(B) The rate of disintegration $R$ is given by $R = R_0 e^{-\lambda t}$.Given $R_0 = 10,000$ disintegrations per minute,$R = 2500$ disintegrations per

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(B) The rate of disintegration $R$ is given by $R = R_0 e^{-\lambda t}$.Given $R_0 = 10,000$ disintegrations per minute,$R = 2500$ disintegrations per minute,and $t = 4$ minutes.Substituting these values into the equation:$\frac{2500}{10000} = e^{-\lambda \times 4}$$\frac{1}{4} = e^{-4 \lambda}$Taking the natural logarithm on both sides:$\ln(\frac{1}{4}) = -4 \lambda$$-\ln(4) = -4 \lambda$$\ln(2^2) = 4 \lambda$$2 \ln(2) = 4 \lambda$$\lambda = \frac{2}{4} \ln(2)$$\lambda = 0.5 \log _e 2$ per minute.

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

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$A$ radioactive element has a rate of disintegration $10,000$ disintegrations per minute at a particular instant. After four minutes it becomes $2500$ disintegrations per minute. The decay constant per minute is (in $log _e 2$)

MHT CET 2017 All MHT CET

A
$0.2$
B
$0.5$
C
$0.6$
D
$0.8$

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Class 12

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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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$A$ radioactive element has a rate of disintegration $10,000$ disintegrations per minute at a particular instant. After four minutes it becomes $2500$ disintegrations per minute. The decay constant per minute is (in $log _e 2$)

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The activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at time $t_2$. If $\lambda$ is the decay constant,then which of the following is correct?

$Rn$ decays into $Po$ by emitting an $\alpha$-particle with a half-life of $4 \text{ days}$. $A$ sample contains $6.4 \times 10^{10}$ atoms of $Rn$. After $12 \text{ days}$,the number of atoms of $Rn$ left in the sample will be:

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