Electrons in Atoms

1

• Electrons in Atoms
• and
• The Quantum Theory
• Unit III
• Ch. 5

2
Electromagnetic Energy

• Frequency (?) measured in units of hertz (sec-1)
• Wavelength (?) - measured units of length mm, nm
• Amplitude - the height of the wave
• Speed (velocity) of electromagnetic energy
  3.00 x 108 m/s
• c ? ?

3
Electromagnetic Spectrum

• Wavelength (?) Description Frequency (?)
• 1-800 m Radio waves 104 - 109
• 10-1 - 10-2 m Radar 109 - 1010
• 10-2 - 10-4 m Microwaves 1010 - 1012
• 10-4 - 10-6 m Infrared 1012 - 1014
• 400-700 nm Visible 1014 - 1015
• 10-8 - 10-10 m Ultraviolet 1015 - 1018
• 10-10 - 10-13 m X-rays 1018 - 1021
• 10-13 - 10-15 m Gamma Rays 1021 - 1023

4

• Spectroscopy
• The method of studying substances exposed to some
  sort of exciting energy.
• Spectrum
• Observed when white light is dispersed into the
  colors of the rainbow by a prism or diffraction
  grating.
• Emission Spectra
• Absorption Spectra

5
The Photoelectric Effect

• The emission of electrons from a metal when light
  shines upon it. If the light frequency was below
  a certain level, no electrons were emitted. The
  wave theory of light predicted that light of any
  frequency could supply enough energy to eject an
  electron. Scientists could not explain why a
  certain minimum frequency was required.

6
Radiation

• Caused by an unstable nucleus which will eject
  either a particle or energy until it reaches a
  more stable arrangement.
• Emission Description
• alpha helium nucleus
• beta high speed electron
• gamma v. high energy X-rays

7
Plancks Hypothesis

• In 1900 Max Planck was studying black body
  radiation. He suggested that hot objects emit
  energy in small specific amount called quanta. A
  quantum is the minimum amount of energy that can
  be gained or lost by an atom.
• Energy is given off (emitted) in little packets
  (or quanta) called photons.

8

• The amount of energy emitted is proportional to
  the frequency of the light emitted according to
  the equation
• E hn
• E energy of a quantum or radiation
• n the frequency of the radiation
• h 6.626 x 10-34 J s (h Plancks constant)
• Einstein (1905) introduced the concept that
  electromagnetic radiation has a dual
  wave-particle nature.

9
Relationship between electromagnetic energy and
electrons

• An electromagnetic wave of a certain frequency
  has only one possible wavelength l c/n
• It has only one possible amount of energy
• E hn
• c and h are constants. If frequency, wavelength
  or energy is known, we can calculate the other
  two. White light can be thought of as a wave or
  as a stream of particles, which Einstein called
  photons. A photon is a particle of radiation
  having zero rest mass and carries a quantum of
  energy.
• Therefore, Ephoton hn

10
The Hydrogen Atom Line-Emission Spectrum

• See p. 127 for an explanation of ground state and
  excited state for an atom.
• Ground state - The smallest orbit an electron can
  occupy.
• The energy of the photon, Ephoton , corresponds
  to the energy difference between the different
  energy levels in an atom E1 and E2 , for
  example.

11
Rutherford-Bohr Atom

• This is referred to as the Planetary Atomic Model
  because they proposed that the negatively-charged
  electrons stay "in orbit" around the
  positively-charged nucleus in the same way that
  the planets stay in orbit around the sun.

12
The Quantum Theory and the Hydrogen Atom

• Energy is given off in quanta. Bohr pointed out
  that the absorption of light by hydrogen at
  definite wavelengths corresponds to definite
  changes in the energy of the electron.
• He concluded that the orbits must have orbits of
  definite diameter.

13
Mechanics

• Newtonian Mechanics - describes visible objects
  at ordinary velocities.
• Quantum Mechanics - describes extremely small
  particles at velocities near that of light

14
Modern Atomic StructureE mc2E h?? mc2
h?mv2 h? mv2 hv/?? ? hv/mv2
h/mvmomentum mv p ? h/p
15
Heisenberg (1927)

• Heisenberg Uncertainty Principle
• It is not possible to know precisely the position
  of an electron and its momentum (velocity) at the
  same instant.

16
Schrödinger

• Developed a mathematical equation to describe the
  wave-like behavior of the electron.
• The equation is very complicated (using second
  partial derivatives)

17

• is the wave function. The equation related the
  amplitude of the wave function (?) to any point
  in space around the nucleus.
• Max Born showed that ?2 gives the probability
  of finding the electron at the point in space for
  which the equation was solved.

18
Einstein

• Proposed that electromagnetic radiation can be
  viewed as a steam of particles called photons.
• The energy of each photon is given by
• E h? h(c/?)
• E mc2 Energy has mass
• mE/c2 (hc/?)/c2 h/?c
• mmass of a photon of light with a wavelength ?

19
Conclusions

• Energy is quantized
• Electromagnetic radiation shows some
  characteristics of matter
• Light as a wave (sine wave)
• Light as a stream of photons
• ? ? ? ? ? ? ? ? ? ?

