Question

The half life of a certain radioactive material against \u0003α-decay is 100 days. After how much time, will the undecayed fraction of the material be 6.25%?

Answer 1

Let t be the required time after which the undecayed fraction of the material will be 6.25%.

Number of nuclei of undecayed material left=`6.25%=6.25/100=1/16`

`∴N=N_0/16`

But 

`N= N_0(1/2)^n`

where `n=t/T`

`⇒N_0/16=N_0(1/2)^n`

⇒n=4

∴Time, 

t=n×T

⇒t=4×100t=400 days