Question

Radioactive cobalt-60 is frequently used in treating cancer. It took 24 years for a 10 gram sample to decay to 0.625 grams. What is the half-life of the sample?

Answer 1

Answer:

Half life is 6 years.

Explanation:

T½ = In2 / λ

Where λ = decay constant.

But N = No * e^-λt

Where N = final mass after a certain period of time

No = initial mass

T = time

N = 0.625g

No = 10g

t = 24 years

N = No* e^-λt

N / No = e^-λt

λ = -( 1 / t) In N / No (inverse of e is In. Check logarithmic rules)

λ = -(1 / 24) * In (0.625/10)

λ = -0.04167 * In(0.0625)

λ = -0.04167 * (-2.77)

λ = 0.1154

T½ = In2 / λ

T½ = 0.693 / 0.1154

T½ = 6.00 years.

The half life of radioactive cobalt-60 is 6 years