Question

Cobalt-60 is used for radiotherapy. It has a half-life of 5.26 years. If 4 g of cobalt-60 is administered, how much remains in 3 years?

Answer 1

Half-life formula

`N(t)=N_0\cdot((1)/(2))^{(t)/(t_(0.5))}`

where:

• N(t): quantity of the substance remaining

,

• N0: initial quantity of the substance

,

• t: time elapsed

,

• t0.5: half-life of the substance

Substituting with t0.5 = 5.26 years, N0 = 4 g, and t = 3 years, we get:

`\begin{gathered} N(t)=4\cdot((1)/(2))^{(3)/(5.26)} \\ N(t)\approx2.7\text{ g} \end{gathered}`

It remains approximately 2.7 g in 3 years