1. Half-Life
Half-life is the time required for half of a sample of a radioactive substance to disintegrate by radioactive decay. Atoms with shorter half-lives are more unstable. The half-life of an isotope is not affected by heat, pressure or any other physical means.

2. Half-life is used by scientists to predict the age of an object.
The isotope C-14 is used to date materials that were once living or came from living things.
C-14 has a half life of yrs. This means that after 5715 yrs, a 100 gram sample of C-14 will be half C-14 and half some other isotope. After yrs, the sample will be 25 g C-14 and 75 grams of some other isotope.

3. Half-life Problems
In many problems, you will be given the total (elapsed) time and the length of one half-life. You have to determine the number of half-lives before working the problem.
To find the number of half-lives divide the elapsed time by the length of one half-live.
Ex. If one half-life is 8 days, and 24 days have gone by, how many half-lives have occurred?

4. Half-life Problems Number of half-lives will be represented by n
Original mass of substance will be mi
Final mass of substance will be mf
Formula: mf = mi 2n

5. How much of a 100 g sample of Rn-222 is left after 15
How much of a 100 g sample of Rn-222 is left after 15.2 days if its half life is 3.8 days?
First find the number of half-lives that have occurred: Divide 15.2 days by 3.8 days to get the number of half lives:
Givens:
Hint:
n = number of half lives,
mi = original mass
mf = final mass

6. How much of a 100 g sample of Rn-222 is left after 15
How much of a 100 g sample of Rn-222 is left after 15.2 days if its half life is 3.8 days?
First find the number of half-lives that have occurred. Divide 15.2 days by 3.8 days to get the number of half lives: 4
Givens:
n = number of half lives =
mi = original mass =
mf = final mass =

7. How much of a 100 g sample of Rn-222 is left after 15
How much of a 100 g sample of Rn-222 is left after 15.2 days if its half life is 3.8 days?
First find the number of half-lives that have occurred. Divide 15.2 days by 3.8 days to get the number of half lives: 4
Givens:
n = 4
mi = 100 g
mf = ? mi
Formula mf = mf = 2n

8. 1. How much of a 100 g sample of Rn-222 is left after 15
1. How much of a 100 g sample of Rn-222 is left after 15.2 days if its half life is 3.8 days?
First find the number of half-lives that have occurred. Divide 15.2 days by 3.8 days to get the number of half lives: 4
Givens:
n = 4
mi = 100 g
mf = ? mi
Formula mf = mf = = = 2n
100 g 16
100 g 24

9. Givens: n = mi = mf = ? n = number of half lives, mi = original mass
2. How much of a 200 g sample of I-131 is left after 16 days if its half life is 8 days?
First find the number of half-lives that have occurred
Givens:
n =
mi =
mf = ?
Formula : mf =
n = number of half lives,
mi = original mass
mf = final mass

10. Givens: n = 2 mi = 200 mf = ? n = number of half lives,
2. How much of a 200 g sample of I-131 is left after 16 days if its half life is 8 days?
First find the number of half-lives that have occurred
Givens:
n = 2
mi = 200
mf = ?
Formula : mf = mf = =
n = number of half lives,
mi = original mass
mf = final mass mi 2n

11. Givens: n = 2 mi = 200g mf = ? n = number of half lives,
2. How much of a 200 g sample of I-131 is left after 16 days if its half life is 8 days?
First find the number of half-lives that have occurred
Givens:
n = 2
mi = 200g
mf = ?
Formula : mf = mf = =
n = number of half lives,
mi = original mass
mf = final mass mi 2n
200g 22
200g 4

12. To Find Original Amount
Rearrange the basic equation so that mi is by itself on one side of the equals sign.
mi = mf x 2n
3. The half life of Iodine-131 is 8 days. If after 24 days there are grams of Iodine-131 left. How much was in the original sample?
n =
mf =
mi =

13. To Find Original Amount
Rearrange the basic equation so that m is by itself on one side of the equals sign.
mi = mf x 2n
After 24 days there are grams of Iodine-131 left. How much was in the original sample?
n = 3
mf = g
mi = ?
mi = g x 23 =

14. 4. After 16 days there are 30. 0 grams of an isotope left
4. After 16 days there are grams of an isotope left. If its half-life is 4.0 days how much was in the original sample?

15. Sometimes you will be given the percent or fractional amount that remains or has decayed instead of the number of days.
To find the number of half lives multiply by ½ until you get the percent or fractional amount that remains
EX: If the problems says that 1/32 remains, multiply ½ x ½ x ½ x ½ x ½ until you get 1/32. The number of half lives will be 5.
Ex: If the problem says that 7/8 has decayed, you must determine that 1/8 remains, then multiply ½ x ½ x ½ until you get 1/8. The number of half-lives will be 3.

16. 5. Ra-226 has a half life of 1599 years
5. Ra-226 has a half life of years. How long would it take 15/16 of a Ra-226 sample to decay?
First determine how much remains: 16/16-15/16 = 1/16
Then determine number of half-lives by multiplying ½ by itself until you get 1/16.
½ x ½ x ½ x ½ = 1/16
Count the number of ½s, so 4 half-lives have gone by.
Multiply 4 x the half life of 1599 years:
4 x 1599 = 6396 years

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GCSE PHYSICS - What is Radiodating? - How can Radiodating be used to Calculate the Age of Rocks? - How can Potassium-40 be used to Date Rocks? - How can Uranium-238 be used to Date Rocks? - GCSE SCIENCE.