An X-rays tube operating at 50 eV and 20 mA . The target material of the tube has mass of 1.0 kg and

Question

An X-rays tube operating at 50 eV and 20 mA . The target material of the tube has mass of 1.0 kg and specific heat $495 \mathrm{~J} \mathrm{~kg}^{-1}{ }^{\circ} \mathrm{C}^{-1}$. One percent of supplied power is converted into X -rays and entire remaining energy goes into heating the target. Then, mark the correct option.

Professor PC Thomas Classes · Answer

(b): Supplied power $=P=V I$ \ $ \Rightarrow \quad P=50 	imes 10^3 	imes 20 	imes 10^{-3} \mathrm{~W}=1 	imes 10^{-3} \mathrm{~W} $\  This power is divided into, $1 \%$ to X-rays $99 \%$ as heat, Hence, rate of heat generation \ $ =\frac{d}{d t} m s 	heta=\frac{99}{100} 	imes 1 	imes 10^{-3} \mathrm{~W} $ \  $ \  \begin{aligned} & \Rightarrow \frac{d 	heta}{d t}=	ext { rate of rise of temperature } \ & =\frac{99 	imes 10^{-3}}{100 	imes m 	imes s}=\frac{99 	imes 10^{-3}}{100 	imes 1 	imes 495}=\frac{10^{-3}}{500}=2 	imes 10^{-6 \circ} \mathrm{Cs}^{-1} \end{aligned} $ \  Also, $\lambda_{	ext {min }}=\frac{h c}{e V}=\frac{12400}{50 	imes 10^3}(\AA)$ $ \ =0.25 	imes 10^{-10} \mathrm{~m} $