Half-Life
Nuclear Chemistry
What is Half-Life?
• The time it takes for half of a given amount of
a radioactive isotope to undergo decay.
Note:
The time for the 1st half life is
the same as the time for the
2nd half life …….
Same isotopes
1/2
1/4
QUESTION?
Does decay slow down, speed
up, or remain constant after
each half-life?
Half-life equal in time
1st Half-Life
2nd Half-Life
Decay slows down
If you have to eat ½ in the same amount of time
– you have to eat slower.
What is Half–Life Used For ?
• Tells the age of a fossil
– Carbon-14 Dating
How many years ago
did the volcano erupt?
6.25 % of
Carbon-14
FACT:
Carbon – 14 has a half-life of 5730 years
Half-Life
1
Amount of Carbon
1/2
2
½ x ½ = 1/4
3
4
1/4 x ½ = 1/8
1/8 x 1/2 = 1/16
%
.5 = 50%
.25 = 25%
.125 = 12.5%
. 0625 = 6.25%
4 x 5730 = 22,920 years
A rock with 25% of potassium-40 was analyzed.
How long ago was the rock formed?
1.25 billion years
Potassium – 40
half-life?
How many half-life does it
take to get 25% of
potassium-40?
Half-Life
Amount
%
1
1/2
.5 = 50%
2
½ x ½ = 1/4
.25 = 25%
2 x 1.25 billion years – 2.5 billions years
Ash from a fire pit was found to have 12.5 % as
much carbon – 14 as would be found in ash today.
How long ago was the ash formed?
5730 years
Carbon-14
half-life?
How many half-life does it
take to get 12.5% of
Carbon-14?
Half-Life
Amount
%
1
1/2
.5 = 50%
2
½ x ½ = 1/4
.25 = 25%
3
1/4 x ½ = 1/8
.125 = 12.5%
3 x 5730 years = 17, 190 years
The half-life of radon-22 is 3.8 days.
How much of a 100 g sample is left
after 15.2 days?
Half-Life
Amount Left
Number
Days
1
3.8
½ of 100 = 50 g
2
7.6
½ of 50 or ¼ of 100 = 25g
3
11.4
½ of 25 or 1/8 of 100 = 12.5g
4
15,.2
½ of 12.5 or 1/16 or 100 = 6.25g
100g
Notice:
Total number of days/ half-life days= number of halflives
Carbon-14 has a half-life of 5,730 years. If
a sample contains 70 mg originally, how
much is left after 17,190 years?
Half-Life
Number
Days
Amount Left
70g
1
5,730
½ of 70 = 35 mg
2
11,460
½ of 35 or ¼ of 70 = 17.5 mg
3
17,190
½ of 17.5 or 1/8 of 70 = 8.75 mg
Mathematical Formula:
Total number of days/ half-life days= number of half-lives
17190/5730 = 3
1/8 of original
1/8 x 70 = 8.75 mg