Question 469: Atoms & Nuclei

Question

Half life of radio-active element is 1600 years. The fraction of sample remains undecayed after 6400 years will be

Accepted Answer

The half-life of a radioactive substance is the time it takes for half of the substance to decay. The remaining fraction of the original substance after a certain number of half-lives can be calculated using the formula:
$$N = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}$$
Where:
$$N$$ is the remaining quantity of the substance,
$$N_0$$ is the initial quantity of the substance,
$$t$$ is the elapsed time,
$$T_{1/2}$$ is the half-life of the substance.
Given that the half-life $$T_{1/2}$$ is 1600 years, and we want to find the amount of substance left after 6400 years, we can use the above formula:
$$\frac{t}{T_{1/2}} = \frac{6400}{1600} = 4$$ half-lives
Therefore,
$$N = N_0 \left(\frac{1}{2}\right)^4$$
$$N = N_0 \left(\frac{1}{2^4}\right)$$
$$N = N_0 \left(\frac{1}{16}\right)$$
The fraction of the original sample remaining undecayed after 6400 years is $$\frac{1}{16}$$.
Thus, the correct answer is:
Option A $$\frac{1}{16}$$

Answer

$$\frac{1}{16}$$

Answer

$$\frac{1}{4}$$

Answer

$$\frac{1}{8}$$

Answer

$$\frac{1}{24}$$

Atoms & Nuclei

Half life of radio-active element is 1600 years. The fraction of sample remains undecayed after 6400 years will be

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