Photons of wavelength $\lambda$ ' are incident on the cathode of a photocell. Electrons are emitted from the…

Photons of wavelength $\lambda$ ' are incident on the cathode of a photocell. Electrons are emitted from the cathode surface. The de-Broglie wavelength of the emitted electrons is (work function is negligible) $(\mathrm{c}=$ velocity of light, $\quad \mathrm{h}=$ Planck's constant, $\quad \mathrm{m}=$ mass of electron $)$
  1. $\sqrt{\frac{\mathrm{mc}}{2 \mathrm{~h} \lambda}}$
  2. $\sqrt{\frac{\mathrm{h} \lambda}{2 \mathrm{mc}}}$
  3. $\sqrt{\frac{2 \mathrm{~h} \lambda}{\mathrm{mc}}}$
  4. $\sqrt{\frac{\mathrm{mh}}{\lambda \mathrm{c}}}$

Solution

Work function is negligible $\begin{array}{l} \therefore \frac{1}{2} \mathrm{mV}^{2}=\frac{\mathrm{hc}}{\lambda} \\ \therefore \frac{1}{2} \frac{\mathrm{m}^{2} \mathrm{~V}^{2}}{\mathrm{~m}}=\frac{\mathrm{hc}}{\lambda} \\ \therefore \mathrm{m}^{2} \mathrm{~V}^{2}=\frac{2 \mathrm{mhC}}{\lambda} \\ \therefore \mathrm{mV}=\sqrt{\frac{2 \mathrm{mhc}}{\lambda}} \end{array}$ $\begin{aligned} \text { de Broglie wavelength } &=\frac{\mathrm{h}}{\mathrm{mV}} \\ &=\mathrm{h} \sqrt{\frac{\lambda}{2 \mathrm{mhC}}}=\sqrt{\frac{\mathrm{h} \lambda}{2 \mathrm{mC}}} \end{aligned}$

Asked in: MHT CET 2020 (13 Oct Shift 2)

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