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. $\frac{hc}{4 eΔ\lambda }$
• B. $\frac{hc}{5 eΔ\lambda }$
• C. $\frac{4 hc}{5 eΔ\lambda }$
• D. $\frac{5 hc}{4 eΔ\lambda }$

Answer 1

Answer: (B)

$\frac{1}{2}mv^{2}_{max}=eV=\frac{hc}{\lambda }$
$\Rightarrow \lambda =\frac{hc}{eV}\Rightarrow \lambda _{1}=\frac{hc}{eV_{1}},\lambda _{2}=\frac{hc}{eV_{2}}\Rightarrow \lambda _{1}-\lambda _{2}=\frac{hc}{eV_{1}}-\frac{hc}{eV_{2}}$
$\Rightarrow Δ\lambda =\frac{hc}{e}\left[\frac{1}{V_{1}} - \frac{4}{5 V_{1}}\right]=\frac{hc}{eV_{1}}\times \frac{1}{5}$
$V=\frac{hc}{5 \cdot eΔ\lambda }$