Question

Chromium-51 has a half-life of 28 days. If Georgia leaves a bottle of 10,000-milligram capsules in her medicine cabinet for a year, what will be the strength in milligrams of each capsule? Round to the nearest milligram

Answer 1

For finding the strength of the capsules after one year, we will use half-life formula. The formula is:

A = A₀ $(\frac{1}{2})^\frac{t}{h}$

where, A= Final amount

A₀ = Initial amount

t= time elapsed

h= half-life

Here, in this problem A₀ = 10000 milligram, t= 1 year or 365 days

and h= 28 days

So, A = 10000 $(\frac{1}{2} )^\frac{365}{28}$

⇒ A = 10000 $(\frac{1}{2})^1^3^.^0^4$

⇒ A = 1.187

So, the strength of the capsules after one year will be 1.187 milligrams.