MHTCET 14 May 2023 Shift 2 Solved Paper

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:$\frac{t}{T_{1/2}}=\frac{6400}{1600}=4\;\text{half-lives}$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 $\frac{1}{16}$