An electron having de-Broglie wavelength

Question:

An electron having de-Broglie wavelength $\lambda$ is incident on a target in a X-ray tube. Cut-off wavelength of emitted X-ray is:

  1. (1) 0

     

  2. $\frac{2 m^{2} c^{2} \lambda^{2}}{h^{2}}$

  3. $\frac{2 m c \lambda^{2}}{h}$

  4. $\frac{\mathrm{hc}}{\mathrm{mc}}$


Correct Option: , 3

Solution:

$\lambda=\frac{h}{m V}$

kinetic energy, $\frac{\mathrm{P}^{2}}{2 \mathrm{~m}}=\frac{\mathrm{h}^{2}}{2 \mathrm{~m} \lambda^{2}}=\frac{\mathrm{hc}}{\lambda_{\mathrm{c}}}$

$\lambda_{\mathrm{C}}=\frac{2 \mathrm{~m} \lambda^{2} \mathrm{c}}{\mathrm{h}}$

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