A photo sensitive metallic surface emits electrons when X-rays of wavelength $\lambda$ fall on it. The…

A photo sensitive metallic surface emits electrons when X-rays of wavelength $\lambda$ fall on it. The de-Broglie wavelength of the emitted electrons is (Neglect the work function of the surface, $m$ is mass of the electron, $h$ is Planck's constant, $c$ is the velocity of light)
  1. $\sqrt{\frac{2 m c}{h \lambda}}$
  2. $\sqrt{\frac{h \lambda}{2 m c}}$
  3. $\sqrt{\frac{ m c}{h \lambda}}$
  4. $\sqrt{\frac{h \lambda}{ m c}}$

Solution

de-Broglie wavelength $\lambda_0=\frac{h}{p}=\frac{h}{\sqrt{2 m E_k}}$ And $E_K=h v=\frac{h c}{\lambda}$ $\therefore \quad \lambda_v=\frac{h}{\sqrt{2 m \times \frac{h c}{\lambda}}}=\sqrt{\frac{\lambda h}{2 m c}}$

Asked in: AP EAMCET 2016

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