Question

What is the shortest wavelength present in the radiation of an X-ray machine whose accelerating potential is $50,000V$?

• A. $0.0248nm$
• B. $0.0124nm$
• C. $0.0062nm$
• D. $0.0031nm$

Answer 1

The correct option is A $0.0248nm$

Graph of intensity vs frequency of X-rays emitted is



Energy of an electron accelerated through potential $V_0=e{V}_0$.
The lowest frequency of X-rays is obtained when the the entire energy of electron is coverted to energy of emitted photon.
i.e $\frac{hc}{{\lambda }_0}=e{V}_0$
$\Rightarrow \frac{12431}{{\lambda }_0}=50000eV$
$\Rightarrow {\lambda }_0=\frac{12431}{50000}=0.248\stackrel{\circ }{A}=0.0248nm$