Consider a point source emitting \( \alpha \)-particles and recepto...

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Consider a point source emitting \( \alpha \)-particles and receptor of area \( 1 \mathrm{~cm}^{2} \) placed \( 1 \mathrm{~m} \) away from source. Receptor records any \( \alpha \)-particle falling on it. If the source contains \( N_{0}=3.0 \times 10^{16} \) active nuclei and the receptor records a rate of \( A=50000 \) counts/second. Assume that the source emits alpha particles uniformly in all directions and the alpha particles fall nearly normally on the window. If decay constant is \( 3 n \times 10^{-(n+1)} \), then find the value of \( n \)
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