Solved: PHYSICS Question for NEET | Sushrut

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NEET PHYSICSEasy

The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be:

A

2/3

B

2/3√2

C

1/2

D

1/2√2

Step-by-Step Solution

Identify the Concept: Radioactive decay follows first-order kinetics . The activity ( $A$ ) remaining after time $t$ is related to the initial activity ( $A_0$ ) by the formula $A = A_0 (\frac{1}{2})^n$ , where $n$ is the number of half-lives elapsed .
Calculate Number of Half-lives ( $n$ ):

Given Half-life ( $T_{1/2}$ ) = 100 hours.
Given Time elapsed ( $t$ ) = 150 hours.
$n = \frac{t}{T_{1/2}} = \frac{150}{100} = 1.5 = \frac{3}{2}$ .

Calculate Fraction of Activity:

Fraction remaining = $\frac{A}{A_0} = (\frac{1}{2})^{n}$ .
$\frac{A}{A_0} = (\frac{1}{2})^{3/2} = \frac{1}{2^1 \times 2^{0.5}} = \frac{1}{2\sqrt{2}}$ .

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