Question

How much fraction will be broken in a radioactive substance equal to its average age?

Answer 1

$\bold{\huge{\underline{Question}}}$

How much fraction will be broken in a radioactive substance equal to its average age?

$\bold{\huge{\underline{Answer- }}}$According to the question we know that here Time is a average age

now,

$\bold{\huge{\underline{Step-1}}}$

$\bold{\underline{How\: much \:fraction \:will\: be\: decomposed}}$

Now, using the formula $\boxed{ \boxed{N = No \: e {}^{ - \lambda \: t} }}$

$N = No \: e {}^{ - \lambda \: t} \: \\ \\ \\ N = No \: e {}^{ - \lambda \: \times \frac{1}{t} } \\ \\ \\ N = No \: e {}^{ - 1} \\ \\ \\ N = \frac{No}{e}$

now , How much decomposed = No - N

$\bold{\underline{Decomposed\: part }}$= $\frac{No -N }{No}$

$= \frac{No - \frac{No }{e} }{No} \\ \\ \\ = \frac{No(1 - \frac{1}{e}) }{No}$

Decomposed part = $\boxed{ \boxed{(1 - \frac{1}{e} )}}$

Answer 2

HIII.....

GOOD MORNING:-)

HERE IS YOUR ANSWER:--------

DECOMPOSED PART= (1-1/e)

HOPE THIS HELPS YOU