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Nuclei

Question
CBSEENPH12040106

Radioactive material 'A' has a decay constant '8λ' and material 'B' has decay constant 'λ'. Initially, they have a same number of nuclei. After what time, the ratio of a number of nuclei of material 'B' to that 'A' will be 1/e?

  • 1/λ

  • 1/7λ

  • 1/8λ

  • 1/9λ

Solution

B.

1/7λ

Take comma space straight N subscript straight A over straight N subscript straight B space equals space 1 over straight e
Then
straight N subscript straight A over straight N subscript straight B space equals space straight e to the power of negative 8 λt end exponent over straight e to the power of negative λt end exponent
1 over straight e space equals space straight e to the power of minus to the power of 7 λt end exponent
minus 1 space equals space minus 7 λt
straight t space equals space fraction numerator 1 over denominator 7 straight lambda end fraction