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

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The half-life of cobalt-60 is 5.20 yr. how many

garcias18

14.03.2022

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

Step-by-step explanation:

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

Formula of half life : $N(t) = N(0)e^{\frac{-0.693t}{t\frac{1}{2}}}$

Where N(0) = Initial amount

N(t) = Quantity remaining after time

t = time

$\frac{t}{2} =\text{half life}$

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

t = time = 6.55 years

$\frac{t}{2} =\text{half life} = 5.20 yr$

Substitute the values in the formula

Therefore,

$N(t) = 2 e^{\frac{-0.693 \times 6.55}{5.20}}$

N(t) =0.835

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

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