The light of wavelength $\lambda^{\prime}$ incident on the surface of metal having work function $\phi$…

The light of wavelength $\lambda^{\prime}$ incident on the surface of metal having work function $\phi$ emits the electrons. The maximum velocity of electrons emitted is $(c=$ velocity of light, h=Planck's constant, m=mass of electron $)$
  1. $\left[\frac{2(\mathrm{~h} \mathrm{C}-\phi)}{\mathrm{m} \lambda}\right]$
  2. $\left[\frac{2(\mathrm{~h} \mathrm{c}-\lambda \phi)}{\mathfrak{m \lambda}}\right]^{\frac{1}{2}}$
  3. $\left[\frac{2(h \mathrm{C}-\lambda)}{m \lambda}\right]^{\frac{1}{2}}$
  4. $\left[\frac{2(\mathrm{~h} \mathrm{v}-\phi) \lambda}{\mathrm{mC}}\right]$

Solution

$\mathrm{hv}-\phi=\mathrm{E}_{\max }=\frac{1}{2} \mathrm{mv}^{2}$ $\frac{\mathrm{hc}}{\lambda}-\phi=\frac{1}{2} \mathrm{mv}^{2}$ $\mathrm{v}^{2}=2 \frac{(\mathrm{hc}-\lambda \phi)}{\lambda \mathrm{m}}$

Asked in: MHT CET 2020 (16 Oct Shift 2)

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