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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%? - CBSE (Science) Class 12 - Physics

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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

  Is there an error in this question or solution?
Solution 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%? Concept: Radioactivity - Introduction of Radioactivity.
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