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JEE Main & Advanced Physics Photo Electric Effect, X- Rays & Matter Waves Question Bank Critical Thinking

  • question_answer
    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 heat 495 J kg-1 \[^{o}{{C}^{-1}}\]. One percent of the supplied electric power is converted into X-rays and the entire remaining energy goes into heating the target. Then                                            [IIT 1995]

    A)            A suitable target material must have a high melting temperature

    B)            A suitable target material must have low thermal conductivity

    C)            The average rate of rise of temperature of target would be 2 °C/s

    D)            The minimum wavelength of the X-rays emitted is about \[0.25\times {{10}^{-10}}\,m\]

    Correct Answer: C

    Solution :

     \[P=VI=50\times {{10}^{3}}\times 20\times {{10}^{-3}}=1000\,\,W\]                    Power converted into heat = 990 W                    \[ms\Delta T=990\,\Rightarrow \Delta T={{2}^{o}}C/\sec \]                    Now \[\frac{hc}{{{\lambda }_{\min }}}=eV\]\[\Rightarrow \,{{\lambda }_{\min }}=\frac{hc}{eV}=0.248\times {{10}^{-10}}m\]


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