Question #205431

An important radioisotope for industrial and medical applications is 60Co with a half life of 5.2 years and a molar mass of 60 grams/mole. What minimum initial mass of 60Co is required for a sealed cource of 60Co to have an activity of 10 Ci after 30 months where 1Ci=3.7x1010 Bq. 


1
Expert's answer
2021-06-11T11:21:02-0400

Convert from Ci to Bq: 10 Ci is 3.7·1011 Bq.


Determine decay constant:


λ=ln2t=0.0111 month1.\lambda=\frac{\ln2}{t}=0.0111\text{ month}^{-1}.

Find initial activity:


A=A0eλt, A0=Aeλt=5.161011 Bq.A=A_0e^{-\lambda t},\\\space\\ A_0=\frac{A}{e^{-\lambda t}}=5.16·10^{11}\text{ Bq}.

Activity can be expressed as a product of decay constant and number of particles:


A=λN.A=\lambda N.

Find initial N:


N0=A0λ=1.221022.N_0=\frac{A_0}{\lambda}=1.22·10^{22}.

Find the amount of substance:


n0=N0NA=0.0203 mol.n_0=\frac{N_0}{N_A}=0.0203\text{ mol}.

Find the mass:


m0=noM=1.22 g.m_0=n_o\Mu=1.22\text{ g}.


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