Q158 / 160 · AP EAMCET 2022 (07 Jul Shift 2) · Physics

A radioactive element of mass $1 \mathrm{~kg}$ after $N$ years is left with only. $125 \mathrm{~g}$. If the half life of the element is $12.5 \mathrm{y}$, then the value of $N$ is

  • Correct answer
    A
    37.5 years
  • B
    25.0 years
  • C
    50.0 years
  • D
    75.0 years

Solution

( ) Given: Initial amount of radioactive substance is $1 \mathrm{~kg}$ and half-life is $12.5 \mathrm{y}$. Decay scheme will be $1 \mathrm{~kg} \xrightarrow{125 y} 500 \mathrm{~g} \xrightarrow{125 y} 250 \mathrm{~g} \xrightarrow{125 y} 125 \mathrm{~g}$ So time required is $t=3 \times T_{1 / 2}=3 \times 12.5=37.5 \text { years }$

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

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