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 :
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 = ?
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 =
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