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13.Nuclei
medium
A certain radioactive material can undergo three different types of decay, each with a different decay constant $\lambda_1$, $\lambda_2$ and $\lambda_3$ . Then the effective decay constant is
A
$\lambda_{eff} =\frac{\lambda_1+\lambda_2+\lambda_3}{3}$
B
$\frac{1}{\lambda_{eff}}=\frac{1}{\lambda_{1}}+\frac{1}{\lambda_{2}}+\frac{1}{\lambda_{3}}$
C
$\lambda_{eff} =\lambda_1+\lambda_2+\lambda_3$
D
$\frac{1}{\lambda_{eff}}=\frac{1}{3}(\frac{1}{\lambda_{1}}+\frac{1}{\lambda_{2}}+\frac{1}{\lambda_{3})}$
Solution
$\frac{d N}{d t}=-\lambda_{1} N-\lambda_{2} N-\lambda_{3} N=-\left(\lambda_{1}+\lambda_{2}+\lambda_{3}\right) N$
$\lambda_{\mathrm{eff}}=\lambda_{1}+\lambda_{2}+\lambda_{3}$
Standard 12
Physics
