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

  • question_answer
    X-ray beam of intensity \[{{I}_{0}}\]passes through an absorption plate of thickness d. If absorption coefficient of material of plate is \[\mu \], the correct statement regarding the transmitted intensity I of X-ray is                                             [MP PET 1999]

    A)            \[I={{I}_{0}}(1-{{e}^{-\mu d}})\]                                     

    B)            \[I={{I}_{0}}{{e}^{-\mu d}}\]

    C)                    \[I={{I}_{0}}(1-{{e}^{-\mu /d}})\]                            

    D)                    \[I={{I}_{0}}{{e}^{-\mu /d}}\]

    Correct Answer: B

    Solution :

                       If intensity of X-ray is decreased by dI, when it passes through a length dx of absorbing material then, the amount of observed intensity is mI dx. Thus, ? dI = mI dx   or \[\frac{dI}{dx}+\mu I=0\] On solving this equation I = I0e? mx =I0e?md    (x =d)


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