JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Modern Physics

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The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then:

(A) $x$ and $y$ have same decay rate initially and later on different decay rate.
(B) $x$ and $y$ decay at the same rate always.
(C) $x$ -will decay faster than $y$ .
(D)y-will decay faster than x.✓ Correct

Answer: (D)

Solution

The activity is

R = λ N

. The condition links the constants through

\frac{ln 2}{λ _{x}} = \frac{1}{λ _{y}}

, so

λ_{y} = \frac{λ _{x}}{ln 2} \approx 1.44 λ_{x}

. With equal initial numbers of atoms, the larger decay constant gives the larger activity, and

λ_{y} > λ_{x}

. Element

y

decays faster than element

x

JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Single correct option

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