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

No

Work function of the metal, φ_O = 4.2 eV

Charge on an electron, e = 1.6 x 10^-19 C

Planck’s constant, h = 6.626 x 10^–34 Js

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

Speed of light, c = 3 x 10⁸ m/s

The energy of the incident photon is given as:

E = hc/λ = (6.626 x 10^–34) x ( 3 x 10⁸) /(330 x 10⁻⁹)

=6.0 x 10⁻¹⁹J

=(6.0 x 10⁻¹⁹J)/(1.6 x 10⁻¹⁹ ) = 3.76 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.