Question

Which of the relations is correct for radioactive atom ?
(A)
Half-life = Average life
(B)
Half-life = 2 x Average life (c)
Half-life = 1.6931 x Average life (D)
Half-life = 0.6931 x Average life​

Answer 1

Half life = 0.6931/lambda

Average life = 1/lambda

So, Half life = 0.6931 × Average life

Thus, option D is correct..

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Answer 2

The relations which is correct for radioactive atom is half life =$0.6931\times {\text {Average life​}}$

Explanation:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

$t_{\frac{1}{2}=\frac{0.6931}{\lambda}$

$\lambda$ = rate constant

$\lambda=\frac{0.6931}{t_\frac{1}{2}}$

Average life is is the time in which concentration reduces to 1/e of the original concentration.

$t_{av}=\frac{1}{\lambda}$

$t_{av}=\frac{t_\frac{1}{2}}{0.6931}$

Thus half life =$0.6931\times {\text {Average life​}}$

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