Chapter Seven

1
Chapter Seven

• Atomic Structure

2
Outline

• History The Classic View of Atomic Structure
• Light and the Quantum Theory
• Quantum View of Atomic Structure

3
Cathode Ray Tube
Cathode rays move from cathode to anode
Cathode rays are the same regardless of the
cathode material (aluminum, iron, copper)
4
Cathode Ray Tube
Cathode rays are deflected in a magnetic field.
They have a charge.
5
Investigating Cathode Rays

• J.J. Thomson used the deflection and the
  magnetic field strength together, to find the
  cathode ray particles mass to charge ratio
• me /e 5.686 x 10-12 kg/C

6
Investigating Cathode Rays

• George Stoney names the cathode-ray particle
  the electron
• Robert Millikan determines a value for the
  electrons charge
• e 1.602 x 10-19 C

7
Investigating Cathode Rays

• Knowing the mass-to-charge ratio, and the charge,
  we can find the mass of an electron
• me 9.109 x 10-31 kg/electron

• Some investigators thought that cathode rays
  were negatively charged ions.
• But this mass is much smaller than even a
  hydrogen atom.
• Since cathode rays are the same regardless of
  the cathode material, these tiny particles must
  be a negative part of all matter.

8
J.J. Thomsons Model

• J.J. Thomson proposed an atom with a positively
  charged sphere containing equally spaced
  electrons inside.

9
Alpha Scattering ExperimentRutherfords
observations
A few alpha particles were deflected by the foil.
A very few bounced back to the source!
Most of the alpha particles passed through the
foil.
10
Alpha Scattering Experiment Rutherfords
conclusions
Nucleus is MUCH smaller than suggested here.

• Most of the alpha particles pass through
  undeflected ? Most of the atom
  is empty space.
• A few alpha particles are greatly deflected
  ? The nucleus is
  very tiny and is positively charged.

11
Rutherfords Model of the Atom

• can be visualized as a giant indoor football
  stadium.
• The nucleus can be represented by a pea in the
  center of the stadium.
• The electrons are a few bees buzzing throughout.
• The roof of the stadium prevents the bees from
  leaving.
• Electrons remain in the atom because they are
  strongly attracted to the positively charged
  nucleus.

12
Protons And Neutrons

• Rutherfords experiments also told him the amount
  of positive nuclear charge.
• The positive charge was carried by particles that
  were named protons
• The proton charge was the fundamental unit of
  positive charge
• The nucleus of a hydrogen atom consisted of a
  single proton
• Scientists introduced the concept of atomic
  number which represents the number of protons in
  the nucleus of an atom
• James Chadwick discovered neutrons in the
  nucleus, which have nearly the same mass as
  protons and no charge

13
Mass Spectrometry

• Research into cathode rays showed that a
  cathode-ray tube also produced
  .
• Unlike cathode rays, these particles were
  ions.
• The metal of the cathode M ? e- M

positive particles
Cathode rays
14
Mass Spectrometry

• In mass spectrometry a stream of positive ions
  having equal velocities is brought into a
  magnetic field.
• All the ions are deflected from their straight
  line paths.
• The lightest ions are deflected the most the
  heaviest ions are deflected the least.
• The ions are thus separated by mass.

15
A Mass Spectrometer
Which isotope of mercury appears to be most
abundant?
Ions are deflected according to mass
16
A Mass Spectrum For Mercury
Mass spectrum of an element shows the abundance
of its isotopes.
The mass spectrum of a compound can
give information about the structure of
the compound.
17
The Wave Nature Of Light

• Electromagnetic waves originate from the movement
  of electric charges
• The movement produces fluctuations in electric
  and magnetic fields
• Electromagnetic waves require no medium
• Electromagnetic radiation is characterized by its
  wavelength, frequency, and amplitude.

18
Simplest Wave Motion
19
An Electromagnetic Wave
the wiggles seen here indicate field strength.
The waves dont wiggle as they propogate
20
Wavelength And Frequency

• Wavelength is the distance between any two
  identical points in consecutive cycles
• Wavelength is denoted by the Greek letter ?
  (lambda)
• Frequency of a wave is the number of cycles of
  the wave that pass through a point in a unit of
  time
• Frequency is denoted by the Greek letter v (nu)
  and is measured in hertz.

What are the units of wave-length?
21
Wavelength And Frequency

• The relationship between wavelength and
  frequency
• c ?v
• where c is the speed of light (3.00 x 108 m/s)

22
The Electromagnetic Spectrum
Communications involve longer wavelength, lower
frequency radiation.
UV, X-rays are shorter wavelength, higher
frequency radiation
Visible light is a small portion of the spectrum.
23
A Continuous Spectrum

• White light from a lamp contains all wavelengths
  of visible light.
• When that light is passed through a prism, the
  different wavelengths are separated.
• We see a spectrum of all rainbow colors from red
  to violet a continuous spectrum.

