RADIOACTIVE DECAY

Radioactive Decay

#	Isotope	Decay-product	Disintegration Formula	Half-life
1	Bismuth-210	Polonium-210	Bi²¹⁰ à Po²¹⁰	5.0 days
2	Carbon-14	Nitrogen-14	C¹⁴ à N¹⁴	5,700 years
3	Polonium-218	Lead-214	Po²¹⁴à Pb²¹⁴	2 x 10^-4 seconds
4	Potassium-40	Argon-40 & Calcium-40	K⁴⁰ à Ar⁴⁰ & Ca⁴⁰	1.3 x 10⁹ years
5	Radium-226	Radon-222	Ra²²⁶à Rn²²²	1.62 x 10³ years
6	Rubidium-87	Strontium-87	Rb⁸⁷ à Sr⁸⁷	4.9 x 10¹⁰ years
7	Thorium-230	Radium-226	Th²³⁰à Ra²²⁶	8.0 x 10⁴ years
8	Uranium-238	Lead-206	U²³⁸ à Pb²⁰⁶	4.5 x 10⁹ years
9	Imaginatium-123	Fantasium-123	Im¹²³ à Fa¹²³	1 second
10	Earthsciencium-204	Studentogen-199	Ea²⁰⁴ à St¹⁹⁹	10 minutes

On a separate piece of paper, answer the seven questions, draw the chart below and fill it in all of the information for each isotope in the table above (all 10 of them). If it helps, draw the block to represent the sample. Then, answer the additional questions.

1. Note: 20 gram sample.

1. What is the radioactive isotope? Bismuth-210	5. What is the decay-product? Polonium-210
2. What is its chemical symbol of the isotope? Bi²¹⁰	6. What is its chemical symbol of the decay-product? Po²¹⁰
3. What is its atomic mass of the isotope? 210	7. What is its atomic mass of the decay-product? 210
4. How much time does one half-life take? (Include the units.) 5.0 days

Number of Half-lives	Percentage of Radioactive Isotope	Percentage of Decay-product	Amount of Time Passed (in _Days_)	Amount of Isotope	Amount of Decay-Product	Isotope Fraction	Decay-Product Ratio*
0	100%	0%	0	20	0	1/1	0:1
1	50%	50%	5.0	10	10	1/2	1:2
2	25%	75%	10.0	5	15	1/4	3:4
3	12.5%	87.5%	15.0	2.5	17.5	1/8	7:8
4	6.25%	93.75%	20.0	1.25	18.75	1/16	15:16
5	3.125%	96.875%	25.0	0.625	19.375	1/32	31:32
6	1.5625%	98.4375%	30.0	0.3125	19.6875	1/64	63:64
7	0.78125%	99.21875%	35.0	0.15625	19.84375	1/128	127:128
8	0.390625%	99.609375%	40.0	0.078125	19.921875	1/256	255:256

* The ratio between decay-product compared to the whole sample.

2. Note: 10 gram sample.

1. What is the radioactive isotope? Carbon-14	5. What is the decay-product? Nitrogen-14
2. What is its chemical symbol of the isotope? C¹⁴	6. What is its chemical symbol of the decay-product? N¹⁴
3. What is its atomic mass of the isotope? 14	7. What is its atomic mass of the decay-product? 14
4. How much time does one half-life take? (Include the units.) 5,700 years

Number of Half-lives	Percentage of Radioactive Isotope	Percentage of Decay-product	Amount of Time Passed (in _years_)	Amount of Isotope	Amount of Decay-Product	Isotope Fraction	Decay-Product Ratio*
0	100%	0%	0	10	0	1/1	0:1
1	50%	50%	5,700	5	5	1/2	1:2
2	25%	75%	11,400	2.5	7.5	1/4	3:4
3	12.5%	87.5%	17,100	1.25	8.75	1/8	7:8
4	6.25%	93.75%	22,800	0.625	9.375	1/16	15:16
5	3.125%	96.875%	28,500	0.3125	9.6875	1/32	31:32
6	1.5625%	98.4375%	34,200	0.15625	9.84375	1/64	63:64
7	0.78125%	99.21875%	39,900	0.078125	9.921875	1/128	127:128
8	0.390625%	99.609375%	45,600	0.0390625	9.9609375	1/256	255:256

* The ratio between decay-product compared to the whole sample.

