Unit 19 Notes –Nuclear Physics
Chapter 32
Nuclear Structure
A= atomic mass numberZ= atomic number
N= number of neutronsA = Z + N
Notation:
where X is an element symbol
proton: because the proton is the nucleus of a hydrogen atom
neutron:
electron: because electron has no nucleus A = 0 and Z=-1 because it has a negative charge
isotope: nuclei with same number of protons but different number of neutrons
nucleon: general name for particles in the nucleus, i.e. protons and neutrons
atomic mass unit: amu or u:1u = 1.660540x10-27 kg
(define relative to having mass of exactly 12u)
Mass Defect of nucleus and Nuclear Binding Energy
-binding energy – energy required to separate a stable nucleus into its constituent protons and neutrons
-see example 32-6
-In Einstein’s theory of special relativity, mass and energy are equivalent:
- change Δm in mass of a system is equivalent to a change ΔE0 in the rest energy of the system by an amount
ΔE0 = (Δm)c2
c, of course, is the speed of light; E is energy; m is mass
- the energy equivalent of 1 u is
E = mc2 = (1.660540x10-27 kg)(2.99792x108 m/s)2
= 931.5 MeV
(note that this is over 6 orders of magnitude larger than electron energies)
- Since mass and energy are equivalent, mass can be expressed in terms of energy:
1 u = 931.5 MeV/c2
-the binding energy used to disassemble the nucleus appears as extra mass of the separated nucleons.
- in other words, the sum of the individual masses of the separated protons and neutrons is greater by an amount Δm than the mass of the stable nucleus
- the difference in mass is known as the mass defect of the nucleus
Strong Nuclear Force
-The attractive force that holds the nucleus together – without it, the electrostatic force would cause the nucleus to fly apart.
-Acts on short ranges - only a couple of fermis (1 fermi = 1 femtometer = 10-15 m)
-Always attractive
-Nearly equal strength between proton-proton, proton-neutron, and neutron-neutron
-Does not act on electrons
Stability
Stability is determined by competition between repulsive electrostatic force and attractive strong nuclear force.
Radioactivity
α-rays – least penetrating, blocked by 0.01 mm of lead
β-rays – next most penetrating, blocked by 0.1 mm of lead
γ-rays – most penetrating, blocked by 100 mm of lead
The disintegration process that produces α-rays, β-rays, and γ-rays must obey these laws:
-conservation of mass/energy
-conservation of electric charge
-conservation of linear momentum
-conservation of angular momentum
-conservation of nucleon number
α decay
-an α-ray consists of positively charged particles, each one being the nucleus of helium. thus, an α particle has a charge of +2e and a nucleon number of A=4.
-Example:
parent nucleus (uranium) daughter nucleus (thorium) + α particle (helium nucleus)
-Note that the sum of the A numbers on each side of the equation are equal (238=234+4) and the sum of the Z numbers on each side of the equation are equal (92=90+2). This is conservation of nucleon number
-Since the parent and daughter nuclei are different, this is called transmutation
-when α decay occurs, the energy released appears as kinetic energy of the recoiling daughter nucleus and the α particle
β- decay
-a β-ray consists of negatively charged particles, or β-particles
-experiments show β- particles are electrons()
-Example:
parent nucleus (thorium) daughter nucleus (protactinium) + β- particle (electron)
-note that law of conservation of nucleon is still followed
-the electron emitted does NOT actually exist within the parent nucleus and is NOT one of the orbital electrons. the electron is created when a neutron decays into a proton and an electron; when this occurs, the proton number of the parent nucleus increases from Z to Z +1 and the nucleon number remains unchanged. the electron is usually fast-moving and escapes from the atom, leaving behind a positively charged atom
-it turns out that the decay of a neutron emits not only a proton and an electron, but also a neutrino (“little neutral one”, so named by Fermi after being hypothesized by Pauli). this was discovered when it was found that electrons given off in beta decay have energies less than that predicted by conservation of energy (and cons.of momentum). the neutrino is very small in mass and has no charge. the neutrino given off in β- decay is actually an antineutrino. the neutrino itself is given off in β+ decay.
β+ decay
-in some cases, the particle emitted by the nucleus is a positron, rather than an electron
-a positron, aka β+ particle, , has the same mass as an electron, but carries a charge of +e instead of –e.
γ decay
-the nucleus, like electrons, only exists in discrete energy levels. when it goes from an excited state to a lower state, a photon is emitted. The photon is very high energy and is called a γ-ray.
-general formula:
excited energy state lower energy state + γ-ray
-Note that this is NOT transmutation. The identity of the element doesn’t change.
See example 32-3, 32-4, active example 32-1
Radioactive Decay Series
-when an unstable parent nucleus decays, the resulting daughter nucleus is sometimes also unstable. if so, the daughter then decays and produces its own daughter, and so on, until a completely stable nucleus is produced.
-this sequential decay is called a radioactive decay series
-Example radioactive decay series for
Induced Nuclear Reactions
-nuclear reaction – occurs whenever the incident nucleus, particle, or photon causes a change to occur in a target nucleus:
incident α particle + nitrogen (target) oxygen + proton
-in this case, the incident particle changes nitrogen to oxygen, so this is called induced nuclear transmutation
Nuclear Fission
-nuclear fission – splitting of a massive nucleus into two less-massive fragments
-example:
neutron + U-235 compound nucleus (unstable) barium + krypton + 3 neutrons
-this is only one possibility for when U-235 undergoes fission.
-Those produced neutrons can the hit another U-235 and cause it to undergo fission.
-This is a chain reaction. read section in book on chain reactions p1071-1072
-See example 32-7
Nuclear Fusion
-nuclear fusion – two light nuclei combine to form a more massive nucleus
Particles to know:
Name#protons#neutrons#electrons
hydrogen 101
deuterium111
tritium121
deuteron – nucleus of deuterium 110
triton – nucleus of tritium120
positron – “positive electron” – is the antiparticle of an electron; same mass of electron, charge of +e
Practice
- Identify Z, N, and A for the following isotopes: (a)(b)(c)
- What are the nuclear radii of (a) and (b)
- Complete the following nuclear reaction:
- Complete the following nuclear reaction:
- Complete the following nuclear reaction:
- Complete the following nuclear reaction, and determine the amount of energy it releases:
- The atomic mass of gold-197 is 196.96654 u. How much energy is required to completely separate the nucleons in a gold-197 nucleus?
- The atomic mass of lithium-7 is 7.01435 u. How much energy is required to completely separate the nucleons in a lithium-7 nucleus?
- Calculate the average binding energy per nucleon of (a) and (b)
- Find the number of neutrons released by the following fission reaction:
- Complete the following fission reaction and determine the amount of energy it releases:
- Find the energy released in the following fusion reaction:
Solutions
1. (a)
(b)
(c)
2. (a)
(b)
3.
4.
5.
6.
7.
8.
9. (a)
(b)
10.
Sn neutrons = 132 50 = 82
Mo neutrons = 101 42 = 59
U neutrons = 235 92 = 143
neutrons released = 1 + 143 82 59 = 3
11.
U neutrons = 235 92 = 143
Sb neutrons = 133 51 = 82
The missing atom is .
12.
1