Question

The ground state energy of hydrogen atoms is -13.6 eV. The photon emitted during the transition of electron from n = 3 to n = 1 unknown work function. The photoelectrons are emitted from the material with a maximum kinetic energy of 9 eV. Calculate the threshold wavelength of the material used.

Answer 1

For a transition from n = 3 to n = 1 state, the energy of the emitted photon,

hv = E₂ – E₁ = ${\displaystyle 13.6[\frac{1}{1^2}-\frac{1}{3^2}]}$ eV = 12.1 eV.

From Einstein’s photoelectric equation,

hv + K_max + W₀

∴ W₀ = hv – K_max = 12.1 – 9 = 3.1 eV

Threshold wavelength,

λ_th = ${\displaystyle \frac{\text{hc}}{{\text{W}}_0}}$

= ${\displaystyle \frac{6.62\times {10}^{-34}\times 3\times {10}^8}{3.1\times 1.6\times {10}^{-19}}}$

= 4 × 10^–7m