+91-8076753736[email protected]
logo
logo
-->

Wave Optics

Question
CBSEENPH12040047
Wired Faculty App

Two radioactive materials X1 and X2 have decay constant 5 λ respectively. If initially, they have the same number of nuclei, then the ratio of the number of nuclei of X1 to that of X2 will be 1/e after a time

  • λ

  • λ/2

  • 1/4λ

  • e/λ

Solution

C.

1/4λ

If N is the number of radioactive nuclei present at some instant then
straight N space equals space straight N subscript straight o straight e to the power of negative λt end exponent The space constant space straight N subscript straight o space represents space the space number space of space radioactive space nuclei space at space straight t space equals 0 Now comma space straight N subscript 1 over straight N subscript 2 space equals straight e to the power of negative straight lambda subscript 1 straight t end exponent over straight e to the power of negative straight lambda subscript 2 straight t end exponent Or space straight N subscript 1 over straight N subscript 2 space equals space straight e to the power of negative 5 λt end exponent over straight e to the power of negative straight lambda subscript 2 straight t end exponent space equals space straight e to the power of negative 4 λt end exponent but space straight N subscript 1 over straight N subscript 2 space equals space 1 over straight e space left parenthesis as space provided right parenthesis therefore comma 1 over straight e space equals space 1 over straight e to the power of 4 λt end exponent or space 4 λt space equals space 1 straight t space equals space fraction numerator 1 over denominator 4 straight lambda end fraction

Some More Questions From Wave Optics Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation