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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.

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.

Grade:11

1 Answers

Samyak Jain
333 Points
2 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
t1/2 = ln2 / \lambda,  t1/2 = ln2 /(n/N)
t1/2 = N.ln2 / n .

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