On increasing the operating voltage in a X-ray tube by 1.5 times, the shortest wavelength decreases

Question

On increasing the operating voltage in a X-ray tube by 1.5 times, the shortest wavelength decreases by 26 pm . The original value of operating voltage is $n 	imes 10^3 \mathrm{~V}$, then the value of $n$ is $\_\_\_\_$ .

Professor PC Thomas Classes · Answer

(16) : $K E=\frac{h c}{\lambda_{	ext {min }}} \Rightarrow \lambda_{	ext {min }}=\frac{h c}{K E}$ $ \ \begin{aligned} & \lambda_1-\lambda_2=1.24 	imes 10^4\left(\frac{1}{V}-\frac{1}{1.5 V}ight) \AA \ & 26 	imes 10^{-2}=1.24 	imes 10^4 	imes \frac{1}{3 V} \ & 	herefore V=\frac{1.24 	imes 10^4}{3 	imes 26 	imes 10^{-2}}=15.9 	imes 10^3 \mathrm{~V} \end{aligned} $ \  So, $n 	imes 10^3=15.9 	imes 10^3 \Rightarrow n \approx 16$.