Electrons of mass $m$ with de-Broglie wavelength $\lambda$ fall on the target. The cut-off wavelength…

Electrons of mass $m$ with de-Broglie wavelength $\lambda$ fall on the target. The cut-off wavelength $\lambda_0$ is equal to [ $h=$ Planck's constant, $C=$ velocity of light $]$
  1. $\frac{2 m c \lambda^2}{h}$
  2. $\frac{m c \lambda}{h}$
  3. $\frac{2 h}{m c \lambda^2}$
  4. $\frac{2 m c \lambda}{h}$

Solution

Using de-Broglie equation $\lambda=\frac{h}{p}$ where $p=\sqrt{2 m E}$ $\Rightarrow \lambda=\frac{h}{\sqrt{2 m E}}$ Energy of the X-ray emitted $E=\frac{h c}{\lambda_0}$ $\therefore \lambda=\frac{h}{\sqrt{2 m \times \frac{h c}{\lambda_0}}} \Rightarrow \lambda_0=\frac{2 m c \lambda^2}{h}$ .

Asked in: MHT CET 2022 (08 Aug Shift 1)

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