3. Note: 50 gram sample

1. What is the radioactive isotope? Polonium-218	5. What is the decay-product? Lead-214
2. What is its chemical symbol of the isotope? Po²¹⁴	6. What is its chemical symbol of the decay-product? Pb²¹⁴
3. What is its atomic mass of the isotope? 218	7. What is its atomic mass of the decay-product? 214
4. How much time does one half-life take? (Include the units.) 2 x 10^-4 seconds

Number of Half-lives	Percentage of Radioactive Isotope	Percentage of Decay-product	Amount of Time Passed (in seconds)	Amount of Isotope	Amount of Decay-Product	Isotope Fraction	Decay-Product Ratio**
0	100%	0%	0	50	0	1/1	0:1
1	50%	50%	2 x 10^-4	25	25	1/2	1:1
2	25%	75%	4 x 10^-4	12.5	37.5	1/4	3:1
3	12.5%	87.5%	6 x 10^-4	6.25	43.75	1/8	7:1
4	6.25%	93.75%	8 x 10^-4	3.125	46.875	1/16	15:1
5	3.125%	96.875%	10 x 10^-4	1.5625	48.4375	1/32	31:1
6	1.5625%	98.4375%	12 x 10^-4	0.78125	49.21875	1/64	63:1
7	0.78125%	99.21875%	14 x 10^-4	0.390625	49.609375	1/128	127:1
8	0.390625%	99.609375%	16 x 10^-4	0.1953125	49.8046875	1/256	255:1

** Ratio between decay-product and isotope.

4. Note: 100 gram sample. Also note: This is a tough one!!! For this one, we will pretend that both decay-products are perfectly equal.

1. What is the radioactive isotope? Potassium-40	5. What is the decay-product? Argon-40 & Calcium-40
2. What is its chemical symbol of the isotope? K⁴⁰	6. What is its chemical symbols of the decay-products? Ar⁴⁰ & Ca⁴⁰
3. What is its atomic mass of the isotope? 40	7. What is its atomic mass of the decay-product? 40 (for both)
4. How much time does one half-life take? (Include the units.) 1.3 x 10⁹ years

Number of Half-lives	Percentage of Radioactive Isotope	Percentage of Decay-product		Amount of Time Passed (in _years_)	Amount of Isotope	Amount of Decay-Product (of each)	Isotope Fraction
Number of Half-lives	Percentage of Radioactive Isotope	Ca⁴⁰	Ar⁴⁰	Amount of Time Passed (in _years_)	Amount of Isotope	Amount of Decay-Product (of each)	Isotope Fraction
0	100%	0%	0%	0	100	0	1/1
1	50%	0.25%	0.25%	1.3 x 10⁹	50	0.25	1/2
2	25%	0.375%	0.375%	2.6 x 10⁹	25	0.375	1/4
3	12.5%	0.4375%	0.4375%	3.9 x 10⁹	12.5	0.4375	1/8
4	6.25%	0.46875%	0.46875%	5.2 x 10⁹	6.25	0.46875	1/16
5	3.125%	0.484375%	0.484375%	6.5 x 10⁹	3.125	0.484375	1/32
6	1.5625%	0.4921875%	0.4921875%	7.8 x 10⁹	1.5625	0.4921875	1/64
7	0.78125%	0.49609375%	0.49609375%	9.1 x 10⁹	0.78125	0.49609375	1/128
8	0.390625%	0.498046875%	0.498046875%	10.4 x 10⁹	0.390625	0.498046875	1/256

5. Note: 100 grams of sample.

1. What is the radioactive isotope? Radium-226	5. What is the decay-product? Radon-222
2. What is its chemical symbol of the isotope? Ra²²⁶	6. What is its chemical symbol of the decay-product? Rn²²²
3. What is its atomic mass of the isotope? 226	7. What is its atomic mass of the decay-product? 222
4. How much time does one half-life take? (Include the units.) 1.62 x 10³ years

