MCQ
Electrons with de-Broglie wavelength $\lambda$ fall on the target in an $\mathrm{X}$-ray tube. The cut-off wavelength of the emitted $\mathrm{X}$ rays is
  • $\lambda_0=\frac{2 \mathrm{mc} \lambda^2}{\mathrm{~h}}$
  • B
    $\lambda_0=\frac{2 \mathrm{~h}}{\mathrm{mc}}$
  • C
    $\lambda_0=\frac{2 \mathrm{~m}^2 \mathrm{c}^2 \lambda^3}{\mathrm{~h}^2}$
  • D
    $\lambda_0=\lambda$

Answer

Correct option: A.
$\lambda_0=\frac{2 \mathrm{mc} \lambda^2}{\mathrm{~h}}$
a
de-Broglie wave length is $\lambda=\frac{ h }{\sqrt{2 mE }} \ldots$ $(1)$

Where $E$ is the linetic energy of the electrons. The cut-off wave length is

$\lambda_0=\frac{ hc }{ E }$

From equation $(1)$ :

$E=\frac{h^2}{2 m \lambda^2}$

Hence, $\lambda_0=\frac{2 mc \lambda^2}{ h }$

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