The Nucleus

1
The Nucleus

• Rutherford scattering showed most of the mass of
  an atom was concentrated in a tiny (10-15 meter)
  region and all the positive charge resided there
• Simplest nucleus is hydrogen (one proton)
• All other elements have additional mass beyond
  the mass of the number of protons they contain
• Additional mass comes from a neutral particle
  called the neutron

2
The Nucleus

• The protons and neutrons have both wave and
  particle properties just like electrons and the
  interactions are very complicated
• Later we will find that both protons and neutrons
  are NOT elementary particles but have an internal
  structure and are made of quarks

3
The Nucleus

• We will follow a historical development to look
  at nuclear properties and well do final
  explanations at the end of the semester
• Proton
• Positive Charge of 1.6 x 10-19 Coulomb
• Mass of 1.6726 x 10-27 kg
• Neutron
• No charge
• Mass of 1.6749 x 10-27 kg

4
The Nucleus

• All nuclei are some combination of neutrons and
  protons
• The number of protons is the atomic number, Z
• The total count of nucleons (protons and
  neutrons) is the atomic mass number, A
• The neutron number, N is A - Z

5
The Nucleus

• We will specify a specific nuclide with the
  symbol
• Nuclei with the same number of protons but
  differing neutron counts are isotopes
• Hydrogen has three,
• These may be written

6
The Nucleus

• Elements in nature occur as a mixture of isotopes
  called the natural abundance
• Electron scattering experiments show the radius
  of the nucleus is about
• This implies that the nuclear density is
  constant, so just packed billiard balls

7
The Nucleus

• Convenient to have a specified mass unit
• Define a unified mass unit such that the mass of
  Carbon-12 is 12.000000u.
• Proton is 1.007276u
• Neutron is 1.008665u
• Hydrogen atom is 1.007825u
• 1u 1.6605 x 10-27 kg 931.5 Mev/c2

8
The Nucleus

• Just like electrons, both protons and neutrons
  have an intrinsic angular momentum we called spin
• Value of spin quantum number are -1/2, 1/2
• A nucleus as a whole has nuclear spin that can be
  either integral or half-integral

9
Binding Energy

• The mass of any nuclide is less than the mass of
  its constituent parts!!!
• Where did the mass go?
• Appears as the binding energy (energy of the
  bonds between the nucleons)
• The binding energy is just missing mass times c2

10
Binding Energy

• So, we can find out how much energy is involved
  in holding the protons and neutrons together by
  measuring nuclear masses and comparing to
  constituent masses
• Remarkable picture when we compute the binding
  energy per nucleon

11
Binding Energy
Error! Should be H-2 H-3
12
Binding Energy

• Has to be a big repulsive force between the
  protons that are tightly packed together
• Must be a much stronger force holding them
  together
• This is called the strong nuclear force
• Force is same for proton-proton, proton-neutron,
  neutron-neutron!!!

13
Binding Energy

• The nuclear force is a short-range force
• It is too weak to even reach from one side of a
  large nucleus to the other
• We can tell this by looking at the stable nuclei,
  that is nuclei that are not observed to fall
  apart spontaneously
• Well talk about nuclear decay later

14
Binding Energy

• As Z increases, it takes more neutrons to
  stabilize the nucleus
• Since repulsion between protons goes as 1/r2 this
  force extends outward forever
• Strong nuclear force goes to zero for distance
  much greater than 10-15 meters
• The billiard balls have to be almost touching

15
Binding Energy

• There are NO completely stable nuclides above
  Z82.
• No naturally occurring nuclides above Z92
• Above these limits the nuclei decay or fall apart
  in some fashion to get below these limits
• The weak nuclear force participates in one form
  of decay

16
Radioactivity

• In 1896, Becquerel discovers that minerals
  containing uranium can fog film wrapped in black
  paper and not exposed to sunlight
• Curies continued and found two new elements with
  the same properties
• The fogging didnt depend on any chemical
  preparations, temperature or other parameter
• Seemed to be coming from the nucleus

17
Radioactvity

• The phenomenon was called radioactivity and some
  kind of rays were coming from the nuclei of
  atoms in the minerals
• Three kinds of rays were identified
• They were called alpha, beta and gamma rays

18
Radioactivity
The alpha particles bend as a positive particle
would. The beta particles bend as a negative
particle would. The gamma rays are
unbent. Alphas are Helium nuclei, betas are
electrons and gammas are short wavelength photons
19
Alpha Decay

• The unstable nuclei simply cannot overcome the
  proton repulsion indefinitely
• We saw from the binding energy graph that
  helium-4 nuclei are very stable
• Inside big nuclei, two protons and two neutrons
  seem to form a little gang that hangs together

20
Alpha Decay

• Periodically in their motions, they sneak away
  and escape to the outside through a process
  called tunneling
• This is an example of the uncertainty principle
  where the alpha borrows a little energy for a
  short time and escapes
• Once the alpha is outside it has a lot of energy
• Calculate the mass differences

21
Alpha Decay
22
Beta Decay

• Involves the weak nuclear force
• Neutron turns into a proton plus electron plus
  anti-neutrino
• Proton turns into a neutron plus positron plus
  neutrino
• Neutrino needed to conserve energy, angular
  momentum and lepton number

23
Beta Decay

• The general formulas for beta decay are

24
Gamma Decay
Just like an electron can be in an excited state,
so neutrons and protons inside a nucleus can be
in an excited state, usually via a collision or
as a result of an alpha or beta decay leaving an
excited daughter. Simply give up a photon to
lower the energy.
25
Conservation Laws

• Examination of decays shows that the total number
  of nucleons in any nuclear process remains
  constant
• So, we have a new conservation law
• You can change protons into neutrons and vice
  versa, but the number of nucleons doesnt change!