Question

Minimum wavelength of X-rays produced in an X-ray tube is $0.39A^0$. The accelerating voltage required for electron to produce this radiation is($h=6.62\times {10}^{-34}Js$)

• A. $21.02kV$
• B. $31.82kV$
• C. $36.06kV$
• D. $30.04kV$

Answer 1

The correct option is B $31.82kV$

The relationship between de Broglie wavelength $\left(\lambda \right)$ and the momentum (p) of a photon is given by:
$\lambda =\frac{h}{p}$.
Minimum wavelength of X-rays produced in an X-ray tube is $0.39A^o$. The energy of this ray is:

$E=\frac{hc}{\lambda }=\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{1.6\times {10}^{-19}\times 0.39\times {10}^{-10}}=31.82$eV.

The accelerating voltage required for electron to produce this radiation is $31.82eV.$

So, the answer is option (B).