Half-Lives
Question of the Day
Question: How are the two kinds of dating
(aging) similar? Different?
Answer: … … …
Turn In:
-What’s Up
-Computer Lab: Rocks & Minerals
-Current Event Article, Summary, & Evaluation
(staple together)
Half- Life
Some minerals contain radioactive
elements.
 The rate at which these elements decay
(turn into other elements) can help us
determine the absolute age of the rock
that contains that mineral.
 Some examples


Uranium, Radium, Plutonium
Transmutation
 Transmutation-
a radioactive
element changing (decaying) into
a another substance
 dependent on HALF-LIFE
 HALF-LIFE the time it takes for
half of a radioactive sample to
decay (turn into something else)
Half-Life
 Half-Life
times can vary,
depending upon the radioactive
element, from a few fractions of
a second to several million years
Half-Life
Original Amount
Fraction = 1/1
After One Half-Life
Fraction = 1/2
After two half-lives
Fraction = 1/4
What fraction of the original population would be left after
3 half-lives?
After 4?
After 5?
1/8
1/16
1/32
Why is this important?
How long it takes for certain elements
to decay
 Can help us with absolute dating
 Helps scientists estimate the ages of
rocks and fossils

Solving Half-Life Problems

Every half-life problem will ask one of
the following:
Time
 Fraction
 Sample Size
 Number of half-lives

Table for Solving Half-Life Problems
# of HalfLives
Fraction
0
1/1
1
1/2
2
1/4
3
1/8
4
1/16
Always the Same
Time
Sample
Changes Based upon Problem
For each problem
 Determine
what is being asked (what
is the question asking)
 Draw a picture of the amount of
original sample left after radioactive
decay (if necessary)
 Fill in the chart using the information
from the problem
 Use your completed chart to solve the
problem
Let’s try some…
Sample Problem#1

A sample takes 0.05 seconds to decay 1
half-life
a. How many half-lives will have passed
after 0.25 seconds?
b. What fraction of the original sample
will be left after this time (0.25
seconds)?
c. If the original sample is 10 grams,
how many grams are left after 0.25
seconds?
Let’s try some…
Sample Problem#1

A sample takes 0.05 seconds to decay 1
half-life
a. How many half-lives will have passed
after 0.25 seconds?

STEP 1- fill in the top row of your
sample #1 chart in your notes
Sample Problem #1
# of Half
Lives
Fraction
(Undecayed)
Time
Sample
Let’s try some…
Sample Problem#1

A sample takes 0.05 seconds to decay 1
half-life
a. How many half-lives will have passed
after 0.25 seconds?
STEP 1- fill in the top row of your sample
#1 chart in your notes
 STEP 2- fill in the first two columns of
your chart in your notes

Sample Problem #1
# of Half
Lives
Fraction
(Undecayed)
0
1/1
1
1/2
2
1/4
3
1/8
4
1/16
5
1/32
Time
Sample
Let’s try some…
Sample Problem#1

A sample takes 0.05 seconds to decay 1
half-life
a. How many half-lives will have passed
after 0.25 seconds?
STEP 1- fill in the top row of your sample
#1 chart in your notes
 STEP 2- fill in the first two columns of your
chart in your notes
 STEP 3- fill in the “Time” column in
your chart using the information from
the problem

Sample Problem #1
# of Half
Lives
Fraction
(Undecayed)
Time
0
1/1
0 sec
1
1/2
0.05 sec
2
1/4
0.10 sec
3
1/8
0.15 sec
4
1/16
0.20 sec
5
1/32
0.25 sec
Sample
Let’s try some…
Sample Problem#1

A sample takes 0.05 seconds to decay 1
half-life
a. How many half-lives will have passed
after 0.25 seconds?

Determine your solution from the chart:

5 half- lives
Let’s try some…
Sample Problem#1

b. What fraction of the original sample
will be left after this time (0.25
seconds)?

Determine your solution from the chart:
Sample Problem #1
# of Half
Lives
Fraction
(Undecayed)
Time
0
1/1
0 sec
1
1/2
0.05 sec
2
1/4
0.10 sec
3
1/8
0.15 sec
4
1/16
0.20 sec
5
1/32
0.25 sec
Sample
Let’s try some…
Sample Problem#1

b. What fraction of the original sample
will be left after this time (0.25
seconds)?

Determine your solution from the chart:

1/32 of the original sample
Let’s try some…
Sample Problem#1

c. If the original sample is 10 grams,
how many grams are left after 0.25
seconds?
Complete the final column of your chart
starting with 10 grams at 0 half-lives
 Divide each number by 2 to fill in the next
row

Sample Problem #1
# of Half
Lives
Fraction
(Undecayed)
Time
Sample
0
1/1
0 sec
10 grams
1
1/2
0.05 sec
5 grams
2
1/4
0.10 sec
2.5 grams
3
1/8
0.15 sec
1.25 grams
4
1/16
0.20 sec
0.625 grams
5
1/32
0.25 sec
0.3125
grams
Let’s try some…
Sample Problem#1

c. If the original sample is 10 grams,
how many grams are left after 0.25
seconds?

Determine your solution using the
chart:

0.3125 grams
Sample Problem #2

If it takes a sample 12 hours to go
through 4 half-lives, how long is each
half-life?
Divide the amount of time by the number of
half-lives that have passed
12 hours ÷

4 hours =
3 hours
# of Half
Lives
Fraction
0
1/1
1
1/2
2
1/4
3
1/8
4
1/16
5
1/32
Time
Sample