Integration in physics
N
uclear
Physics
Rutherford’s experiment
Rutherford found that the nucleus is tens of thousands of times smaller in radius than the atom itself;
Experiments show that we can model a nucleus as a sphere with a radius R that depends on the total number of nucleons (neutrons and protons) in the nucleus.
Size of the nucleus
The neutrons and protons are grouped together in the nucleus, which is at the center of the atom;
If the atom were the size of your classroom, the nucleus would be the size of a single grain of sand at the center of the room;
Most of an atom’s mass is concentrated in the nucleus.
The radius of most nuclei obeys the empirical equation
,
where
=1.2
fm or 1.2 × 10-15
m
Isotops
Atoms of the same element that have the same number of protons (Z) but a different number of neutrons (N) or A are known as ISOTOPES.
These have similar chemical properties, because the number of protons in the nucleus equals the number of electrons in the shells.
The atomic mass
Because the atomic masses are so small, the (unified) atomic mass unit (u or amu) is used instead of the kg;
1 u = 1.660538921(73) × 10-27 kg or 931.494 MeV/c2 is defined as 1/12 of the mass of one atom.
Particle Type |
Mass [kg] |
Mass [u] |
Mass [MeV/c2] |
Electron |
9.109 × 10-31 |
0.000549 |
0.511 |
Neutron |
1.675 × 10-27 |
1.008665 |
939.6 |
Proton |
1.673 × 10-27 |
1.007277 |
938.3 |
Hydrogen
|
1.674 × 10-27 |
1.007825 |
938.9 |
Carbon-12 |
1.993 × 10-26 |
12.00000 |
11 177.9 |
The Strong Nuclear Force
It has been shown experimentally that a strong nuclear force acts on all nucleons and it is nearly independent of charge. Electrons do not “feel” this force;
Holds protons and neutrons together in a nucleus;
Mostly attractive, and it can exceed the Coulomb repulsive force;
Short-range force, as it acts over distances comparable to the nucleus size.
T
he
Strong Nuclear Force Range
Attractive in the range: 1 to 5 fm, but repulsive below ~1 fm (= 10-15 m)
Nuclear Stability
Light nuclei (Z < ~20) are most stable if they contain equal numbers of protons and neutrons (i.e. N = Z);
N > Z in heavy nuclei (Z > ~20);
As the number of protons increases the electrostatic repulsion among them increases, too, and so more neutrons are required to increase the attractive nuclear force among the nucleons;
Eventually the Coulomb repulsive force prevails and no stable nuclei exist for Z >83.
Radioactivity
1 Bq = 1 decay/s
1 Ci = 3.7 × 1010 Bq
The spontaneous disintegration of certain atomic nuclei accompanied by the emission of the three main types of radiation: alpha particles, beta particles or gamma rays
There are 3 (main or historical) types of nuclear radiation:
alpha (α) decay (
both
Z and A change):
beta () decay (
,
,
Z changes, A stays the same):
gamma (γ) decay (high-energy photon emission, A and Z do not change):
Other types of radiation
Beta (-) decay
Beta (+) decay
Note
: the neutrino
and its antiparticle
have no charge or mass, but have spin and kinetic energy
The Math of Radioactivity
Radioactivity appears to be a random process;
The decay rate is proportional to the number of unstable nuclei in a sample:
Show
that:
The
decay constant 𝛌
)
is positive and indicates how fast the radioactive material decays.
- initial number of radioactive nuclei
The
positive rate of decay
is also called activity (measured in Bq or Ci):
with
- initial activity.
Half-life of radioactive decay
The
half-life,
,
of a radioactive substance is the time it takes for half of a given
number of its nuclei to decay: