Question

The half-life of cobalt-60 is 5.20 yr. how many milligrams of a 2.000-mg sample remains after 6.55 years?

Answer 1

0.835 mg of a 2.000-mg sample remains after 6.55 years.

Explanation:

We are given that The half-life of cobalt-60 is 5.20 yr.

Formula of half life :
`N(t) = N(0)e^{(-0.693t)/(t(1)/(2))}`

Where N(0) = Initial amount

N(t) = Quantity remaining after time

t = time

`(t)/(2) =\text{half life}`

So, N(0) = Initial amount = 2 mg

t = time = 6.55 years

`(t)/(2) =\text{half life} = 5.20 yr`

Substitute the values in the formula

Therefore,

`N(t) = 2 e^{(-0.693 * 6.55)/(5.20)}`

`N(t) =0.835`

Hence 0.835 mg of a 2.000-mg sample remains after 6.55 years.