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? A. 1.2 g B. 2.7 g C. 3.3 g D. 2.1 g E. 0.2 g

Answer 1

B. 2.7 g

Explanation:

The half life of a substance is the time taken for the substance to reduce to half of its original amount. It is given by:

`A=A_o*((1)/(2))^(t)/(t_(1/2))\\ Where\ A\ is \ the \ amount \ of \ substance\ remaining\ after\ t\ years, \\A_o \ is \ the\ initial\ value\ of \ the\ substance,\ t_(1/2) is\ the\ half\ life\ and\\t\ is\ the\ years\ spent`

Given that:

Ao = 4 g, t = 3 years, t(1/2) = 5.26 years. Therefore:

`A=A_o*((1)/(2))^(t)/(t_(1/2))\\A=4*((1)/(2) )^(3)/(5.26)=4*0.6735=2.7\\ A=2.7\ g`