Question

A radioactive isotope of the element potassium decays to produce argon. If the ratio of argon to potassium is found to be 31:1, how many half-lives have occurred?

Answer 1

Answer:

Explanation:

Argon to potassium ratio after 1 half life = 1:1

After 2 half lives = 75/25= 3:1

After 3 half lives = 87.5/12.5= 7:1

After 4 half lives = 93.75/6.25 = 15:1

After 5 half lives = 96.875/3.125 = 31/1

Answer 2

For a radioactive isotope of the element potassium decays in a ratio of 31:1 to produce argon, total 5 half-lives have occurred.

What is half-lives?

Half lives is the time interval which is need to decay the atomic nuclei of a radioactive sample.

A radioactive isotope of the element potassium decays to produce argon.

The ratio of argon to potassium, found to be 31:1. We have to reach at the 31:1 by the half lives.

The argon-potassium ratio after the first half life is 1:1. Now the arogon is added. Thus, the ratio become after two half lives is,

$r=\dfrac{75}{25}\\r=\dfrac{3}{1}$

Similarly, for the third half lives,

$r=\dfrac{87.5}{12.5}=\dfrac{7}{1}$

For the fourth half lives,

$r=\dfrac{93.75}{6.25}=\dfrac{15}{1}$

After fifth half lives the ratio become,

$r=\dfrac{96.875}{3.125}=\dfrac{31}{1}$

Hence, for a radioactive isotope of the element potassium decays in a ratio of 31:1 to produce argon, total 5 half-lives have occurred.

Learn more about the half lives here;

https://brainly.com/question/2320811