COMEDK Exam 2020 Solved Paper

Decays constants of radioactive materials X1 and X2 is given as λ1=5λ and λ2=λ
If N0 be the initial number of nuclei in both radioactive materials, then according to radioactive decay law,
NX1=N0e−λ1t
and NX2=N0e−λ2t
∴

NX1

NX2

=‌

N0e−λ1t

N0e−λ2t

1

e

=e(−λ1+λ2)t
[ Given,

NX1

NX2

=

1

e

]
⇒e−1=e−(λ1−λ2)t
⇒(λ1−λ2)t=1
⇒t=

1

λ1−λ2

=

1

5λ−λ

=‌

1

4λ