Question

The half life of cobalt-60 is 5.3 years. If a certain rock currently contains 10.0g of cabals -60 how much cobalt-60 will remain in the rock after 21.2 years

A. 1.25g

B. 2.50g

C. 0.63g

D. 5.00g

Answer 1

T = half life of cobalt-60 = 5.3 years

λ = decay constant for cobalt-60 = ?

decay constant is given as

λ = 0.693/T

inserting the values

λ = 0.693/5.3 = 0.131

N₀ = initial amount of cobalt-60 = 10 g

t = time of decay = 21.2 years

N = final amount of cobalt-60 after time "t"

final amount of cobalt-60 after time "t" is given as

N = N₀
`e^(-\lambda t)`

inserting the values

N = 10
`e^(-(0.131) (21.2))`

N = 10
`e^(-(0.131) (21.2))`

N = 10 x 0.0622 g

N = 0.63 g

hence

C. 0.63 g