Kelvi

Radioactive material A has decay constant 8 $\lambda$ and material B has decay constant $\lambda.$ Initially, they have the same number of nuclei. After what time, the ratio of number of nuclei of material B to that of A will be $\frac{1}{e}$ ?

hard

Nuclei

2017

physics

$\frac{1}{7\lambda}$

$\frac{1}{8\lambda}$

Explanation

To solve this problem, we need to use the concept of radioactive decay. $\\$ The number of nuclei remaining after time $t$ for a radioactive material is given by the equation: $\\ N(t) = N_0 e^{-\lambda t} \\$

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Radioactive material A has decay constant 8 λ \lambda λ and material B has decay constant λ. \lambda. λ. Initially, they have the same number of nuclei. After what time, the ratio of number of nuclei of material B to that of A will be 1e \frac{1}{e} e1​ ?

Explanation

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Radioactive material A has decay constant 8 $\lambda$ and material B has decay constant $\lambda.$ Initially, they have the same number of nuclei. After what time, the ratio of number of nuclei of material B to that of A will be $\frac{1}{e}$ ?