Nuclear Physics Notes
Nuclear Decay – The Basics
Atoms contain protons, neutrons, and electrons. The atomic number is
the number of protons in an atom. The protons reside in the nucleus.
Neutrons are also located in the nucleus of the atom. Electrons (as far
as Physics is concerned) circle the nucleus in discrete circular orbits
in specific levels (the Bohr model of the atom). An atom is generally
indicated by its atomic symbol including the mass number and the atomic
massnumber
number. Symbolatomicnumber
It can also be indicated by its name followed by
its isotopic mass (ex. Carbon-12 or Uranium-235). Since it is the
number of protons that define the identity of the atom, given its atomic
name or its atomic number you can identify the atom. The atomic mass
 number) is the sum of the protons and neutrons. The mass of the
(mass
electrons is negligible (approximately .0005 of the mass of the proton
or neutron) and so is ignored in mass calculations.
When an atom undergoes nuclear decay, the Law of Conservation of Mass
holds for the top numbers (at least on a whole number basis). So, the
total of the mass numbers on the left hand side (reactant side) of the
reaction must equal the total of the mass numbers on the right hand side
(product side) of the reaction. Similarly, the law of conservation of
charge holds for the bottom number.
For example, H12  H11  ____
the total on the top is 3. The total
2
1
on the bottom is 2. So, H1  H1  ____ 32 and the element is Helium because
the atomic number is 2. H12  H11  He 23

There are only a handful of nuclear decay types that you must memorize.

Alpha decay – The nucleus emits as a product a helium nucleus (alpha

particle) - He 24
0
Beta decay – The nucleus emits an electron (beta particle) e1
. The
actual process is that a neutron breaks down into a proton and an

electron that is ejected from the nucleus.

hf 00
Gamma decay – The nucleus emits a photon (gamma particle)
0
Positron decay – The nucleus emits a positron (anti-electron) e1

Electron capture – This is the only one that has a reactant other than
the mother atom. An electron smashes into the nucleus and converts a

proton into a neutron.
Half-Life
Nuclear decay reactions have a half-life that is only a function of the
stability (or lack thereof) of the nucleus that is caused by the strong
nuclear force. Temperature changes do not change the speed of


radioactive decay; concentrations do not affect them.
follow a zero-order kinetic law.
At  Ao (.5)
They simply
t
t1/ 2life
Binding Energy and Einstein’s Equation

Theoretically,
the mass of an atom should be the sum of the masses of
all the protons and the neutrons in the nucleus. So, for example a
Uranium-235 atom, which has 92 protons and 143 neutrons. Its mass
mass  92 * m proton  143* mneutron
should equal mass  92 *1.67E  27  143*1.67E  27 ; however, its actual mass is
mass  3.9245E  25kg
3.9017E-25 kg. Those numbers don’t match. What happened to the missing
mass -- the MASS DEFECT??
 BINDING ENERGY that holds the nucleus together in an effort to
It became
prevent it from blasting apart because of the strong electrical
kQq
repulsions ( Felectric  2 ) between the protons. This lost mass obeys the
d
2
equation E  mc . So for this uranium isotope, the mass defect is
m  3.9245E  25  3.9017E  25
This allows the binding energy to be
m  2.28E

27kg

E mc 2  2.28E  27 * (3E8)2
. That may not seem like much energy, but that is
E  2.052E 10J
the amount of energy PER ATOM of Uranium. So, in a mole of Uranium
atoms (6.02E23 atoms) there is 1.235E14J of energy or on a per gram
basis that is 5.25E11 J of energy. 525,661,276,596 J of energy per
gram. That’s billions of Joules of energy in one gram of Uranium. To
put that in perspective, that is enough energy to lift all 6 billion
people on earth (assuming an average mass of 70 kg (150 pounds))to a
height of 12.5 meters (41 feet) above the ground. The power of the
strong force (c2=9E16) is 10 million times stronger than the
electromagnetic force (k=9E9) which is 100 PENTILLION times stronger
than gravity (G=6.67E-11). It is almost incomprehensible how much
energy is stored.
In fact, it is the release of binding energy as light when a
supermassive star goes supernova that allows the star to outshine entire
galaxies (billions of stars) when it explodes.