The work function for a certain metal is 4.2 eV.
Question:

The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm?

Solution:

No

Work function of the metal, $\phi_{0}=4.2 \mathrm{eV}$

Charge on an electron, = 1.6 × 10−19 C

Planck’s constant, h = 6.626 × 10−34 Js

Wavelength of the incident radiation, λ = 330 nm = 330 × 10−9 m

Speed of light, c = 3 × 108 m/s

The energy of the incident photon is given as:

$E=\frac{h c}{\lambda}$

$=\frac{6.626 \times 10^{-34} \times 3 \times 10^{8}}{330 \times 10^{-9}}=6.0 \times 10^{-19} \mathrm{~J}$

$=\frac{6.0 \times 10^{-19}}{1.6 \times 10^{-19}}=3.76 \mathrm{eV}$

It can be observed that the energy of the incident radiation is less than the work function of the metal. Hence, no photoelectric emission will take place.