.1\times 1.6\times 10^{-19}}$
$=4\times 10^{-7}m$