A radio active element has rate of disintegration 8000 disintegrations per minute at a particular instant. After four minutes it becomes 2000 disintegrations per minute. The decay constant per minute

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A radio active element has rate of disintegration 8000 disintegrations per minute at a particular instant. After four minutes it becomes 2000 disintegrations per minute. The decay constant per minute is

TestHub · Accepted Answer

The rate of disintegration is given by the radioactive decay law:

$R = R_{0} e^{- λ t}$

Given $R_{0} = 8000$ disintegrations per minute, $R = 2000$ disintegrations per minute, and $t = 4$ minutes.

Substituting the values:

$2000 = 8000 e^{- 4 λ}$

$e^{- 4 λ} = \frac{2000}{8000} = \frac{1}{4}$

Taking the natural logarithm on both sides:

$- 4 λ = lo g_{e} (\frac{1}{4})$

$4 λ = lo g_{e} 4$

$4 λ = 2 lo g_{e} 2$

$λ = \frac{2}{4} lo g_{e} 2 = 0.5 lo g_{e} 2$

Answer: $0.5 lo g_{e} 2$

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