# 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%? - Physics

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%?

#### Solution

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