Radioactive disintegration is always a first order reaction for a first order reaction. Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation.
Kt=2.303log[At][Ao]
where [Ao]= initial concentration
[At]= concentration at time ‘t’
t21=K0.693 K=t210.693=6.930.693⇒0.1yents−1 {t}_{ 90%} =\frac{ 2.303}{ 0.1} \mathrm{log}\frac{ [ 100]}{ [ 10]} {t}_{ 90%} =23.03 years.