What is the rate constant, k, for the decay of carbon-14?

Question

The wrappings from a mummy discovered in an Egyptian tomb in the Valley of Kings was dated by counting its ¹⁴C content. ¹⁴C decays by a first-order process with a half-life of 5730 years.

What is the rate constant, k, for the decay of carbon-14? Show your work, including units and the equation you used.

Answer 1

For a first order reaction, one equation you can use to find the value of the rate constant (k), is...

t_1/2 = ln 2 / k

t_1/2 = half life = 5730 yrs

ln 2 = 0.693

k = ?

Solving for k, we have...

5730 yrs = 0.693 / k

k = 0.693 / 5730 yrs

k = 0.000121 yrs^-1 = 1.21x10^-4 yrs^-1