The half-life of the radioactive isotope of chromium 51Cr24 is 27.8 days. How long does it take for 80%

The half-life of the radioactive isotope of chromium 51Cr24 is 27.8 days. How long does it take for 80% of the atoms to decay?

51 Cr 24

T = 27.8 days.

Find:

t decay of 80% of atoms.

Half-life is the length of time during which half of the original number of nuclei decays.

To solve the problem, we will apply the law of radioactive decay.

Let’s write the law in the form of a formula:

N = N0 * 2 ^ (- t / T).

Where N is the number of non-decayed nuclei;

N0 is the initial number of cores;

t is the time interval;

T is the half-life.

N / N0 = 2 ^ (- t / T) = 1 – 0.8;

2 ^ (- t / T) = 0.2 = 1/5;

2 ^ (t / T) = 5;

t = T * ln 5 / ln 2 = 27.8 * ln 5 / ln 2 = 64.5496 days.