Question

In the Coolidge tube experiment, if the applied voltage is increased to three times, the short wavelength limit of continuous $X-ray$ spectrum shifts by $20\,pm$ . What is the initial voltage (in $kV$ ) applied to the tube? [Round off your answer to the nearest integer]

Answer 1

$\because$ cut-off wavelength for continuous x-ray is given as :
$\lambda_{\min }=\frac{h c}{e V_{0}}$
$\therefore \frac{ hc }{ eV _{0}}=\lambda \& \frac{ hc }{3 \,eV _{0}}=\lambda-\Delta \lambda$
$\left( V _{0}=\right.$ accelerating voltage $)$
$\Rightarrow V _{0}=\frac{2 hc }{3 e \Delta \lambda}=41 \,kV$