To determine the percentage of \(^{131}\text{I}\) remaining after 4 days, we can use the half-life formula. The expression for the remaining quantity after a certain time is given by:
\[ N(t) = N_0 \left( \frac{1}{2} \right)^{\frac{t}{T_{1/2}}} \]
Where:
- \(N(t)\) is the remaining quantity after time \(t\).
- \(N_0\) is the initial quantity.
- \(T_{1/2}\) is the half-life of the substance.
- \(t\) is the elapsed time.
Given:
- \(T_{1/2} = 8.04\) days
- \(t = 4\) days
Now, we can calculate how many half-lives have elapsed in 4 days:
\[ \text{Number of half-lives} = \frac{t}{T_{1/2}} = \frac{4 \text{ days}}{8.04 \text{ days}} \approx 0.4975 \]
Next, we can use this to find the remaining percentage:
\[ N(t) = N_0 \left( \frac{1}{2} \right)^{0.4975} \]
Calculating \(\left( \frac{1}{2} \right)^{0.4975}\):
\[ \left( \frac{1}{2} \right)^{0.4975} \approx 0.7071 \quad (\text{using a calculator}) \]
To find the percentage remaining:
\[ \text{Percentage remaining} = 0.7071 \times 100% \approx 70.71% \]
Since this value is approximately 71%, it does not exactly match any of the available options, but the closest approximation would be 75%.
Therefore, the answer is:
B. 75%