20
Wave Mechanical Model of the Atom

• Bohrs model was based on classical physics and
  was shown to be inadequate.
• Mid-1920s a new approach was taken by de
  Bröglie, Heisenberg and Schrödinger.
• De Bröglie proposed that the electron, which had
  been considered a particle only, also showed wave
  properties.
• Schrödinger attacked the problem by putting
  emphasis on the wave properties.

21
Atomic Orbitals Quantum Numbers

• The quantum theory describes the behavior of
  electrons. There are four quantum numbers which
  are needed to describe the electron in an atom
  (n, l, m, s). Remember, no two electrons in an
  atom can have the same four quantum numbers.

22

• n, The Principal Quantum Number represents the
  main energy level, its "size".
• Can have values of 1, 2, 3, 4,

23

• l, Angular Momentum Quantum Number, describes the
  "shape" of the orbital. These are multiple energy
  states that are grouped very close together. Can
  have values from 0 to n-1. The number of
  sublevels for energy level "n" n
• n 1 1 sublevel
• n 2 2 sublevels
• n 3 3 sublevels
• n 4 4 sublevels

24

• m, Magnetic Quantum Number, describes the
  orientation (direction) of the orbital in space
  that is, the direction in which it points. Can
  have values from -l to l
• Degenerate orbitals are those orbitals with the
  same size (n) and shape (l) which have the same
  energy.
• the three 2p orbitals
• the five 3d orbitals

25

• s, Electron Spin Quantum Number. Electrons can
  spin either clockwise or counterclockwise.
• s can have one of two values depending on the
  direction of the rotation 1/2 or -1/2

26
Quantum Number Overview

• n - principal quantum number - size of energy
  level
• values 1, 2, 3, 4,
• l - energy sublevel - shape of the orbital
• values 0 to n-1
• m - orbital Q.N. - orientation in space
  (direction)
• values - l to l
• s - spin Q.N.
• values 1/2, -1/2

27
Rules for Filling Orbitals

• Aufbau Principle - Build up the electrons from
  the bottom
• Pauli Exclusion Principle - No two electrons can
  have the same set of four (4) quantum numbers.
• Hund's Rule - Add one electron to each orbital of
  degenerate orbitals until all orbitals have at
  least one electron. Then start pairing up the
  remaining electrons.

28
The Apparent Contradiction

• Waves can act as particles, and particles can act
  as waves
• Bohrs atomic model explained light in terms of
  particle properties.
• Electrons (like light) have properties of both
  waves and particles
• Wave-particle duality of nature applies to all
  waves and all particles

29
Electron Configuration

• When we write the electron configuration for a
  specific atom, we must specify the energy level
  (principal quantum number, 1,2,3,...), the
  sublevel (angular momentum quantum number, s, p,
  d, f) and the number of electrons in each
  sublevel (indicated via a superscript).

30
Electron Configuration

• For example, the electron configuration for
  magnesium (which has 12 electrons) is
• 1s22s22p63s2
• When you add up all the exponents, you should get
  the total number of electron for that particular
  atom (in this case, 2 2 6 2 12)

31
Modern Atomic Structure

• 1. The division between matter and energy is
  becoming even less clear.
• 2. de Bröglie Hypothesis (1923) led the way to
  the present theory of atomic structure.

32
Electron Dot DiagramsgtgtgtRules ltltlt

• The elemental symbol represents the nucleus and
  all electrons not in the outer shell
• Write out the electron configuration (1s22s2)
  selecting those electrons in the outer energy
  level only
• Each side represents an orbital. Draw dots to
  represent electrons in that orbital

33
Quantum Theory

• The quantum theory describes the behavior of the
  electrons.
• There are four quantum numbers needed to describe
  the electron in an electron (n, l, m, s)
• No two electrons can have the same four quantum
  numbers

34
Principal Quantum Number, n

• Represents the size of the energy level
  (orbital)

35
Energy Sublevels, l

• Describes the shape of the orbital
• These are multiple energy states that are grouped
  very close together
• The number of sublevels (for each level) n
• n1 ? 1 sublevel
• n2 ? 2 sublevels
• n3 ? 3 sublevels
• n4 ? 4 sublevels

36
Orbital Quantum Number, m

• Describes the orientation of the orbital in
  space the direction in which it points.
• Degenerate orbitals those orbitals with the same
  size (n) and shape (l) which have the same
  energy. e.g.,
• the three 2p orbitals
• the five 3d orbitals

37
Electron Spin Quantum Number, s

• Electrons can spin either clockwise or
  counterclockwise
• s will have one of two values depending on the
  direction of rotation 1/2 or -1/2

38
Distribution of Electrons

• How are electrons distributed among the energy
  levels?
• In a neutral atom
• e-s protons atomic no.
• Electrons always fill the energy level and
  sublevel to produce the lowest energy arrangement
• No two electrons can have the same 4 quantum
  numbers
• (Pauli Exclusion Principle)
• The max. no. of e- in energy level n 2n2

39
Aufbau Principle

• Build up the electrons from the bottom
• The Aufbau Hotel

40
Hunds Rule

• Add one electron to each orbital of degenerate
  orbitals until all orbitals have at least one
  electron. Then start pairing up the remaining
  electrons.

41
Pauli Exclusion Principle

• No two electrons can have the same set of four
  (4) quantum numbers

42
Heisenberg Uncertainty Principle

• It is not possible to know precisely the position
  of an electron and its momentum (velocity) at the
  same instant.