CALCULATING HALF-LIFE
Aim: How can we measure how much
of a radioactive element decayed?
DO NOW: If we start with 4.5 grams of Radon222 and over a period of time we have 3.4
grams left over. What is the fraction remaining
of this sample?
3.4g / 4.5g =
What is half-life?
• The amount of time it takes for the
mass of a radioactive sample to
decay by half.
• Half-life is AMOUNT OF TIME
• Table N
EXAMPLE!!
Consider a 10 g sample of Au-198. (Table
N)
What decay mode does Au-198 have?
(3) Alpha decay!
What half-life does Au-198 have?
(4) 2.69 days
Let’s see Au-198
At 0 half-life or 0 days, there are 10 g
present.
After 1 half-life or 2.69 days, there are 5 g
remaining.
After 2 half-life or 5.38 (2 x 2.69) days, (5)
2.5grams remain.
After 3 half-life or 8.07 (3 x 2.69) days, (6)
1.25 grams remain.
Calculating Fraction Remaining…
What is a fraction?
THE RATIO BETWEEN A PART AND A
WHOLE.
…NOW I NEED 8 VOLUNTEERS 
Fraction Remaining
# of Half-Lives
Fraction Remaining
0
1
1
½
2
¼
3
1/8
4
1/16
5
1/32
Example 1
• If 1.00 gram of a 16.00 gram sample of sodium-25
remains unchanged after 237 seconds, what is
the fraction remaining?
Step 1: What was the mass of the original sample?
 16.00 gram
Step 2: What is the mass that is remaining after the
given period of time?
1.00 grams
Step 3: What is the fraction remaining?
 1/16
EXAMPLE 3
If 1.00 gram of a 16.00 gram sample of sodium-25
remains unchanged after 237 seconds, how many
half-lives have passed?
Step 1: What was the mass of the original sample?
16.00 grams
Step 2: What is the mass that is remaining after the
given period of time?
1.00 grams
Step 3: What is the fraction remaining?
1/16
Step 4: How many half-lives have passed?
4
Calculating total time
FORMULA:
# of half-lives x length of half-life = total time
Example 6
A sample of wood is found to contain 1/8 as much C-14 as
ipresent in the wood of a living tree. How old is the
tree?
Step 1: Figure out the fraction remaining.
 1/8
Step 2: Figure out the number of half- lives passed.
3
Step 3: Figure out the length of one half-life (Table N or
given in the problem).

Step 4: Multiply the number of half-lives by the length of
one half-life.
3x =