Question 138: Atoms & Nuclei

Question

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If $\lambda_{A}$ and $\lambda_{B}$ are decay constants of A and B respectively, then choose the correct relation from the given options.

Accepted Answer

We are given that the half-life of A is the same as the average life of B. The relationship between half-life ($T_{1/2}$) and the decay constant ($\lambda$) is:
$T_{1/2} = \frac{\ln 2}{\lambda}$
For the average life ($	au$), the relationship with the decay constant is:
$	au = \frac{1}{\lambda}$
According to the given information, the half-life of A is equal to the average life of B:
$T_{1/2(A)} = 	au_{B}$
Now, we can substitute the relationships for half-life and average life:
$\frac{\ln 2}{\lambda_{A}} = \frac{1}{\lambda_{B}}$
To find the correct relationship between $\lambda_{A}$ and $\lambda_{B}$, we can rearrange the equation:
$\lambda_{A} = \lambda_{B}  \ln 2$

Answer

$\lambda_{\mathrm{A}}=\lambda_{\mathrm{B}} \ln 2$

Answer

$\lambda_{\mathrm{A}} \ln 2=\lambda_{\mathrm{B}}$

Answer

$\lambda_{\mathrm{A}}=2 \lambda_{\mathrm{B}}$

Answer

$\lambda_{\mathrm{A}}=\lambda_{\mathrm{B}}$

Atoms & Nuclei

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If \lambda_{A} and \lambda_{B} are decay constants of A and B respectively, then choose the correct relation from the given options.

Choose the correct answer: