Question

The decay of the isotope iodine-131 is first-order with a rate constant of 0.138 d−1. All radioactive decay is first order. How many days will it take for 90% of the isotope to decay to Xe-131?

Answer 1

Answer:

16.7 days

Explanation:

We are given;

A radioactive isotope Iodine-131`

The decay rate is 0.138 d⁻¹

The percent decayed is 90%

We are suppose to calculate the number of days for the decay.

• Using the formula;

$In(\frac{[A_{0}]}{[A]})=kt$

Where, $[A_{0}]$ is the initial concentration and $[A]$ is the new concentration.

• Rearranging the formula;

$t=In(\frac{[A_{0}]}{[A]})/k$

Assuming the initial concentration is x, then the final concentration after 90% decay will be 0.10x

Therefore;

$t=In(\frac{[x]}{[0.10x]})(\frac{1}{0.138})$

$t=In(\frac{[1]}{[0.10]})(\frac{1}{0.138})$

$t=In(10.0)(\frac{1}{0.138})$

$t=(2.3026)(\frac{1}{0.138})$

$t=16.685$

Time = 16.7 days

Therefore, it will take 16.7 days for 90% of I-131 to decay to Xe-131