The count rate of a Geiger-Muller counter for | vedclass

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Question

(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

Vedclass · Accepted Answer

$80$

Vedclass · Answer

(B) The radioactive decay law is given by the formula: $A = A_0 \left( \frac{1}{2} ight)^{t/T_{1/2}}$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} ight)^4$$5 = A_0 \left( \frac{1}{16} ight)$$A_0 = 5 	imes 16 = 80\, s^{-1}$Therefore,the initial count rate was $80\, s^{-1}$.

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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