Number of Half-lives	Percentage of Radioactive Isotope	Percentage of Decay-product	Amount of Time Passed (in _years_)	Amount of Isotope	Amount of Decay-Product	Isotope Fraction	Decay-Product Ratio**
0	100%	0%	0	100	0	1/1	0:1
1	50%	50%	1.62 x 10³	50	50	1/2	1:1
2	25%	75%	3.24 x 10³	25	75	1/4	3:1
3	12.5%	87.5%	4.86 x 10³	12.5	87.5	1/8	7:1
4	6.25%	93.75%	6.48 x 10³	6.25	93.75	1/16	15:1
5	3.125%	96.875%	8.1 x 10³	3.125	96.875	1/32	31:1
6	1.5625%	98.4375%	9.72 x 10³	1.5625	98.4375	1/64	63:1
7	0.78125%	99.21875%	11.34 x 10³	0.78125	99.21875	1/128	127:1
8	0.390625%	99.609375%	12.96 x 10³	0.390625	99.609375	1/256	255:1

** Ratio between decay-product and isotope.

6. Note: 1,000 grams of sample.

1. What is the radioactive isotope? Rubidium-87	5. What is the decay-product? Strontium-87
2. What is its chemical symbol of the isotope? Rb⁸⁷	6. What is its chemical symbol of the decay-product? Rn²²²
3. What is its atomic mass of the isotope? 87	7. What is its atomic mass of the decay-product? 87
4. How much time does one half-life take? (Include the units.) 4.9 x 10¹⁰ years

Number of Half-lives	Percentage of Radioactive Isotope	Percentage of Decay-product	Amount of Time Passed (in _years_)	Amount of Isotope	Amount of Decay-Product	Isotope Fraction	Isotope Ratio***
0	100%	0%	0	1,000	0	1/1	1:1
1	50%	50%	4.9 x 10¹⁰	500	500	1/2	1:2
2	25%	75%	9.8 x 10¹⁰	250	750	1/4	1:4
3	12.5%	87.5%	14.7 x 10¹⁰	125	875	1/8	1:8
4	6.25%	93.75%	19.6 x 10¹⁰	62.5	937.5	1/16	1:16
5	3.125%	96.875%	24.5 x 10¹⁰	31.25	968.75	1/32	1:32
6	1.5625%	98.4375%	29.4 x 10¹⁰	15.625	984.375	1/64	1:64
7	0.78125%	99.21875%	34.3 x 10¹⁰	7.8125	992.1875	1/128	1:128
8	0.390625%	99.609375%	39.2 x 10¹⁰	3.90625	996.09375	1/256	1:256

*** Ratio between isotope and the whole sample.

7. 200 grams of sample.

1. What is the radioactive isotope? Thorium-230	5. What is the decay-product? Radium-226
2. What is its chemical symbol of the isotope? Th²³⁰	6. What is its chemical symbol of the decay-product? Ra²²⁶
3. What is its atomic mass of the isotope? 230	7. What is its atomic mass of the decay-product? 226
4. How much time does one half-life take? (Include the units.) 8.0 x 10⁴ years

Number of Half-lives	Percentage of Radioactive Isotope	Percentage of Decay-product	Amount of Time Passed (in _years_)	Amount of Isotope	Amount of Decay-Product	Isotope Fraction	Isotope Ratio***
0	100%	0%	0	200	0	1/1	1:1
1	50%	50%	8	100	100	1/2	1:2
2	25%	75%	16	50	150	1/4	1:4
3	12.5%	87.5%	24	25	175	1/8	1:8
4	6.25%	93.75%	32	12.5	187.5	1/16	1:16
5	3.125%	96.875%	40	6.25	193.8	1/32	1:32
6	1.5625%	98.4375%	48	3.125	196.9	1/64	1:64
7	0.78125%	99.21875%	56	1.563	198.4	1/128	1:128
8	0.390625%	99.609375%	64	0.781	199.2	1/256	1:256

*** Ratio between isotope and the whole sample.

8. 50 gram sample.

1. What is the radioactive isotope? Uranium-238	5. What is the decay-product? Lead-206
2. What is its chemical symbol of the isotope? U²³⁸	6. What is its chemical symbol of the decay-product? Pb²⁰⁶
3. What is its atomic mass of the isotope? 238	7. What is its atomic mass of the decay-product? 206
4. How much time does one half-life take? (Include the units.) 4.5 x 10⁹ years

Number of Half-lives	Percentage of Radioactive Isotope	Percentage of Decay-product	Amount of Time Passed (in _years_)	Amount of Isotope	Amount of Decay-Product	Isotope Fraction	Isotope Ratio****
0	100%	0%	0	50	0	1/1	1:0
1	50%	50%	4.5	25	25	1/2	1:1
2	25%	75%	9	12.5	37.5	1/4	1:3
3	12.5%	87.5%	13.5	6.25	43.75	1/8	1:7
4	6.25%	93.75%	18	3.125	46.88	1/16	1:15
5	3.125%	96.875%	22.5	1.563	48.44	1/32	1:31
6	1.5625%	98.4375%	27	0.781	49.22	1/64	1:63
7	0.78125%	99.21875%	31.5	0.391	49.61	1/128	1:127
8	0.390625%	99.609375%	36	0.195	49.8	1/256	1:255

**** Ratio of isotope to decay-product.

9. 123 gram sample.

