Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
An X-ray tube is operating at 50 kV and 20 mA. The target material of the tube has a mass of\[1.0\,kg\]and specific hea\[495\,Jk{{g}^{-10}}{{C}^{-1}}\]. One percent of the supplied electric power is converted into X-rays and the entire remaining energy goes into heating the target. Then (1) a suitable target material must have a high melting temperature (2) the average rate of rise of temperature of target would be\[2{}^\circ C/s\] (3) the minimum wavelength of the X-rays emittled is about\[0.25\times {{10}^{-10}}m\] (4) a suitable target material must have low thermal conductivityA) 1, 2 and 3 are correct.
B) 1 and 2 are correct.
C) 2 and 4 are correct.
D) 1 and 3 are correct.
Correct Answer: A
Solution :
\[P=Vi\] \[=50\times {{10}^{3}}\times 20\times {{10}^{-3}}=1000W\] Power converted into heat = 990 W \[ms\Delta T=990\Rightarrow \Delta T={{2}^{o}}C/s\] Now, \[\frac{hc}{{{\lambda }_{\min }}}=eV\] \[\Rightarrow \] \[{{\lambda }_{\min }}=\frac{hc}{eV}=0.248\times {{10}^{-10}}m\]
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