Physics 114

1
Complex atoms

• Physics 114

2
Announcements

• Read sections 6 and 7 from chapter 28 GRR
  (complex atoms)
• Practice tests in the library
• Lecture notes are also available in the library
• To schedule make up tests contact Ahlam Al Rawi
  
• 2-5520
• Ahlam_at_phys.ksu.edu

3
Concepts

• Electron distributions
• Quantum numbers, quantum state
• Pauli principle
• Periodic table

4
Particles and waves

• Massive particles (electron, proton, baseball)
• lh/p pmv
• Energy
• For electron only (KE in eV, l in nm!)

• Massless particles photons
• lc/f
• Energy
• Eghfhc/l
• If photon and electron have the same wavelength
  l, their energies are different!

5
Particle in a boxWhere is the electron?

• (Amplitude of matter wave)2probability to find
  particle at this place.
• More chances to find the particle at a antinode
• No chance at a node
• Quantized energy stated

6
Hydrogen atom

• Energy levels in H

• n- principle quantum number determines the
  energy level
• What about electron distribution in atom?

7
Electron distributions

• Same n, different shapes. Other quantum numbers
  play a role

• Quantum state of electron in atom is defined by a
  set of 4 numbers
• Principle quantum number n
• Orbital quantum number l
• Magnetic quantum number ml (same as lz)
• Spin projection ms

8
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)

9
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

10
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

11
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

12
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

13
State leveling

• 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

14
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

15
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