Question

The half-life of bismuth-210, 210bi, is 5 days. (a) if a sample has a mass of 184 mg, find the amount remaining after 15 days.

Answer 1

Answer:- 23.0 mg

Solution:- Radioactive decay obeys first order kinetics and the first order kinetics equation is:

$lnN=-kt+lnN_0$

where, $N_0$ is the initial amount of radioactive substance and N is it's amount after time t. k is the decay constant.

From given information, Original amount, $N_0$ of the radioactive substance is 184 mg and we are asked to calculate the amount N after 15 days. It means, t = 15 days

Half life is given as 5 days. From the half life, we could calculate the decay constant k using the equation:

$k=\frac{0.693}{t_1_/_2}$

where, $t_1_/_2$ is the symbol for half life. let's plug in the value of half like to calculate k:

$k=\frac{0.693}{5days}$

$k=0.1386day^-^1$

Let's plug in the values in the first order kinetics equation and solve it for N:

$lnN=-0.1386day^-^1(15days)+ln184mg$

$lnN=-2.079+5.215$

lnN = 3.136

$N=e^3^.^1^3^6$

N = 23.0 mg

So, 23.0 mg of Bi-210 would be remaining after 15 days.