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JEE Main & Advanced Physics Photo Electric Effect, X- Rays & Matter Waves Question Bank Self Evaluation Test - Dual Nature of Radiation and Matter

  • question_answer
     A cylindrical rod of some laser material \[5\times {{10}^{-2}}m\] long and \[{{10}^{-2}}\] m in diameter contains \[2\times {{10}^{25}}\] ions \[6.6\times {{10}^{-7}}m.\] per m3. If on excitation all the ions are in the upper energy level and de-excite simultaneously emitting photons in the same direction, calculate the maximum energy contained in a pulse of radiation of wavelength \[6.6\times {{10}^{-7}}m.\] If the pulse lasts for\[{{10}^{-7}}s\]. the average power of the laser during the pulse is        

    A) 532 MW

    B) 352 MW

    C) 235MW

    D) 325 MW

    Correct Answer: C

    Solution :

    [c] Total number of ions in the rod \[N=\left( 2\times {{10}^{25}} \right)\times \left[ \frac{\pi }{4}\times {{\left( {{10}^{-2}} \right)}^{2}} \right]\times \left( 5\times {{10}^{-2}} \right)\] \[=7.85\times {{10}^{19}}\] The energy of excitation \[E=N\times \frac{hc}{\lambda }\] \[\left( 7.85\times {{10}^{19}} \right)\times \frac{\left( 6.6\times {{10}^{-34}} \right)\times \left( 3\times {{10}^{8}} \right)}{6.6\times {{10}^{-7}}}\] \[=23.55J\] Average power P \[=\frac{E}{t}=\frac{23.55}{{{10}^{-7}}}=23.55\times {{10}^{7}}W=235MW\]


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