The intensity of gamma radiation becomes 1/8t | vedclass

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(B) The intensity of radiation after traveling a distance $x$ is given by $I' = I_0 e^{-\mu x}$,where $I_0$ is the initial intensity and $\mu$ is the

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$12$

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(B) The intensity of radiation after traveling a distance $x$ is given by $I' = I_0 e^{-\mu x}$,where $I_0$ is the initial intensity and $\mu$ is the absorption coefficient.Given that after $x_1 = 36 \, mm$,$I_1 = I_0 / 8$.Substituting this into the formula: $I_0 / 8 = I_0 e^{-\mu (36)} \implies 8 = e^{36\mu} \implies \ln(8) = 36\mu \implies 3 \ln(2) = 36\mu \implies \mu = \frac{\ln(2)}{12}$.We need to find the distance $x_2$ where the intensity becomes half,i.e.,$I_2 = I_0 / 2$.Using the formula: $I_0 / 2 = I_0 e^{-\mu x_2} \implies 2 = e^{\mu x_2} \implies \ln(2) = \mu x_2$.Substituting the value of $\mu$: $\ln(2) = \left( \frac{\ln(2)}{12} \right) x_2$.Solving for $x_2$: $x_2 = 12 \, mm$.

The intensity of gamma radiation becomes $1/8$th of its initial value after traveling a distance of $36 \, mm$. After traveling what distance (in $mm$) will the intensity become half?

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