Key Concepts of Radioactive Decay

Question 1

What is radioactive decay and how do you mathematically express it?

Answer 1

Question 2

What formula gives the decay constant λ?

Answer 2

Question 3

What formula relates activity A(t) and time?

Answer 3

Question 4

How can you quickly determine the number of half-lives passed?

Answer 4

Question 5

What formula do you use for total disintegrations?

Answer 5

Question 6

What formula relates half-life and the remaining activity?

Answer 6

Question 7

How do you identify a problem asking for total disintegrations?

Answer 7

Question 8

How is mean-life related to half-life?

Answer 8

Question 9

How do you break down a word problem involving radioactive decay?

Answer 9

Question 10

Example 3.1 (Half-Life and Activity)

I-125 has a half-life of 60 days and initial activity of 10 mCi. What is its activity after 30 days?

Answer 10

Question 11

Example 3.2 (Activity after Multiple Half-Lives)

A source has a half-life of 12 hours and an initial activity of 10 mCi. What is the activity after 3 days?

Answer 11

Question 12

Example 3.3 (Decay Rate and Half-Life)

Ir-192 decays at a rate of 0.94% per day. What is its half-life?

Answer 12

Question 13

Example 3.4 (Finding Half-Life)

A radioactive source has an initial activity of 10 mCi. After 3 days, its activity is 0.16 mCi. What is the half-life?

Answer 13

Question 14

Example 3.5 (Total Disintegrations)

A patient receives a permanent I-125 implant with an initial activity of 10 mCi and a half-life of 59.5 days. How many total disintegrations occur?

Question 15

Answer 15

This formula is derived from the exponential decay model, where the activity decreases with time, and it provides a way to calculate how much of the radioactive substance has decayed after a given period.

Question 16

A 4.0-mCi source with a 2.69-day half-life is implanted. The prescribed dose is 2.80 × 10^13 disintegrations. Find the time the source needs to be removed.

Answer 16