The half-life of bromine-74 is 25 min. How much of a 4.0 mg sample remains after 75 min?

• A. 0.50 mg
• B. 3.0 mg
• C. 2.0 mg
• D. 1.0 mg

Answer: (D)

Verified step by step guidance

1. Identify the given information: the half-life (\(t_{1/2}\)) of bromine-74 is 25 minutes, the initial amount (\(N_0\)) is 4.0 mg, and the total time elapsed (\(t\)) is 75 minutes.
2. Determine the number of half-lives that have passed by dividing the total time by the half-life: \(n = \frac{t}{t_{1/2}}\).
3. Use the half-life decay formula to find the remaining amount: \(N = N_0 \times \left(\frac{1}{2}\right)^n\).
4. Substitute the values of \(N_0\), \(n\), and calculate the power of one-half raised to \(n\) to find the fraction remaining.
5. Multiply the initial amount by this fraction to find the remaining mass of bromine-74 after 75 minutes.