AMU 2026 — science PYQ

1. Understand the Formula:

   The remaining amount of a radioactive substance after a certain number of half-lives ($n$) is given by the formula:

   $$N=N_0{\left(\frac{1}{2}\right)}^n$$

   Where:

   • $N$ = Remaining amount of the sample

   • $N_0$ = Original amount of the sample

   • $n$ = Number of half-lives passed

2. Given Data:

   According to the problem, the sample reduces to $\frac{1}{8}$ of its original amount:

   $$\frac{N}{N_0}=\frac{1}{8}$$

3. Substitute and Solve for $n$:

   Equating the given fraction to the half-life formula:

   $${\left(\frac{1}{2}\right)}^n=\frac{1}{8}$$

   We know that $8$ can be written as a power of $2$, which is $2^3$:

   $${\left(\frac{1}{2}\right)}^n={\left(\frac{1}{2}\right)}^3$$

4. Conclusion:

   By comparing the exponents on both sides:

   $$n=3$$

Therefore, the number of half-lives passed is 3.