How much of a 814.2 mg gold-198 sample will remain after 13.5 days?

Question

Gold-198 has a half-life of 2.7 days. How much of a 814.2 mg gold-198 sample will remain after 13.5 days?

Answer 1

Fraction remaining = 0.5ⁿ where n = number of half lives elapsed.

n = 13.5 days/2.7 days = 5 half lives have elapsed

Fraction remaining = 0.5⁵ = 0.03125

mass remaining = 0.03125 x 814.2 mg = 25.44 mg