Question

A light from Paschen series of hydrogen atom is able to eject photoelectrons from a metal. Then the work function of the metal is

• A. 3.4 eV
• B. 1.54 eV
• C. 0.85 eV
• D. 1.1 eV

Hint:

Use energy levels from Bohr model.
Paschen series = transitions to \(n = 3\)

Answer 1

The Correct Option is B

For Paschen series: transition to \(n = 3\) Minimum energy photon in Paschen series corresponds to \(n = 4 \rightarrow n = 3\) \[ E = 13.6 \left( \frac{1}{3^2} - \frac{1}{4^2} \right) = 13.6 \left( \frac{1}{9} - \frac{1}{16} \right) = 13.6 \times \frac{7}{144} \approx 0.66 \text{ eV} \] But for the FIRST line in Paschen, use: \[ E = 13.6 \left( \frac{1}{3^2} - \frac{1}{\infty} \right) = 13.6 \times \frac{1}{9} = 1.51 \text{ eV} \] Therefore, maximum energy of photon = 1.54 eV. So, work function must be less than or equal to 1.54 eV.