(B) The radioactive decay law is given by the formula: $A = A_0 \left( \frac{1}{2} \right)^{t/T_{1/2}}$Given:Initial time $t = 2\, hours = 120\, minut

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(B) The radioactive decay law is given by the formula: $A = A_0 \left( \frac{1}{2} \right)^{t/T_{1/2}}$Given:Initial time $t = 2\, hours = 120\, minutes$Half-life $T_{1/2} = 30\, minutes$Final count rate $A = 5\, s^{-1}$Number of half-lives $n = \frac{t}{T_{1/2}} = \frac{120}{30} = 4$Substituting the values into the formula:$5 = A_0 \left( \frac{1}{2} \right)^4$$5 = A_0 \left( \frac{1}{16} \right)$$A_0 = 5 \times 16 = 80\, s^{-1}$Therefore,the initial count rate was $80\, s^{-1}$.

Class 12 Physics Nuclei Law of Radioactivity by Rutherford and Soddy and Half Life and Mean Life

Medium

The count rate of a Geiger-Muller counter for the radiation of a radioactive material with a half-life of $30\, minutes$ decreases to $5\, s^{-1}$ after $2\, hours$. The initial count rate was..........$s^{-1}$.

AIPMT 1995 All AIPMT

A
$25$
B
$80$
C
$625$
D
$20$

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Nuclei

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Law of Radioactivity by Rutherford and Soddy and Half Life and Mean Life

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AIPMT 1995 Paper All AIPMT years →

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The count rate of a Geiger-Muller counter for the radiation of a radioactive material with a half-life of $30\, minutes$ decreases to $5\, s^{-1}$ after $2\, hours$. The initial count rate was..........$s^{-1}$.

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If $M_0$ is the initial mass of a radioactive substance with a half-life of ${t_{1/2}} = 5 \text{ years}$,what is the amount of substance remaining after $15 \text{ years}$?

The half-life of a substance is $20 \ min$. The time taken between $33\%$ decay and $67\%$ decay will be ....... $min$.

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