TG EAMCET 2 May 2025 Shift 2 Paper

Step 1: Formula for Remaining NucleiWe use the formula $N=N_0 \left(\frac{1}{2}\right)^n$, where:$N=$ number of nuclei left$N_0=$ starting number of nuclei$n=$ number of half-lives passedStep 2: Setting Up the RatioThe question asks for the ratio of nuclei left in $A$ and $B$, so: $\frac{N_A}{N_B} = \frac{ \left(\frac{1}{2}\right)^n A }{ \left(\frac{1}{2}\right)^{n_B} }$Step 3: Simplifying the RatioThis simplifies to: $\frac{N_A}{N_B} = \left(\frac{1}{2}\right)^{n_A - n_B}$Step 4: Finding Number of Half-lives for Each SubstanceThe number of half-lives $n$ is found by dividing total time by half-life:For $A$ : $n_A = \frac{9}{1.5} = 6$For $B: n_B = \frac{9}{4.5} = 2$Step 5: Plugging In the Values$\frac{N_A}{N_B} = \left(\frac{1}{2}\right)^{6-2} = \left(\frac{1}{2}\right)^4$Step 6: Final Answer$\left(\frac{1}{2}\right)^4 = \frac{1}{16}$ So, the ratio of the remaining nuclei in $A$ and $B$ after 9 days is $\frac{1}{16}$.