Bi-210 is a beta emitter with a half-life of 5.0 days. If a sample contains 1.2 g of Bi-210, how many beta emissions occur in 5.0 days?

Solution 93P :

Step 1 :

Given :

Half life of Bi -210 (t1/2) = 5.0 days.

Mass of Bi-210 = 1.2 g.

Number of beta emissions occur in 5 days = ?

Given:

We know the equation for first order rate equation of kinetics of radioactive delay:

ln () = - k t

Where, A = amount of radioisotope remaining after time "t" has passed.

Ao= initial amount of radioisotope at the beginning of the period

K = rate constant for the radioisotope

t1/2 = for first order reaction

Therefore, k =

k =

= 0.1386

Step 2:

Now, let’s calculate the amount of Bi-210 remaining after the decay has occurred :

ln A - ln A0 = -k t

ln A =

=

ln A = -0.5775

A = e-0.5775

A = 2.14 g