What is the rate constant (in min -1) for the decay of this radionuclide?

Question

Consider the following data for a particular radionuclide: 

Time (min) N_t (g)

0 1.23

3 1.15

6 1.08

9 1.01

12 0.940

What is the rate constant (in min ^-1) for the decay of this radionuclide?

The correct answer is 0.022

Answer 1

For a first order decay (which radionuclide day is), we have the integrated rate law...

[A] = [A]₀ e^-kt and plot of ln [A] vs t yields a linear graph with a slope = -k

From the data provided, and without plotting, we can find the slope by taking the ln 1.23 and ln 0.940 and a time of 12 min.

ln 1.23 = 0.207

ln 0.940 = -0.0619

slope = -0.2689/12 min = -0.022 = -k

k = 0.022 min^-1