 Solution

ID: past-exam-of-the-mphil-in-nuclear-energy-course-of-the-university-of-cambridge/2019/paper-ne1/1/b/solution

The cobalt-60 mass is approximately $5.73 \times 1 0^{- 8} kg$ . The nuclear decay constant follows from the half-life, using a

365.25

λ = \frac{l n 2}{5.27 ( 365.25 ) ( 86400 )} = 4.16784 \times 1 0^{- 9} s^{- 1} .

A = λ N

N = \frac{2.4 \times 1 0 ^{9}}{4.16784 \times 1 0 ^{- 9}} = 5.75838 \times 1 0^{17} .

Convert the supplied atomic mass into molar mass,

M = 0.05993382 kg mo l^{- 1}

m = \frac{NM}{N _{A}} = \frac{( 5.75838 \times 1 0 ^{17} ) ( 0.05993382 )}{6.02214076 \times 1 0 ^{23}} = 5.73088 \times 1 0^{- 8} kg .

This is about

57.3 μ g

of the specified isotope. It is not the total mass of the pellets or capsule, which can also contain other material.

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