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Half Life Calculations 2019.notebook
1
December 18, 2019
May 2212:14 PM
Halflife Calculations
Aim: Halflife calculations for radioisotopes
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The halflife of a radioisotope is the time it takes for half of the substance to fully decay until stable.
The halflife of the metastable Tc99m is six hours.
If my daughter is dosed with 100 mg of the isotope, how many hours will it take for only 1.5625 mg to remain?
Half-life period= 6 hours time= ?initial amount= 100 mg final amount= 1.5625 mg
amount 100 50 25 12.5 6.25 3.125 1.5625
# of decays 0 1 2 3 4 5 6
6 decays x 6 hours = 36 hours passed
Half Life Calculations 2019.notebook
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December 18, 2019
May 2212:16 PM
Definition
Half‐life: the time it takes for 1/2 of the radioisotope sample to decay until stable.
The half‐life is found on Table N.
May 2212:18 PM
5 variables for ALL half‐life problems:• Half‐life • Time lapsed• # of decays (1/2 lives)
# of decays = time lapsed half‐life
Initial and final amounts are linked to the # of 1/2
lives in a decay table.
Decay Table:
• Initial amount• Final amount
amount initial 1/2 1/4 1/8 1/16 amt initial amt initial amt initial amt inital amt
# of decays 0 1 2 3 4 (1/2 lives)
always start time and # 1/2 lives at
zero
Half Life Calculations 2019.notebook
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December 18, 2019
May 2212:18 PM
1) A 62 gram sample of Fe53 decays for 34.04 minutes. What mass of iron remains?
Halflife Problems
May 2212:18 PM
1) A 62 gram sample of Fe53 decays for 34.04 minutes. What mass of iron remains?
Halflife Problems
• Halflife period• # of decays• Time lapsed• Initial amount• Final amount
Half-life period= 8.51 min (Table N)# decays= find using time and HLPtime= 34.04 mininitial amount= 62 gfinal amount= solve for # decays= time = 34.04 min = 4 decays
HLP 8.51 min
amount 62 g 31 g 15.5 g 7.75 g 3.875 g
# of decays 0 1 2 3 4 (1/2 lives)
3.875 g remains after 34.04 min (4 decays)
Half Life Calculations 2019.notebook
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December 18, 2019
May 2212:18 PM
Solving Halflife Problems
2) Iodine131 is used in thyroid scans. What fraction of the sample remains after 24.063 days?
May 2212:18 PM
Solving Halflife Problems
2) Iodine131 is used in thyroid scans. What fraction of the sample remains after 24.063 days?
Half-life period= 8.021 days (Table N)time= 24.063 days# decays= time/HLP= 24.063 days/8.021 days= 3 decaysinitial amount= 1 <-- always start as 1 for initial amount when finding the fraction remaining. A whole number fraction always equals 1.final amount= ?? solve for
amount 1 1/2 1/4 1/8
# of decays 0 1 2 3 (1/2 lives)
1/8 remains after 24.063 days (3 decays)
Half Life Calculations 2019.notebook
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December 18, 2019
May 2212:18 PM
Solving Halflife Problems3) A radioisotope has a halflife of 8.5 minutes. After 25.5 min 10 grams remain. What was the initial amount?
May 2212:18 PM
Solving Halflife Problems
Half-life period= 8.5 min (given in problem)time= 25.5 min# decays= time/HLP= 25.5 min/8.5 min= 3 decaysinitial amount= ?? solve forfinal amount= 10 g
80 g was the initial amount before the sample decayed
3) A radioisotope has a halflife of 8.5 minutes. After 25.5 min 10 grams remain. What was the initial amount?
amount 80g 40g 20g 10g
# of decays 0 1 2 3(1/2 lives)
You need to go backwards using the decay table to find the INITIAL amount you start with at 0 decays.
Half Life Calculations 2019.notebook
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December 18, 2019
May 2212:18 PM
Solving Halflife Problems4) A radioisotope, I131 has decayed to 12 grams after 5 halflives. How much time has lapsed?
5) A radioisotope decayed to 1/16 its original amount in 25 hours. What is the halflife?
May 2212:18 PM
Solving Halflife Problems
6) A scientist is working with a 100.0 g sample of Co60. How many decays did it go through after 26.36 years?
Half Life Calculations 2019.notebook
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December 18, 2019
May 2212:18 PM
Solving Halflife Problems
7) A 200 gram sample of Cr51 is an unstable isotope with a halflife of 28 days. What mass of a sample of Cr51 will remain after 84 period of days?
May 2212:18 PM
8. Cr51 is an unstable isotope with a halflife of 28 days. What fraction of a sample of Cr51 will remain after 84 days?
9. Cr51 is an unstable isotope with a halflife of 28 days. What percentage of a sample of Cr51 will remain after 84 days?
Solving Halflife Problems
Half Life Calculations 2019.notebook
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December 18, 2019
May 2212:55 PM
11. How many halflives have passed if 18.75 grams of a 300 gram sample of Au198 remains unchanged?
Solving Halflife Problems10. There are 5.0 g of 131I left after 40.35 days. How many grams were in the original sample if its halflife is 8.07 days?
May 2212:55 PM
Solving Halflife Problems
12. How much of a 100.0 g sample of 198Au is left after 8.10 days if its halflife is 2.70 days?
13. A 50.0 g sample of 16N decays to 12.5 g in 14.4 seconds. What is its halflife?
Half Life Calculations 2019.notebook
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December 18, 2019
May 2212:55 PM
14. The halflife of 42K is 12.4 hours. How much of a 750 g sample is left after 62.0 hours?
15. What is the halflife of 99Tc if a 500 g sample decays to 62.5 g in 639,000 years?
Solving Halflife Problems
Jan 107:58 AM
1. Which radioactive sample would contain the greatest remaining mass of the radioactive isotope after 10 years?1) 2.0 grams of Au198 3) 4.0 grams of P322) 2.0 grams of K42 4) 4.0 grams of Co60
2. In how many days will a 12 gram sample of I131 decay to 1.5 grams?1) 8.0 2) 16 3) 20 4) 24
3. H3 has a halflife of 12.26 years. Find the fraction remaining after 49 years.
4. Find the fraction remaining of K42 after 25 hours. Hint: See Table N (halflife).
Half Life Calculations 2019.notebook
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December 18, 2019
Jan 107:58 AM
5. 100 grams of a radioisotope decayed to 6.25 grams after 21 years. What is the halflife?
6. 20 grams of a radioisotope is decayed to 2.5 grams in 3.6 seconds. What is the half=life?
7. A radioisotope has a halflife of 2.60 days. 5 grams remain after 10.4 days. What was the initial amount of the radioisotope?
