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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%?
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
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