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