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%?

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#### 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

Concept: Radioactivity - Introduction of Radioactivity

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