A sample of Th-219 requires 3.84 × 10⁻⁶ seconds to decay to 1.50 mg. What was the initial mass of the sample of Th-219? (t _1/2 for Th-219 = 1.05 × 10⁻⁶ s)

• A. 3.00 mg
• B. 5.90 mg
• C. 18.9 mg
• D. 37.8 mg
• E. 56.1 mg

Answer: (C)

Verified step by step guidance

1. Identify the given values: the final mass of Th-219 is 1.50 mg, the time taken for decay is 3.84 × 10^(-6) seconds, and the half-life (t1/2) of Th-219 is 1.05 × 10^(-6) seconds.
2. Use the formula for radioactive decay: N = N0 * (1/2)^(t/t1/2), where N is the final mass, N0 is the initial mass, t is the time elapsed, and t1/2 is the half-life.
3. Rearrange the formula to solve for the initial mass (N0): N0 = N / (1/2)^(t/t1/2).
4. Substitute the known values into the rearranged formula: N0 = 1.50 mg / (1/2)^(3.84 × 10^(-6) s / 1.05 × 10^(-6) s).
5. Calculate the exponent (t/t1/2) and then evaluate the expression to find the initial mass N0.