1. What is the radioactive isotope? Imaginatium-123	5. What is the decay-product? Fantasium-123
2. What is its chemical symbol of the isotope? Im¹²³	6. What is its chemical symbol of the decay-product? Fa¹²³
3. What is its atomic mass of the isotope? 123	7. What is its atomic mass of the decay-product? 123
4. How much time does one half-life take? (Include the units.) 1 second

Number of Half-lives	Percentage of Radioactive Isotope	Percentage of Decay-product	Amount of Time Passed (in seconds)	Amount of Isotope	Amount of Decay-Product	Isotope Fraction
0	100%	0%	0	123	0	1/1
1	50%	50%	1	61.5	61.5	1/2
2	25%	75%	2	30.75	92.25	1/4
3	12.5%	87.5%	3	15.38	107.6	1/8
4	6.25%	93.75%	4	7.688	115.3	1/16
5	3.125%	96.875%	5	3.844	119.2	1/32
6	1.5625%	98.4375%	6	1.922	121.1	1/64
7	0.78125%	99.21875%	7	0.961	122	1/128
8	0.390625%	99.609375%	8	0.48	122.5	1/256

10. 1 gram sample.

1. What is the radioactive isotope? Earthsciencium-204	5. What is the decay-product? Studentogen-199
2. What is its chemical symbol of the isotope? Ea²⁰⁴	6. What is its chemical symbol of the decay-product? St¹⁹⁹
3. What is its atomic mass of the isotope? 204	7. What is its atomic mass of the decay-product? 199
4. How much time does one half-life take? (Include the units.) 10 minutes

Number of Half-lives	Percentage of Radioactive Isotope	Percentage of Decay-product	Amount of Time Passed (in minutes)	Amount of Isotope	Amount of Decay-Product	Isotope Fraction
0	100%	0%	0	1	0	1/1
1	50%	50%	10	0.5	0.5	1/2
2	25%	75%	20	0.25	0.75	1/4
3	12.5%	87.5%	30	0.125	0.875	1/8
4	6.25%	93.75%	40	0.063	0.938	1/16
5	3.125%	96.875%	50	0.031	0.969	1/32
6	1.5625%	98.4375%	60	0.016	0.984	1/64
7	0.78125%	99.21875%	70	0.008	0.992	1/128
8	0.390625%	99.609375%	80	0.004	0.996	1/256

Additional questions:

1. What is a half-life? (What does it mean?) The amount of time that it takes for half of the radioactive isotope to breakdown into its decay-product.

2. What is an isotope? An unstable atom with too many or too few neutrons in its nucleus (compared to “normal” versions of the same atom).

3. What is the decay-product? This is the stable atom that the isotope becomes after it undergoes radioactive decay.

4. When filling the charts for each isotope, what information changes from chart to chart? The quantities of the samples (how many grams), the type of ratio that I was asking for, and (MOST IMPORTANTLY) THE AMOUNT OF TIME THAT IT TAKES FOR ONE HALF-LIFE TO OCCUR FOR EACH TYPE OF ISOTOPE.

5. Does the amount of time for each half-life change throughout the decay of any one isotope? No. The amount of time needed for one half-life remains the same for the isotope. It only changes when you have a different isotope.

6. What percentage of the sample do you have before any half-lives occur? 100%

7. What percentage of the sample should you have after one million half-lives have passed? 100%. When adding the percentage of the remaining isotope to the amount of decay-product you should always have the answer of 100%.

8. How do you calculate the percentage of the isotope and the percentage of the decay-product? The percentage of isotope starts at 100% and is divided in half for each half-life. The decay-product can be calculated in two ways: the easiest way is to subtract the amount of remaining isotope from 100%. The other way is to take the other half of the isotope and add it to the decay-product.

Radioactive Decay

Disintegration Formula

5

Radium-226