Answer: The correct option is B.
Explanation: This is an example of radioactive decay and all the radioactive decay processes follow First order of kinetics.
Expression for the half life of first order kinetics is:
[tex]t_{1/2}=\frac{0.693}{k}[/tex]
We are given:
[tex]t_{1/2}=12.32years[/tex]
Putting in above equation, we get:
[tex]12.32=\frac{0.693}{k}\\k=0.05625year^{-1}[/tex]
Expression to calculate the amount of sample which is unchanged is:
[tex]N=N_oe^{-kt}[/tex]
where,
N = Amount left after time t
[tex]N_o[/tex] = Initial amount
k = Rate constant
t = time period
Putting value of k = 0.05625 and t = 24.6 in above equation, we get:
[tex]N=N_oe^{-0.05625\times 24.6}[/tex]
[tex]\frac{N}{N_o}=0.25[/tex]
The above fraction is the amount of sample unchanged and that is equal to [tex]\frac{1}{4}[/tex]
Hence, the correct option is B.
