Question

The maximum wavelength of radiation that can produce photoelectric effect in a certain metal is $200\, nm$. The maximum kinetic energy acquired by electron due to radiation of wavelength $100\, nm$ will be

• A. 12.4 eV
• B. 6.2 eV
• C. 100 eV
• D. 200 eV

Answer 1

Answer: (B)

Given, $\lambda_{\max }=200\, mn =2 \times 10^{-7} m$
$\therefore $ Work function
$(W)=\frac{h c}{\lambda_{\max }}=\frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{2 \times 10^{-7}}$
$=9.9 \times 10^{-19} J =6.19\, eV$
Energy of photon of wavelength $100\, nm$
$E=\frac{h c}{\lambda}=\frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{1 \times 10^{-7}}$
$=19.8 \times 10^{-19} J= 12.37\, eV$
$\therefore $ Maximum KE of photoelectron
$=E-W=12.37-6.19=6.18\, eV \approx 6.2\, eV$