Question

How many days does it take 16.Og of Gold-198 to decay to 1.0g? (each half-

Answer 1

Answer:

10.8 days (3 sig.figs.)

Explanation:

All radioactive decay is 1st order decay defined by the expression A = A₀e^-kt

which is solved for time of decay (t) => t = ln(A/A₀) / -k

A = final weight = 1.0 gram

A₀ = initial weight = 16.0 grams

k = rate constant = 0.693/t(1/2) = 0.693/2.69 days = 0.258 days⁻¹

t = ln(1/16) / -0.258da⁻¹ = (-2.77/-0.258) days = 10.74646792 days (calculator)

≅ 10 days (1 sig. fig. based on given 1 gram mass)