24
A Line Spectrum

• Light from an electrical discharge through a
  gaseous element (like a neon lamp) does NOT
  contain all wavelengths.
• The spectrum is discontinuous there are big
  gaps.
• We see a pattern of lines this is called a line
  spectrum.

A helium lamp, a neon lamp, a light bulb emit
light each produces an emission spectrum.
25
Visible Spectrum of Hydrogen
This emission from a hydrogen lamp consists of
four wavelengths of light. Not an infinite
number of wavelengthsjust four
26
Line Spectra of Some Elements
The line emission spectrum of an element is a
fingerprint for that element. It can be used
to identify that element!
How could you tell if there was gold in an ore
sample? Look at the emission spectrum from the
sample! Do you see gold lines?
27
Planck

• proposed that atoms could absorb or emit
  electromagnetic energy only in discrete amounts.
• The smallest amount of energy, a quantum, is
  given by
• E hv
• where Plancks constant, h, has a value of 6.626
  X 10-34 Js.
• Plancks quantum hypothesis states that energy
  can be absorbed or emitted only as a quantum or
  as whole multiples of a quantum, thereby making
  variations of energy discontinuous
• Changes in energy can only occur in discrete
  amounts.
• Quantum is to energy as _______ is to matter

28
The Photoelectric Effect

• The photoelectric effect light striking a metal
  surface can cause ejection of electrons.
• The photoelectric effect is used in light
  sensors.
• Why does the photoelectric effect occur?

29
The Photoelectric Effect

• Albert Einstein electromagnetic energy occurs
  in little packets called photons.
• Energy of photon (E) hv
• Photoelectric effect light strikes a surface
  hit surface electrons and transfer their energy
• The energized electrons can overcome their
  attraction and escape from the surface

For one photon. So what is the energy of a mole
of photons of a given frequency?
30
Bohrs Hydrogen Atom

• Niels Bohr proposed that electron energy (En) was
  quantized, that is, that it could have only
  certain specified values (just as energy itself
  is quantized).
• Each specified energy value is called an energy
  level of the atom
• En -B/n2
• n is an integer, and B is a constant (2.179 x
  10-18 J)
• The negative sign represents the force of
  attraction
• The energy is zero when the electron is located
  infinitely far from nucleus.

31
The Bohr Model
Each circle represents an allowed energy level.
Emission atom gives off energy (as a photon)
An electron drops to a lower energy level.
Excitation atom absorbs energy that is exactly
equal to the difference between two energy levels.
An electron attains a higher energy level.
32
Line Spectra Arise Because

• each electronic energy level in an atom is
  quantized.
• Since the levels are quantized, changes between
  levels must also be quantized.

Transition from n 4 to n 2.
Transition from n 3 to n 2.
33
Bohrs Equation

• allows us to find the energy change (?Elevel)
  that accompanies the transition of an electron
  from one energy level to another.
• Initial energy level
  Final energy level
• Ei -B / ni2 Ef -B
  / nf2
• To find the energy difference, just subtract
• ?Elevel -B / nf2 -B / ni2 B(1/ni2
  1/nf2)
• Together, all the photons of this energy produce
  one spectral line.

34
Energy Levels and Spectral Lines for Hydrogen
35
Ground States and Excited States

• When an atom has its electrons in their lowest
  possible energy levels, it is in its ground
  state.
• When an electron has been promoted to a higher
  level, it is in an excited state.
• Electrons are promoted through an electric
  discharge, heat, or some other source of energy.
• An atom in an excited state eventually emits
  photons as the electron drops back down to the
  ground state.

36
Electronic Transitions
Without calculation, determine which transition
(a, b, c, d) corresponds to emission of the
shortest wavelength from a hydrogen atom.
37
De Broglies Equation

• Louis de Broglie matter behaves as both
  particles and waves, just as light does.
• A particle with mass m moving at a speed v will
  have a wave nature consistent with a wavelength
  given by the equation
• ? h/mv
• De Broglies prediction of matter waves led to
  the development of the electron microscope.

38
Uh oh

• de Broglie just messed up our model of the atom.
• We cant talk about where the electron is if
  the electron is a wave. (An ocean wave doesnt
  have an exact locationneither does an electron
  wave)
• Worse the wavelength of a moving electron is
  roughly the size of an atom! How do we describe
  an electron that isnt in the atom??

39
Wave Functions

• We describe the electron mathematically, using
  quantum mechanics (wave mechanics).
• Erwin Schrodinger developed a wave equation to
  describe the hydrogen atom
• An acceptable solution to Schrodingers wave
  equation is called a wave function.
• A wave function represents an energy state of the
  atom.

