Question

A light source of frequency $v$ illuminates a metallic surface and ejects photoelectrons. The photoelectrons having maximum energy are just able to excite the hydrogen atom in ground state. When the whole experiment is repeated with an incident radiation of frequency $\frac{6}{5}v$, the photoelectrons so emitted are able to excite the hydrogen atom which then emit a radiation of six different wavelengths.

• A. The work function of the metal is $3.15\text{eV}$
• B. The work function of the metal is $2.55\text{eV}$
• C. The frequency of radiation is $3.08\times {10}^{15}\text{Hz}$
• D. The frequency of radiation is $3.08\times {10}^{14}\text{Hz}$

Answer 1

Answer: (B), (C)

The correct options are
B The work function of the metal is $2.55\text{eV}$
C The frequency of radiation is $3.08\times {10}^{15}\text{Hz}$

For 1st case,
$E_{max}=hv-w_0=\frac{3}{4}\left(13.6\right)\text{eV}$ ---(1)
For 2nd case, there are six different wavelengths emitted. Therefore $n=4$ (because ${}^4{\text{C}}_2=6)$

$E_{max}=h\left(\frac{6}{5}v\right)-w_0=\frac{15}{16}\left(13.6\right)\text{eV}$ ---(2)
Solving (1) and (2)
$v=3.08\times {10}^{15}\text{Hz}$ and $w_0=2.55\text{eV}$