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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:

Option 1 -

x and y have same decay rate initially and later on different decay rate.

Option 2 -

x and y decay at the same rate always.

Option 3 -

x-will decay faster than y.

Option 4 -

y-will decay faster than x.

2 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 3

Detailed Solution:

${(t_{\frac{1}{2}})}_{x} = {(t_{m e a n})}_{y}$
$\frac{l n 2}{λ_{x}} = \frac{1}{λ_{y}}$

$λ_{x} = (l n 2) λ_{y}$

Given N_x = N_y = N₀

So activity A = $λ N$

$A s λ_{x} < λ_{y} \Rightarrow A_{x} < A_{y}$

So y will decay faster than x.

<!- [if gte mso 9]-> <!- [endif]-> <math> <mrow> <msub> <mrow> <mrow> <mo> (</mo> <mrow> <msub> <mrow> <mi>t</mi> </mrow> <mrow> <mfrac bevelled="true"> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>x</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mrow> <mo> (</mo> <mrow> <msub> <mrow> <mi>t</mi> </mrow> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>y</mi> </mrow> </msub> </mrow> </math> <math> <mrow> <mfrac> <mrow> <mi mathvariant="script">l</mi> <mi>n</mi> <mn>2</mn> </mrow> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>x</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>y</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </math> <math> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo> (</mo> <mrow> <mi mathvariant="script">l</mi> <mi>n</mi> <mn>2</mn> </mrow> <mo>)</mo> </mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>y</mi> </mrow> </msub> </mrow> </math>              <!- [if gte mso 9]-> <!- [endif]->Given Nx = Ny = N0So activity A = <math> <mrow> <mi>λ</mi> <mi>N</mi> </mrow> </math> <!- [if gte mso 9]-> <!- [endif]-> <math> <mrow> <mi>A</mi> <mi>s</mi> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>x</mi> </mrow> </msub> <mo><</mo> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>y</mi> </mrow> </msub> <mo>⇒</mo> <msub> <mrow> <mi>A</mi> </mrow> <mrow> <mi>x</mi> </mrow> </msub> <mo><</mo> <msub> <mrow> <mi>A</mi> </mrow> <mrow> <mi>y</mi> </mrow> </msub> </mrow> </math>           <!- [if gte mso 9]-> <!- [endif]->So y will decay faster than x.

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