40
The Uncertainty Principle

• Werner Heisenberg we cant simultaneously know
  exactly where a moving particle is AND exactly
  how fast it is moving.
• The act of measurement actually interferes with
  the particle.
• A wave function doesnt tell us where the
  electron is. The uncertainty principle tells us
  that we cant know where the electron is.
• However, the square of a wave function gives the
  probability of finding an electron at a given
  location in an atom.

41
Quantum Numbers And Atomic Orbitals

• The wave functions for the hydrogen atom contain
  three parameters that must have specific integral
  values called quantum numbers.
• A wave function with a given set of these three
  quantum numbers is called an atomic orbital.
• These orbitals allow us to visualize the region
  in which the electron spends its time.

42
Quantum Numbers

• When values are given to quantum numbers, a
  specific atomic orbital is defined.
• The principal quantum number (n)
• Is independent of the other two quantum numbers.
• Can only be a positive integer (n 1, 2, 3, 4)
• The size of an orbital and its electron energy
  depend on the value of n.
• Orbitals with the same value of n are said to be
  in the same principal shell.

43
Quantum Numbers (contd)
An orbital for which n 1 the electron spends
much of its time very near the nucleus.
An orbital for which n 2 the electron is often
farther from the nucleus.
An orbital for which n 3 the electron is often
even farther from the nucleus.
44
Quantum Numbers (contd)

• The orbital angular momentum quantum number (l)
• Determines the shape of the orbital.
• Can have positive integral values from 0, 1, 2
  (n 1)
• Orbitals having the same values of n and of l are
  said to be in the same subshell
• Subshells are also designated by a letter
• Value of l 0 1 2 3
• Subshell s p d f
• Each orbital designation represents a different
  region of space and a different shape.

45
Quantum Numbers (contd)

• The magnetic quantum number (ml)
• Determines the orientation in space of the
  orbitals of any given type in a subshell
• Can be any integer from -l to l
• The number of possible values for ml is
• (2l 1), and this determines the number of
  orbitals in a subshell

46
Quantum Numbers Summary
Notice one s orbital in each principal
shell three p orbitals in the second shell (and
in higher ones) five d orbitals in the third
shell (and in higher ones)
47
The 1s Orbital

• The 1s orbital very much like a fuzzy ball, that
  is, the orbital has spherical symmetry.
• An electron in this orbital spends most of its
  time near the nucleus.

The electron cloud doesnt stop at the spheres
surface
the electron just spends very little time
farther out.
48
The 2s Orbital

• The 2s orbital has two regions of high electron
  probability, both being spherical
• The region near the nucleus is separated from the
  outer region by a spherical node a spherical
  shell at which the electron probability is zero.

Node
49
The Three p Orbitals
Three orbitals in the p subshell three
different values of l
50
The Five d Orbital Shapes
Five orbitals in the d subshell five different
values of l
51
Electron Spin

• The electron spin quantum number (ms) explains
  some of the finer features of atomic emission
  spectra
• The number can have two values ½ and ½
• The spin refers to a magnetic field induced by
  the moving electric charge of the electron as it
  spins
• The magnetic fields of two electrons with
  opposite spins cancel one another there is no
  net magnetic field for the pair.

52
The Stern-Gerlach Experiment
Silver has an odd number of electrons, so the ½
and ½ spins do not cancel. The beam of silver
atoms is split in two.
53
Summary

• Cathode rays are negatively charged fundamental
  particles of matter, now called electrons.
• An electron bears one fundamental unit of
  negative electric charge.
• A nucleus of an atom consists of protons and
  neutrons and contains practically all the mass of
  an atom.
• Mass spectrometry establishes atomic masses and
  relative abundances of the isotopes of an element
• Electromagnetic radiation is an energy
  transmission in the form of oscillating electric
  and magnetic fields.

54
Summary (continued)

• The oscillations produce waves that are
  characterized by their frequencies (v),
  wavelengths (?), and velocity (c).
• The complete span of possibilities for frequency
  and wavelength is described as the
  electromagnetic spectrum.
• Plancks explanation of quantization gave us E
  hv
• The photoelectric effect is explained by thinking
  of quanta of energy as concentrated into
  particles of light called photons.
• Wave functions require the assignment of three
  quantum numbers principal quantum number, n,
  orbital angular momentum quantum number, l, and
  magnetic quantum number, ml.

55
Summary (continued)

• Wave functions with acceptable values of the
  three quantum numbers are called atomic orbitals.
• Orbitals describe regions in an atom that have a
  high probability of containing an electron or a
  high electronic charge density.
• Shapes associated with orbitals depend on the
  value of l. Thus, an s orbital (l 0) is
  spherical and a p orbital (l 1) is
  dumbbell-shaped.
• A fourth quantum number is also required to
  characterize an electron in an orbital - the spin
  quantum number, ms.