Chapter 3 Worksheet
1. Write a balanced equation for each of the following reactions, showing mass and charge on all species.
a. tin-121 undergoes beta emission
12150Sn → 0-1β + 12151Sb
b. 67Ga decays giving zinc-67 as the daughter
6731Ga → 01β + 6730Zn
c. 8Be emits an alpha particle
84Be → 42α + 42He
d. oxygen-15 emits a positron
158O → 01β + 157N
e. uranium-236 decays into 3 neutrons and bromine-87
23692U à 14657La + 3 10n + 8735Br
2. Write a complete, balanced equations for each of the following reactions:
a. Sodium-26 decays with beta emission
2611Na → 0-1β + 2612Mg
b. Nitrogen-12 (12N) undergoes radioactive decomposition into carbon (12C)
and one other particle
127N → 126C + 01β
c. Formation of 81Kr by electron capture
8137Rb + 0-1e → 8136Kr
d. 212Bi ® alpha particle + ?
21283Bi → 42α + 20881Tl
e. 241Am is formed through beta decay
24194Pu → 24195Am + 0-1β
3. If a radioactive isotope were to be used for therapeutic purposes, what sorts of properties would be beneficial for this purpose? Think about which properties a radioactive element has and what would be desirable. List all that you can think of. Now do the same for diagnostic isotopes
Therapy: targets organ of interest
relatively short half life (weeks to months)
benign daughter atoms (so radiation decay products don’t do damage)
alpha emission (to localize radiation damage)
Diagnosis: targets organ of interest
very short half life (hours)
benign daughter atoms
beta or gamma emission (to penetrate to outside of body where detectors
are)
4. List at least two other uses for radioactive isotopes (besides therapeutic and diagnostic in the medical field). Explain how the radioactive isotope is used in this capacity.
as a tracer in a biological process: feed radioactive isotope to an organism and track what the organism does with the radioactive isotope, what products are made, what intermediates are made with the product, how long it takes to make them, etc
To measure thickness of material (thickness will be proportional to # of emissions which penetrate material to detector on other side)
to find leaks in a pipeline: put radioactive material in pipeline and walk around outside with geiger counter to find leak by increased radiation count
to measure lubrication: make gears from radioactive metal, run machinery, drain oil, and measure amount of metal in oil from radioactivity of oil.
as plug between two different fluids pumped in a pipeline. when radiation is detected, switch to different outlet/storage tank
to determine the age of rocks or anything made from plants or that consumed plants while alive. a plant has a constant concentration of carbon-14 as long as it continues to “breathe” in carbon dioxide. After it dies, the amount of carbon dioxide decreases as it decays, but is not replenished by “breathing.” This allows us to determine how long ago anything made from plants was made.
5. The half life of radium-226 is 1.60 x 103 years. How long will it take for a 2.50 g sample to decay until only 0.0781 g are leftover?
To find out how many half lives have gone by, use the formula:
(½)n = fraction remaining, where n= number of half-lives
we can use log math (or if you are not familiar with logs, skip to next paragraph).
(½)n = fraction remaining
n log (½) = log (fraction remaining)
n = log (fraction remaining)/ log (½) = log (0.0781/2.50)/log ½ = log 0.03124/log 0.5 = 5 half life periods have elapsed
to calculate without logs, try going through different whole numbers for how many half lives have elapsed
# half lives elapsed → amount remaining (grams)
0 2.50
1 1.25
2 0.625
3 0.3125
4 0.15625
5 0.0781
so, 5 half lives have gone by
5 half lives x 1.60 x 103 years/half life = 8.00 x 103 years.