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Half-LifeNuclear Chemistry
What is Half-Life?• The time it takes for half of a given amount of
a radioactive isotope to undergo decay.
1st Half-Life = decay time to divide in half
2nd Half-Life = decay time to divide in half
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
Does decay slow down, speed up, or remain constant after
each half-life?
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.
QUESTION?
Half-life equal in time
What is Half–Life Used For ?• Tells the age of a fossil
– Carbon-14 Dating
6.25 % of Carbon-14
How many years ago did the volcano erupt?
Half-Life Amount of Carbon %
FACT:Carbon – 14 has a half-life of 5730 years
4 x 5730 = 22,920 years
1
2
344
1/2
½ x ½ = 1/4
1/4 x ½ = 1/81/8 x 1/2 = 1/16
.5 = 50%
.25 = 25%
.125 = 12.5%
. 0625 = 6.25%. 0625 = 6.25%
A rock with 25% of potassium-40 was analyzed. How long ago was the rock formed?
Potassium – 40 half-life?
1.25 billion years How many half-life does it take to get 25% of
potassium-40?
Half-Life Amount %
1
2
1/2 .5 = 50%
½ x ½ = 1/4 .25 = 25%2
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?
Carbon-14half-life?
5730 years How many half-life does it take to get 12.5% of
Carbon-14?
Half-Life Amount %
.125 = 12.5%
1
2
1/2 .5 = 50%
½ x ½ = 1/4 .25 = 25%
3 x 5730 years = 17, 190 years
3 1/4 x ½ = 1/83
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
Notice:Total number of days/ half-life days= number of
half-lives
1
2
3
4
3.8
7.6
11.4
15,.2
½ of 100 = 50 g
½ of 50 or ¼ of 100 = 25g
½ of 25 or 1/8 of 100 = 12.5g
½ of 12.5 or 1/16 or 100 = 6.25g
100g
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 Amount Left
Number Days
Mathematical Formula:Total number of days/ half-life days= number of half-lives
17190/5730 = 31/8 of original
1/8 x 70 = 8.75 mg
70g
1
2
3
5,730
11,460
17,190
½ of 70 = 35 mg
½ of 35 or ¼ of 70 = 17.5 mg
½ of 17.5 or 1/8 of 70 = 8.75 mg