PHYS 221 Recitation
Kevin Ralphs
Week 14
Overview
• Nuclear Physics
– Structure of the Nucleus
– Nuclear Reactions
Nuclear Physics
• Structure of the Nucleus
– The nucleus of made of two types of particle called nucleons:
protons and neutrons
– A nucleus is specified with the following notation
𝐴
𝑍𝑋
Z: Atomic Number – Number of protons
A: Mass Number – Number of nucleons
X: Element Symbol
• Examples
6
3
4
2𝐻𝑒 2𝐻𝑒 2𝐻𝑒
• Nuclei with the same number of protons, but different
number of neutrons are called isotopes
Nuclear Physics
• Structure of the Nucleus
– Atomic Mass
• The atomic mass of an atom is the mass of the nucleons plus
the mass of the electrons
• The periodic table records average values of the atomic mass
weighted by the natural abundance of the isotopes
– Size of the Nucleus
• Scattering experiments have shown that nuclei are
approximately spherical with the following approximate
radius
𝑟 = 𝑟𝑜 𝐴1/3
Nuclear Physics
• Structure of the Nucleus
– Forces within the Nucleus
• Electric Forces due to repulsion between protons
• The strong nuclear force is an attractive force that binds
nucleons together, but only acts over short distances
– Stability of the Nucleus
• The above forces work together to create an equilibrium
within the nucleus
• Although neutrons add stability by spacing the protons
further apart to counterbalance their electric repulsion,
adding too many create an unstable nucleus that will split
Nuclear Physics
• Nuclear Reactions
– Radioactive decay is a spontaneous process where
a nuclei splits into two or more particles
– The original nucleus is referred to as the parent
nucleus with the final result being called decay
products
Nuclear Physics
• Nuclear Reactions
– There are 3 kinds of decay that we will concern ourselves
with:
• Alpha Particles
– An alpha particle is a cluster of 2 protons and 2 neutrons, essentially a
helium nuclei
– In this type of decay, the alpha particle is ejected with the appropriate
numbers adjusted in the daughter nucleus
• Beta Particles
– Beta decay occurs when a proton turns into a neutron or the other way
around
– When this happens, additional particles are kicked out to conserve
charge and some other properties that are beyond the scope of our class
• Gamma Decay
– Nucleons can become excited and emit photons, gamma rays, when they
return to their ground state just like electrons
Nuclear Physics
• Nuclear Reactions
– Conservation Rules
•
•
•
•
Conservation of Mass-Energy
Conservation of Momentum
Conservation of Electric Charge
Conservation of Nucleon Number
Nuclear Physics
• Nuclear Reactions
– Binding Energy
• If we were to total up the individual masses of the nucleons
and compare this to the atomic mass of them together, we
would notice that some of the mass is missing
• We should expect this: The nucleus is stable so it should be a
lower energy system than the individual nucleons
• Due to relativity, we know that this lower energy has to be
accounted for with lower mass
• Note that when doing binding energy calculation, you have
to carry many digits since the change is mass is very small
Nuclear Physics
• Nuclear Reactions
– Half-life
• We cannot predict when a decay process will occur for a specific
nucleus, but if there are many nuclei then we can estimate the
average number of reactions that should occur in a span of time
• It would make sense if the likelihood of a decay event (which is
essentially the rate of decay) was proportional to the amount of nuclei
that could possibly decay which suggests an exponential kind of decay
𝑁 𝑡 = 𝑁𝑜 𝑒 −𝜆𝑡
𝑇1
2
ln 2
=
𝜆
• 𝑇1 2 is the half-life of the element and is the period of time where we
would expect that nearly half of the material had decayed
• Note that N(t) is the number of nuclei left not that number that have
decayed. Likewise No is the number at t=0.
Nuclear Physics
• Nuclear Reactions
– Measuring Radiation
• The “strength” of a radioactive sample is called its
activity and describe how many decay events occur in a
span of time
• Two common units of activity are the curie (Ci) and the
becquerel (Bq)
1 Ci = 3.7 × 1010 decays/s
1 Bq = 1 decays/s
Nuclear Physics
• Nuclear Radiation
– Measuring Radiation
• Radiation can also be measured in the amount of
energy absorbed weighted by the amount of material
that absorbed it
• Dosage can be measure in rems or rads
• Rads give the raw energy absorbed
1 𝑟𝑎𝑑 = 0.01 𝐽 𝑘𝑔
• The same dosage in rads can have different effects on
biological material, so the rem accounts for that
Dose in rem = (dose in rads) x (RBE)