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Grade 11Modern Physics

From a radioactive substance 'n' nuclei decay per second at an instant when total number of nuclei are 'N' .
Find half life of radioactive substance.

astha jha

7 Years agoGrade 11

1 Answer

Samyak Jain

7 Years ago

In radioactive decay, rate of decay (– dN/dt) of nuclei at an instant is proportional to the number of nuclei

present (N) at that instant.

– dN/dt = $\lambda$ .N , $\lambda$ is constant of proportionality.

Here rate of decay = n i.e. – dA/dt = n.

n = $\lambda$ .N $\Rightarrow$ $\lambda$ = n/N

As we know that half life of radioactive substance is

t_1/2 = ln2 / $\lambda$ , t_1/2 = ln2 /(n/N)

t_1/2 = N.ln2 / n .

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