Question

The half-life of cobalt-60 is 5. 20 yr. how many milligrams of a 2. 000 mg sample remain after 6. 55 years?

Answer 1

0.84 milligrams of a 2. 000 mg sample remain after 6. 55 years, according to radioactive decay.

Given data,

$t\frac{1}{2} of Co-60 = 5.20years$

amount of sample = 2.000mg initially = 0.002grams

According to radioactive decay,

$N_{t} = N_{0}e^{-λt}$

($N_{0} - 0.002$ )λ = $\frac{0.693}{t\frac{1}{2} }$ = $\frac{0.693}{5.20}$  = 0.133

According to radioactive decay,

$N_{t} = N_{0}e^{-λt}$

$lnN_{t} = lnN_{0}$ - λt

$lnN_{t}$ = ln0.002 - (0.133×6.55)

       = -6.21 - 0.87 = -7.08 = 0.00084g = 0.84mg

Therefore, 0.84 milligrams of a 2. 000 mg sample remain after 6. 55 years.

Learn more about radioactive decay here:

brainly.com/question/1770619

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