Q156 / 160 · TS EAMCET 2023 (14 May Shift 1) · Physics

The half-life period of element $\mathrm{X}$ is same as the mean life time of element $Y$. Assume initially $\mathrm{X}$ and $\mathrm{Y}$ have same number of atoms. Then

  • A
    Initially $\mathrm{X}$ and $\mathrm{Y}$ have same decay rates
  • B
    Always $\mathrm{X}$ and $\mathrm{Y}$ decay at same rate
  • Correct answer
    C
    $\mathrm{Y}$ decays faster than $\mathrm{X}$
  • D
    $\mathrm{X}$ decays faster than $\mathrm{Y}$

Solution

For element X, $\left(\mathrm{t}_{1 / 2}\right)_{\mathrm{x}}=\frac{0.693}{\lambda_{\mathrm{x}}}$ For element $Y$, $\begin{aligned} & \left(\mathrm{t}_{\text {moan }}\right)_Y=\frac{1}{\lambda_{\mathrm{y}}} \\ & \frac{0.693}{\lambda_{\mathrm{x}}}=\frac{1}{\lambda_{\mathrm{y}}} \Rightarrow \lambda_{\mathrm{x}}=0.693 \lambda_{\mathrm{y}} \\ & \lambda_{\mathrm{x}} < \lambda_{\mathrm{y}} \end{aligned}$ Hence, $Y$ will decay faster rate than $X$.

Hence, the correct answer is option: 'C'.

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