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 $20pm$ . What is the initial voltage (in $kV$ ) applied to the tube? [Round off your answer to the nearest integer]

Answer 1

Answer: 41

$\because$ cut-off wavelength for continuous x-ray is given as :
${\lambda }_{\min }=\frac{hc}{e{V}_0}$
$\therefore \frac{hc}{e{V}_0}=\lambda \&\frac{hc}{3e{V}_0}=\lambda -\Delta \lambda$
$(V_0=$ accelerating voltage $)$
$\Rightarrow V_0=\frac{2hc}{3e\Delta \lambda }=41kV$