Question

The voltage applied to the Coolidge X-ray tube is increased by $25\%$ . As a result, the short wave limit of continuous X-ray spectrum shifts by $\Delta \lambda$ . The initial voltage applied to the tube is

• A. $\frac{hc}{4e\Delta \lambda }$
• B. $\frac{hc}{5e\Delta \lambda }$
• C. $\frac{4hc}{5e\Delta \lambda }$
• D. $\frac{5hc}{4e\Delta \lambda }$

Answer 1

Answer: (B)

$\frac{1}{2}m{v}_{max}^2=eV=\frac{hc}{\lambda }$
$\Rightarrow \lambda =\frac{hc}{eV}\Rightarrow {\lambda }_1=\frac{hc}{e{V}_1},{\lambda }_2=\frac{hc}{e{V}_2}\Rightarrow {\lambda }_1-{\lambda }_2=\frac{hc}{e{V}_1}-\frac{hc}{e{V}_2}$
$\Rightarrow \Delta \lambda =\frac{hc}{e}\left[\frac{1}{V_1}-\frac{4}{5V_1}\right]=\frac{hc}{e{V}_1}\times \frac{1}{5}$
$V=\frac{hc}{5\cdot e\Delta \lambda }$