Chem 112 Class Guide: HALF-LIFE, ENERGY, FISSION AND FUSION
Chapter 21, Sections 4-8 Learning Goals:
Upon completion of Chapter 19, Sections 1-4, you should be able to determine the following:
Calculate the decay constant for a nuclear decay reaction
Calculate the age of a sample based on radioactive decay data
Calculate the energy change in a nuclear reaction
Chapter Reading Guide: Chapter 21, Sections 4-8
Section 4: Rates of Radioactive Decay
Read Chapter 21.4
All radioactive decay processes are first-order. As such, we can use equations from Section
14.4 to calculate various quantities in decay processes.
0.693
2
k
 [ A]t 
ln 
   kt
 [ A]o 
t1 
Where t1/2 is the half-life of the reactant, k is the decay constant, [A]o is the initial
concentration of A, [A]t is the concentration of A after a certain time and t is the elapsed time.
Please note the following two things: 1.) [A]o is ALWAYS greater than [A]t; 2.) t is rarely ever
equal to t1/2.
Example:
If it takes 5.2 min for a 1.000 g sample of 210Fr to decay to 0.250 g, what is the half-life of 210Fr?
To solve this problem, we first need to find k:
  At 
ln 
 kt
  A 
0 

 0.250 g 
  k  5.2 min  ;
 1.000 
So ln 
  5.2 min  k  1.386
k
1.386
 0.27
5.2
Now that we have k, we can find t1/2:
t1 
2
0.693 0.693

 2.6 min
k
0.27
Example:
The half-life of the reaction: U  Pb is 4.5x109 yr. If a sample of a mineral has 75.0
mg of 238U and 18.0 mg of 206Pb, how old is it?
238
206
First, we need to figure out how much 238U we had in the sample originally. We do this by
adding the amount we currently have to the amount of Pb we have, multiplied by the mass
numbers, or:
 238 
U  75.0mg  
18.0mg  75.0mg  20.8mg  95.8mg
 206 
238
We also need to determine k, which we can do with the half-life:
k
0.693
0.693

 1.54 x1010 yr 1
t1
4.5 x109 yr
2
Now we should have all the information we need to find t, or how old the mineral is:
  At 
ln 
 kt
  A 
0 

 75.0mg 
10
1
   1.54 x10 yr  t
95.8
mg


So, ln 
0.245   1.54 x1010 yr 1  t
t
0.245
 1.59 x109 yr
1.54 x1010 yr 1
That’s one old mineral!
Try practice exercises 21.7 and 21.8
Section 5: Detection of Radioactivity
Read Chapter 21.5
Radioactivity can be measured by using a Geiger counter and other means.
There are a few radioisotopes used in medical applications. See Table 21.6 for a complete
list if you are interested.
Section 6: Energy Changes in Nuclear Reactions
Read Chapter 21.6
Most people are familiar with Einstein’s well-publicized equation relating mass and energy:
E  mc 2
However, it is more often used to describe the amount of energy given off in a nuclear reaction:
E  (m)c 2
Where ΔE is the amount of energy produced by the reaction, Δm is the change in mass of
the reaction (always a negative number) and c is the speed of light – 3.0 x 108 m/s. Keep in
mind that 1 J is equal to 1 kg·m2/s2. You must convert your Δm from g to kg, and then once
you calculate ΔE, you must convert J to kJ.
Example:
Calculate the energy released when 12 H  13 H  24 He  01n if
2
1
H  2.01410 amu; 13 H  3.01605 amu; 24 He  4.00260 amu; and 01n  1.00866 amu
First, we need to calculate the change in mass:
m   24 He  01n    12 H  13 H 
m   4.00260 amu + 1.000866 amu    2.01410 amu + 3.01605 amu 
m  1.01126 amu - 5.03015 amu
m  4.01889 amu = -4.01889 g = -0.00401889 kg
Now we can find ΔE:
m

E  mc   0.00401889kg   3.00 x108 
s

2
2
E  3.617 x1014
kg * m2
 3.617 x1014 J  3.617 x1011 kJ
2
s
Try practice exercise 21.9
Section 7: Nuclear Power: Fission
Read Chapter 21.7
Fission is the process of taking one nucleus and splitting it into two or more nuclei. The
fission of 235U requires one neutron to start the reaction. One nucleus of 235U can produce 5
more neutrons, which can then react with 5 more 235U nuclei. This process is called a chain
reaction – once started, the reaction progresses quickly until all starting material is used,
and often produces massive amounts of energy (usually explosively).
Nuclear reactors depend on chain reactions in order to supply electricity. The chain
reactions are controlled by use of control rods – rods made up of elements that absorb
neutrons. This absorption is a highly exothermic process, so the control rods need to be
continually cooled so as not to melt. The steam you see coming out of nuclear power plant
stacks is vaporized water (it is vaporized by the exothermic process).
Section 8: Nuclear Power: Fusion
Read Chapter 21.8
Fusion is the process of taking two or more nuclei and forming one nucleus. This is the
primary type of reaction that occurs in the sun. Generally, fusion involves lighter nuclei
(hydrogen and helium primarily) – these nuclei are readily available on Earth. Fusion also
produces about 100x more energy per mole of reactant than fission does. Given these two
facts and that fusion is largely self-sustaining with little byproducts, it would be ideal to
harness the energy from fusion.
Unfortunately, fusion right now only occurs at super-high temperatures. The only way
currently to start a fusion reaction is to first ignite an atomic bomb (using fission) and then
performing fusion with the heat resulting from the bomb. Obviously, this isn’t an ideal
situation for harnessing energy. Current research has focused on harnessing fusion energy
in a large electromagnetic field, but it currently takes more energy to power the EM field
than the fusion generates.
Learning Resources
Chapter Learning Goals
Chapter 21, Sections 4-8 Learning Goals
Pre Class Assignment: This assignment must be completed prior to the next class. Check your syllabus
for the exact due date and time.
Complete to the pre class assignment
(http://berks.psu.edu/clt/chem112/Half-lifeEnergyFissionAndFusion_HW.docx)
Submit a copy to the dropbox located in ANGEL called “Pre Class Assignment Submission: Halflife, Energy, Fission and Fusion”
End of Chapter Problems:
Practice with these problems if you are having difficulty with any of the concepts covered in this
class guide AFTER we have met in class. If you cannot easily complete these problems, seek
help from your instructor, your mentor or the learning center
Chapter 21: 43, 49