Question

1. What is the age (in y) of mummified primate skin that contains 9.49% of the original quantity of 14C? (The half-life of 14C is 5715 years.)

_____________ y

2. The integrated form of the first-order rate law of nuclear decay is expressed as follows.

−λt = ln(N_t / N_0)

In this equation, λ is the decay constant, t is time, N_t is the number of nuclei remaining at time t, and N_o is the original number of nuclei present.

How much time will a radioactive element require to reduce its activity to exactly four-fifths of its initial activity, if its decay constant λ = 8.6268 ✕ 10⁻² d⁻¹?

__________ d

Answer 1

1)

we have:

Half life = 5715 years

use relation between rate constant and half life of 1st order reaction

k = (ln 2) / k

= 0.693/(half life)

= 0.693/(5715)

= 1.213*10^-4 years-1

we have:

[A]o = 100.0 M

[A] = 9.49 M

k = 1.213*10^-4 years-1

use integrated rate law for 1st order reaction

ln[A] = ln[A]o - k*t

ln(9.49) = ln(100) - 1.213*10^-4*t

2.2502 = 4.6052 - 1.213*10^-4*t

1.213*10^-4*t = 2.3549

t = 19420 years

Answer: 19420 years

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