PHY123

1
Complex atomsStructure of nucleus

• PHY123

2
Concepts

• Quantum numbers, quantum state
• Pauli principle
• Periodic table
• Isotopes
• Binding energy
• Fission and fusion

3
Pauli principle

• Electron has spin 1/2
• Electron is a fermion
• Not more than one electron can be in each quantum
  state (Pauli principle)
• Pauli principle is responsible for periodic table
  (Mendeleev)
• NB. If particle has an integer spin (0 or 1) it
  is a boson - all particles tend to fall in the
  same state.
• Example photons (lasers use this principle)

4
Electron quantum state

• Principle quantum number n1,2,3,4,
• determines energy level, higher E for higher n
• Orbital quantum number l
• For each n l can be 0,1,2,3, (n-1)
• l states are leveled by letters
• s l0 p l1 d l2 f l3 gl4
• E.g. n5, then l can be 0, 1, 2, 3, 4
• Possible l states are s,p,d,f,g
• n1, only l0 s-state is possible

5
Electron quantum state
z

• Orbital quantum number is a vector length l
• Its projection on z axis is another q.n.
  magnetic quantum number ml
• ml can be only integer

6
Electron quantum state
z

• All electrons have spin1/2
• It is a vector
• Its projection on z axis is another q.n. spin
  ms
• ms can be only

7
Possible number of states

• For each given n,l,ml ? 2 possible states
• ms1/2 ms-1/2
• For each given n,l ? 2(2l1) states
• mll, (l-1), 2,1, 0, -1, -2, -(l-1), -l ?
  (2l1)
• For each ml ms1/2 ms-1/2 ? 2
• For each given n ? 2n2 possible states
• l0,1,2,3,4,.(n-1)
• For each l mll, (l-1), 2,1, 0, -1, -2,
  -(l-1), -l ? (2l1)
• For each (l,ml) ms1/2 ms-1/2

8
State labeling

• 2p3 means 3 electrons in p state (l1) at n2
  level
• 4f5 means 5 electrons in f state (l3) at n4
  level
• States filled up from lower to higher n
• For each n from lower to higher l

9
Periodic table

• Elements in increasing mass
• MANpMpNnMn
• But mass does not determine chemical properties
• Atomic number Z does. ZNp- charge of nucleus
  number of electrons

• H Z1 ?1 electron
• n1, l0 (s), ml0
• 1s1
• He Z2 ?2 electrons
• n1, l0 (s), ml0
• 1s2
• 2 e spin up, spin down
• Li Z3 ?3 electrons
• 2 e on 1s shell
• 1 e on n2, l0 (s), ml0
• 1s22s1

10
Electron structure

• 2n2 states for each n
• 2(2l1) states for each n,l
• 2 states for each n,l,ml
• s(l0), p(l1), d(l2), f(l3)
• 2 states in each s subshell
• 6 states in each p subshell
• 10 states in each d subshell
• 14 states in each f subshell

• n1,2,3,4.
• l0,1,2,(n-1)
• ml-l,-1,0,1,l
• ms1/2 -1/2
• 3p4 4 electrons on
• n3, l1 subshell

11
Test problem 1

• The following configuration is allowed
  1s22s22p63s3
• True
• False

12
Test problem 2

• The following configuration is allowed
  1s22s22p63s23p54s2
• True
• False

13
Test problem 3

• The following configuration is allowed
  1s22s22p62d1
• True
• False

14
Atomic spectra

• Forbidden (not completely though), allowed
  transitions (Dl1), because photon has spin 1
  and angular momentum is conserved
• Inner energy shells (called K-shells) see
  almost full potential of the nucleus proportional
  to (Z-1)2
• Observe atomic spectra in X-ray scattering

15
Nucleons and nuclei

• Proton and neutron are called nucleons
• 1u1.66054x10-27kg931.5MeV/c2
• Protons have positive charge , neutrons have zero
  charge
• A new kind of force strong force holds
  nucleons inside nucleus. Unlike EM force strong
  force is short distance ? nuclei are very
  tightly packed

16
Nucleus radius

• Volume proportional to the number of nucleons

17
Isotopes

• Mass of the nucleus does not determine chemical
  properties Atomic number Z does.
• Same chemical element (ZNp) can have different
  number of neutrons isotopes
• Carbon Z6?6 p, but it can have
• 5n 11C, 6n 12C, 7n 13C, 8n 14C, 9n 15C,
  10n 16C
• Only 12C is stable (98.9 of C on Earth)

18
Masses of nuclei and nucleons

• Lets compare nucleus mass with the sum of
  nucleon masses (from appendix D in Giancoli)
• Al Z13 ? 13 p, A27? 27-1314 n
• M(13p14n)13x1.007276u14x1.00866527.215898u
• M(Al)26.981538u
• Where did (27.215898-26.9815380.23436u) go?
• Recall that mass is a form of energy
• To extract a nucleon from the nucleus you must
  supply energy W
• M(Al)WM(13p)M(14n)
• Hence M(Al)ltM(13p)M(14n)
• W is called binding energy

19
Binding energy per nucleon
20
Nuclear fission

• Discovered by German scientists Otto Hahn and
  Fritz Strassmann in 1938
• 235U splits into two nuclei when bombarded by
  neutrons
• More neutrons are produced in the reaction
• n 235U?141Ba92Kr3n
• This means a chain reaction is possible when the
  minimum mass of uranium reaches critical mass
• Tremendous amount of energy is released

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Chain reaction
Uncontrollable chain reaction fission bomb
Controllable chain reaction nuclear reactors
22
Nuclear reactor
23
Fusion reactions in the Sun

• The key is to bring two protons together close
  enough for the strong force to overcome
  electrostatic repulsion need high T
• 1H1H?2Hen
• 1H2H?3Heg
• 3He3He?4He1H1H
• This is how heavier (Zgt1) elements were produced
  in the first place (only upto iron or nickel)
• Heavier elements are produced in the middle of
  the starts or supernova explosions by absorbing
  extra energy
• Fission bomb is used to ignite fusion bomb
  hydrogen bomb