Geology
Mrs. Benya
Name:
Date:
Half-life and Radioactive Decay Problems
Radioactive Decay Example:
If a radioactive isotope of Uranium (atomic number 92, mass number 238) emits 4 alpha
particles and 2 beta particles during the course of radioactive decay, what are the atomic
number and mass number of the daughter product?
Answer:
U 92 - [ 4 (2α ) – 2 ( -1β)]
238
4
0
92 – 8 + 2 = 86 (atomic #) (Radon)
238 – 16 222 (mass # )
1. If a radioactive isotope of Radium (atomic number 88, mass number 226) emits 5 alpha
particles and 3 beta particles during the course of radioactive decay, what are the atomic
number and mass number of the daughter product?
2. If a radioactive isotope of Lead (atomic number 82, mass number 214) emits 2 alpha
particles and 4 beta particles during the course of radioactive decay, what are the atomic
number and mass number of the daughter product?
3. If a radioactive isotope of Radon (atomic number 86, mass number 222) emits 4 alpha
particles and 4 beta particles during the course of radioactive decay, what are the atomic
number and mass number of the daughter product?
4. If a radioactive isotope of Uranium (atomic number 92, mass number 234) emits 5
alpha particles and 1 beta particle during the course of radioactive decay, what are the
atomic number and mass number of the daughter product?
Half life example A: Uranium 235 has a half life of 713 million years. If you begin with
10 grams of U235 , how much will you have after 1 half life?, 2 half lives, 3, 4?
# of ½ lives grams parent remaining
0
10
1
5
2
2.5
3
1.25
4
0.675
grams daughter formed
0
5
7.5
8.75
9.335
Half life example B: You find a rock with 7/8th daughter & 1/8th parent. If the parent
material has a half-life of 50,000 years, how old is the rock?
First find how many ½ lives have past using chart:
Parent Daughter # ½ lives Ratio P:D % P:D
1
0
0
1:0
100%: 0%
½
½
1
1:1
50% : 50%
¼
¾
2
1:3
25% : 75%
1/8
7/8
3
1:7 12.5% : 87.5%
Then multiply # of half lives x length of half life
(3 ½ lives) x 50,000 years = 150,000 years old
5. Radium 226 has a half life of 1600 years. If you begin with a sample of 25 g of Ra88,
how much will you have after 1 half life, 2 half lives, 3, 4?
6. You find a sample that has 1/16th Carbon 14 and 15/16th Carbon 12. If the half life of
Carbon 14 is 5730 years, how old is the sample?
7. You find a sample of rock that contains 10 g of lead 210 (half life equals 20.4 years)
and 30 g of lead 206 (stable daughter product). How old is the sample?