Honors Chemistry
Ms. Ye
Name __________________________
Date ______________ Block ______
Half-Life= the time it takes for ____________________________________________________
The half-life for a specific isotope is assumed to be the same no matter how much of it you have.
Solving Half-Life Problems
Set up a table showing the mass, time elapsed, the fraction remaining, and number of halflives starting with the initial conditions and ending when the full time has elapsed (any of the
4 variables can be the unknown)
Number of Half-Lives Time Elapsed Mass Remaining
0
0
(Initial amount)
1
(half-life)
×
2
(2 x half-life)
× ×
3
(3 x half-life)
× × ×
…
…
…
Fraction Remaining
1 (100%)
(50%)
(25%)
(12.5%)
…
For each half-life elapsed:
 Cut the mass remaining in half
 Increase the time elapsed by an amount equal to the half-life
 Add one to the number of half-lives
***NOTE: # of half-lives and time must START AT 0
Example: An ore that once contained 320 g of Cobalt—60 now contains only 20 grams of the
radioactive material. The half-life of Co—60 is 5.26 years. How long has it been decaying?
Number of Half-Lives Time Elapsed Mass Remaining Fraction Remaining
0
0
320 grams
1 (100%)
1
5.26 yrs
160 grams
1/2 (50%)
2
10.52 yrs
80 grams
1/4 (25%)
3
15.78 yrs
40 grams
1/8 (12.5%)
4
21.04 yrs
20 grams
1/16 (6.25%)
The half-life of Co—60 is 5.26 years. Every 5.26 years, the amount of Co—60 remaining is cut in half (every halflife, you have half of the previous mass left). When there is only 20 grams of Co remaining (a.k.a. 300 grams
have decayed into Ni-60), 4 half-lives have passed, or 21.04 years.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Practice: Set up a table like the example to help you solve the following problems.
Note: you do not always have to fill in each column.
1) If the half-life of Radon-222 is 3.823 days, how long will it take for 30 grams of
7.5 grams? _______________
Number of Half-Lives Time Elapsed Mass Remaining Fraction Remaining
0
0
30
1 (100%)
1
2
3
Rn to decay to
Honors Chemistry
Ms. Ye
Name __________________________
Date ______________ Block ______
2) How many grams of N will be left from a 16 gram sample after 21.6 seconds? The half-life of N-16
is 7.13 seconds__________
Number of Half-Lives Time Elapsed Mass Remaining Fraction Remaining
0
0
1 (100%)
1
2
3
3) How many half-lives will it take for 50 g of Tc to decay to 6.25 g? ______________
Number of Half-Lives Time Elapsed Mass Remaining Fraction Remaining
0
1 (100%)
1
2
3
4) The half-life of K-42 is 12.36 hours. After 62.0 hours, 1.0 g remains unchanged from a sample of
K. How much K was in the original sample? _________
Number of Half-Lives Time Elapsed Mass Remaining Fraction Remaining
0
1 (100%)
5) If 80 mg of a radioactive element decays to 10 mg in 30 minutes, what is the element’s half-life in
minutes? __________
Number of Half-Lives Time Elapsed Mass Remaining Fraction Remaining
0
1 (100%)
1
2
3
Honors Chemistry
Ms. Ye
Name __________________________
Date ______________ Period ______
Half-life Homework:
1. The half-life of polonium-218 is 3.0 minutes. If you start with 40.0g of polonium, how long will it be
before you have 2.5g of the isotope left?
2. Tritium (Hydrogen-3) has a half-life of 12.3 years. If 16g of tritium was released during a mishap at
the nuclear power plant, what mass of tritium will be left after 36.9 years? 73.8 years?
3. How many half-lives does Thorium-234 go through if a 256g sample decays to 16.0g?
Honors Chemistry
Ms. Ye
Name __________________________
Date ______________ Period ______
4. What is the half-life of an unknown isotope which decays from 8.0g to 2.0g in 32 years?
5. A 55.0g sample of Thorium-234 is known to be 144 days old. Thorium-234 has a half-life of 24 days.
What was the original mass of Thorium?
6. A sample of bone excavated from an ancient burial site was dated using carbon-14 dating. It was
found that the bone marrow contained only ¼ of the carbon-14 found in bone marrow today. If
the half-life of carbon-14 is 5730 years, how old are the bones?