Question

Krypton consists of several radioactive isotopes, some ofwhich are listed in the following table.

Which of these isotopes is most stable, and which isotope is “hottest”? How long does it take for 87.5% of each isotope to decay?

Short answer

Longest half-life = ⁸¹Kr =$2.1\times {10}^5$ years

Hottest =⁷³Kr = 27 seconds

Time taken to decay 87.5% of each isotope is given below.

81 sec

34.5 mins

44.4 hours

$6.3\times {10}^5$years

Step-by-step solution

Determining the most stable and hottest isotopes

The one with the longest half-life is the most stable isotope.

From the table given above, we know that,

⁸¹Kr = 2.1 × 10⁵ years

The one with the shortest half-life is the one with the hottest half-life.

So, the required isotope is:

⁷³Kr = 27 seconds

Calculating the amount of time takes for 87.5% of each isotope to decay 

• Half-life = 100/2 = 50 percent decay
• Half-life = 50/2 = 25 percent decay
• Half-life = 25/2 = 17.5 percent decay

To modify the question, we need to find the time it takes for 3 half-lives to decay.

Representation of 3 half-lives

Representation of 3 half-lives

So, the complete table is:

Isotope	Half-life	Time taken to decay 87.5% of each isotope
Kr- 73	27 sec × 3	81 sec
Kr- 74	11.5 min × 3	34.5 mins
Kr- 76	14.8 hours × 3	44.4 hours
Kr- 81	× 3	years