Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

The half-life of radium is 1622 years. How long will it take for seven-eighth of a given amount of radium to decay?

3244 years

6488 years

4866 years

811 years

Determine Fraction Remaining: The problem states that $7/8$ of the radium decays. Therefore, the fraction of the nuclei remaining undecayed is: $\frac{N}{N_0} = 1 - \frac{7}{8} = \frac{1}{8}$
Apply Radioactive Decay Law: Radioactive decay follows first-order kinetics. The amount of substance remaining $N$ after $n$ half-lives is given by the formula $N = N_0 (\frac{1}{2})^n$ .
Calculate Number of Half-lives ( $n$ ): $\frac{1}{8} = \left(\frac{1}{2}\right)^n \Rightarrow \left(\frac{1}{2}\right)^3 = \left(\frac{1}{2}\right)^n$ Comparing the powers, we get $n = 3$ half-lives.
Calculate Total Time ( $t$ ): The total time elapsed is the number of half-lives multiplied by the half-life period ( $T_{1/2}$ ). $t = n \times T_{1/2} = 3 \times 1622 \text{ years} = 4866 \text{ years}$ .

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