Understanding Half Life: A Worksheet Answer Key

How long does it take a 100.00g sample of As-81 to decay to 6.25g?

The half life of As-81 is 33 seconds;

6.25 g = 100 × (1/2)^n, where n is the number of half lives

(1/2)^n = 0.0625 n = 4

Thus, the time taken = 33 ×4 = 132 seconds

Therefore, it takes 132 seconds or 2 mins 12 seconds for it to decay to 6.25 g.

Answer: 132 seconds (2 Minutes 12 seconds)

Explanation: Half life is basically the time it takes for a compound to decay to half of its original mass. In this problem, the compound is As. The half life of As-81 is 33 seconds. This means it takes 33 seconds for 100 g of As-81 to decay to 50g. The question, however, is to find the time it takes for it to decay to 6.25g. We find how many half lives it would take:

• 100 --> 50 (First half life)
• 50 --> 25 (Second half life)
• 25 --> 12.5 (Third half life)
• 12.5 --> 6.25 (Fourth half life)

This means the total time is 4 * 33 (Half life) = 132 seconds (2 Minutes 12 seconds).

half life worksheet answer key 1. How long does it take a 100.00g sample of As-81 to decay to 6.25g?

The time it takes for a 100.00g sample of As-81 to decay to 6.25g is 132 seconds or 2 minutes 12 seconds.