Two radioactive substances A and B have decay constants 5λ and λ respectively. At t=0 they have the same number of nuclei. The ratio of the number of nuclei of A to those of B will be (1/e)² after a time interval

The correct option is D
12λ
Decay equation is given by
N = N₀e⁻λt
Where, λ is Decay constant; N is number of atoms at time t
So, the number of atoms of A is given by,
NA = N₀e⁻⁵λt
And that of B are given by,
NB = N₀e⁻λt
Taking ratio we get:
NA/NB = e⁻⁴λt
Given that:
NA/NB = e⁻²;
So, this will happen when,
t = 12λ