Q158 / 160 · AP EAMCET 2023 (18 May Shift 2) · Physics

A radioactive material whose half life period is 2 years weighs $1 \mathrm{~g}$ and is stored in the laboratory for 4 years. Then the amount of remaining radioactive material is

  • A
    $0.5 \mathrm{~g}$
  • B
    $0.125 \mathrm{~g}$
  • Correct answer
    C
    $0.25 \mathrm{~g}$
  • D
    $0.0625 \mathrm{~g}$

Solution

Half life, $\mathrm{T}_{1 / 2}=2$ year Quantity of substance, $\mathrm{N}_0=1 \mathrm{~g}$ Using law of radio activity, $\mathrm{N}=\mathrm{N}_0 \mathrm{e}^{-\lambda \mathrm{t}}$ Decay constant, $\lambda=\frac{0.693}{\mathrm{~T}_{1 / 2}}$ $\begin{aligned} & =\frac{0.693}{2}=0.346 \\ & =0.35 \text { per year } \\ & \text { Thus, } \mathrm{N}=1 \times \mathrm{e}^{-0.35 \times 4}=0.25 \mathrm{~g} \end{aligned}$

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

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