Half Life Practice

1
Half Life Practice
2

• If the half-life of iodine-131 is 8.10 days, how
  long will it take a 50.00 g sample to decay to
  6.25 g?

3

• What percentage of 50g is 6.25g?
• 6.25g 50g 12.5
• How many half-lives leave you with 12.5 of the
  parent isotope?
• 3
• If 1 half-life 8.1 days, 3 half-lives are equal
  to 24.3 days.
• 8.1 days 3 24.3 days

4

• The half-life of hafnium-156 is 0.025 seconds.
  How long will it take a 560 g sample to decay to
  one-fourth      of its original mass?

5

• One-fourth is equal to 25.
• How many half-lives result in 25 of the parent
  isotope being left?
• 2
• 0.025 seconds/half-life 2 half-lives 0.05 sec

6

• Chromium-48 has a short half-life of 21.6 hours.
  How long will it take 360.00 g of chromium-48 to
  decay      to 11.25 g?

7

• What percentage of 360g is 11.25g?
• 11.25g 360g 100 3.125
• How many half-lives result in 3.125 of the
  parent isotope?
• 5
• If 1 half life 21.6 hours, then 5 half-lives
  would be equal to
• 21.6hrs 5 108 hrs

8

• Potassium-42 has a half-life of 12.4 hours. How
  much of an 848 g sample of potassium-42 will be
  left after      62.0 hours?

9

• T-chart time!

Half Life Amount (g)
0 (initial) 848
1 (12.4 hours) 424
2 (24.8 hours) 212
3 (37.2 hours) 106
4 (49.6 hours) 53
5 (62.0 hours) 26.5

OR 62 hours 12.4 hours/HL 5 Half-Lives 5
half lives leave you with 3.125 of your parent
isotope, so 848g 3.125 26.5g
10

• Carbon-14 has a half-life of 5730 years. How much
  of a 144 g sample of carbon-14 will remain
  after      1.719 104 years?

11

• 1.719 104 17,190 years
• If 1 half-life is equal to 5730 years, how many
  half-lives are in 17,190 years?
• 17,190years 5730years/HL 3 HL
• T-chart time!

Half Life Amount (g)
0 144
1 72
2 36
3 18
12

• What is the half-life of a 100.0 g sample of
  nitrogen-16 that decays to 12.5 grams in 21.6
  seconds?

13

• First, we realize that we are left with 12.5 of
  the parent isotope (Nitrogen-18).
• We need to find out how many half-lives leave us
  with 12.5 of the parent isotope.
• 1 half life 50 parent isotope
• 2 half lives 25 parent isotope (half of 50)
• 3 half lives 12.5 parent isotope (half of 25)
• If 21.6 seconds is enough time for 3 half-lives,
• 1 half life 7.2 seconds. (21.6 divided by 3)

14

• All isotopes of technetium are radioactive, but
  they have widely varying half-lives. If an 800.0
  gram sample of technetium-99 decays to 100.0 g of
  technetium-99 in 639,000 years, what is its
  half-life?

15

• We are left with 100g out of 800g. What
  percentage is that?
• 12.5
• How many half-lives leave us with 12.5 of the
  parent isotope?
• 3
• If 3 half-lives are equal to 639,000 years, how
  long is 1 half-life?
• 213,000

16

• A 208 g sample of sodium-24 decays to 13.0 g of
  sodium-24 within 60.0 hours. What is the
  half-life of this      radioactive isotope?

17

• We are left with 13g out of 208g. What
  percentage is that?
• 13g 208g 100 6.25
• How many half-lives result in 6.25 of the parent
  isotope?
• 4
• If 4 half-lives have occurred in 60 hours, how
  much time is in 1 half-life?
• 60 hours 4 half-lives 15 hours per half-life