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Question: In a sample of a radioactive substance what fraction of the initial number of nuclei will remain und...

In a sample of a radioactive substance what fraction of the initial number of nuclei will remain undecayed after a time t = T/2, where, T = half life of radioactive substance –

A

1/21/\sqrt{2}

B

122\frac{1}{2\sqrt{2}}

C

1/4

D

12–1\frac{1}{\sqrt{2}–1}

Answer

1/21/\sqrt{2}

Explanation

Solution

Fraction of nuclei which remain undecayed is

f = = N0e−λtN0\frac { \mathrm { N } _ { 0 } \mathrm { e } ^ { - \lambda \mathrm { t } } } { \mathrm { N } _ { 0 } } = e–lt = = 12\frac { 1 } { \sqrt { 2 } }