Atoms and Nuclei Part 2

Given,
(τ1∕2)x=(τ)y...(i)
Here, τ

1

2

= half-life period of radioactive elementand t = mean life period of radioactive element.
As we know the expression,
Half-life of the radioactive element x,
τ

1

2

=

ln(2)

λx

Mean life of the radioactive element y,
τ=

1

λy

Substituting the values in Eq (i), we get

ln(2)

λx

=

1

λy

λx=0.693λy
Initially they have same number of atoms,
Nx=Ny=N0
As we know that,
Activity,
A = λ N
As,
λx<λy
⇒ Ax<Ay
Therefore, y will decay faster than x.