What is the half-life of magnesium-28

Question

sixty grams of magnesium-28 decayed into 7.5 grams after 63 hours. What is the half-life of magnesium-28?

Answer 1

The starting expression is

 

N(t) = N₀ exp[-t / λ]

 

Where N₀ is the amount of material at the start (here 60 g), t is the time elapsed (here 63 hr), and N(t) is the amount left after that time has passed (here 7.5 g). This will give the decay rate (λ), but the problem asks for the half-life (t_1/2); the two are related via

 

t_1/2 = ln[2] / λ.

 

Plugging the values into the first equation gives λ = 0.033 hr^-1, which leads to t_1/2 = 21 hr. This agrees with the literature value: http://www.wolframalpha.com/input/?i=half-life+of+magnesium+28