Question

In an X-ray tube, the voltage applied is $20kV$. The energy required to remove an electron from $L$ shell is $19.9KeV$. In the X-rays emitted by the tube

• A. Minimum wavelength will be $62.1nm$
• B. Energy of the characteristic $x-$rays will be equal to or less than $19.9KeV$
• C. $L_{\alpha }$ $x-$ray may be emitted
• D. $L_{\alpha }$ $x-$ray will have energy $19.9KeV$

Answer 1

Answer: (A), (B), (C)

The correct options are
A Minimum wavelength will be $62.1nm$
B Energy of the characteristic $x-$rays will be equal to or less than $19.9KeV$
C $L_{\alpha }$ $x-$ray may be emitted

A, B and C

$V=20KV=2\times {10}^{4}V$
$E=19.9KeV$
$=19.9\times {10}^3\times 1.6\times {10}^{-19}J$
$E=h\nu =\frac{hc}{\lambda }$
$\Rightarrow \lambda =\frac{hc}{E}=\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{19.9\times 1.6\times {10}^{-16}}$
$=62.1\times {10}^{-9}m$
$=62.1nm$
So minimum wavelength will be $62.1nm$.

It is given that the energy required to remove an electron from L shell is 19.9KeV. Electrons are emitted from K or L shell. So energy equal to or less than 19.9KeV is required and $L_{\alpha }$ x-ray may be emitted.