Electronic Structure of Atoms

1
Electronic Structure of Atoms

• In this chapter we will explore, the quantum
  theory and its importance in the study of
  chemistry. We will look more closely at the
  nature of light and how our study of light has
  changed the quantum theory to explain how
  electrons are arranged in an atom.

2
The Wave Nature of Light

• Much of our present understanding of the
  electronic structure of atoms has come from
  analysis of light either emitted or absorbed by
  substances.
• Light we see, visible light, is an example of
  electromagnetic radiation, which is also known as
  radiant energy because it carries energy through
  space.
• Many different forms of electromagnetic
  radiation, from radio waves to gamma rays, differ
  from each other but also share many fundamental
  characteristics
• Speed of light (c) in a vacuum is 3.00 X 108 m/s
• Wavelength (?) is from one point on one wave to
  the same point on the next wave expressed in
  meters.
• Frequency (?) is the number of complete
  wavelengths or cycles that pass a certain point
  each second expressed as cycles/second or Hertz.
• The inverse relationship between the frequency
  and the wavelength of electromagnetic radiation
  can be expressed by the equation c??
• Sample Exercise 6.2 pg 215

3
Electromagnetic Spectrum
4
Quantized Energy and Photons

• When solids are heated, they emit radiation as
  seen in the red glow of stove and the bright
  white light of a tungsten light bulb.
• The wavelength distribution of the radiation
  depends on temperature.
• In 1900, Max Planck assumed that energy can be
  either be released or absorbed by atoms only in
  discrete chunks of some minimum size. Planck
  gave the name quantum to the smallest quantity of
  energy that can be emitted or absorbed as
  electromagnetic radiation.
• He proposed that the energy, E, of a single
  quantum equals a constant time the frequency, ?,
  of the radiation Eh?
• The constant H is called Plancks constant and
  has a value of
• 6.626 X 10-34 Joule seconds.
• According to Plancks theory, matter is allowed
  to emit and absorb energy only in whole number
  multiple of h?, such as 2h?, 3h? and 4h?.
• This theory can be compared to walking up stairs.
  As you can only step on individual stairs or
  multiples stairs but not between them so your
  increase in potential energy is restricted to
  certain values and is therefore quantized.

Shows the device built by NIST researchers to
perform a high-precision measurement of Planck's
constant, the number which describes the
bundle-like nature of matter and energy at the
atomic and subatomic scales. The electrical power
associated with the mechanical motions of the
system contains quantities proportional to
Planck's constant.
5
Photoelectric Effect and Photons

• In 1905, Einstein used Plancks quantum theory to
  explain the photoelectric effect.
• Experiments had shown that light shining on a
  clean metal surface causes the surface to emit
  electrons. Each metal has a minimum frequency of
  light below which no electrons are emitted.
• Einstein assumed that the radiant energy striking
  the metal surface does not behave like a wave but
  rather as if it were a stream of tiny energy
  packets. Each energy packet, called a photon
  behaves like a tiny particle.
• Extending Plancks quantum theory, Einstein
  deduced that each photon must have an energy
  equal to Plancks constant times the frequency of
  the light.
• Analysis of data from the photoelectric
  experiment showed that the energy of the ejected
  electrons was proportional to the frequency of
  the illuminating light. This showed that whatever
  was knocking the electrons out had an energy
  proportional to light frequency. The remarkable
  fact that the ejection energy was independent of
  the total energy of illumination showed that the
  interaction must be like that of a particle which
  gave all of its energy to the electron!
• This fit in well with Planck's hypothesis that
  light in the blackbody radiation experiment could
  exist only in discrete bundles with energy.
• Sample Exercise 6.3 and Practice Exercise pg 217

6
Line Spectra

• The work of Planck and Einstein paved the way for
  understanding how electrons are arranged in
  atoms.
• In 1913, Danish physicist Niels Bohr offered a
  theoretical explanation of line spectra. Most
  common radiation sources, including light bulbs
  and stars, produce radiation containing many
  different wavelengths.
• A spectrum is produced when radiation from such
  sources is separated into its different
  wavelength components. A prism spreads light from
  a white light source into its component
  wavelengths of a continuous range. A rainbow
  occurs when raindrops acts as a prisms to
  separate sunlight.
• Not all radiation sources produce a continuous
  spectrum.
• When a high voltage is applied to tubes that
  contain different gases under reduced pressure,
  the gases emit different colors of light.
• When that light is passed through a prism only a
  few wavelengths are present in the resultant
  spectra which is called a line spectra.

7

• When scientists first detected the line spectrum
  of hydrogen in the mid 1800s, they were
  fascinated by it simplicity. At that time, only
  the four lines in the visible portion of the
  spectrum were observed as shown in 6.13 pg 219.
• These lines correspond to wavelengths of 410nm,
  434 nm, 486nm and 656nm.
• In 1885, a Swiss named Johann Balmer showed that
  the wavelengths of these four visible lines of
  hydrogen fit a simple formula.
• Soon Balmers equation was extended to a more
  general one, called the Rydberg equation.

8
Bohrs Model

• Rutherfords discovery of the nuclear nature of
  the atom suggests that the atom can be thought of
  as a microscopic solar system in which
  electrons orbit the nucleus.
• To explain the line spectrum of hydrogen, Bohr
  assumed that electrons move in circular orbits
  around the nucleus.
• According to classic physics though, an
  electrically charged particle (such as an
  electron) that moves in a circular path should
  continuously lose energy by emitting
  electromagnetic radiation. As the electron loses
  energy, it should spiral into the positively
  charged nucleus. But since hydrogen atoms are
  stable this must not be happening. Borh based his
  model therefore on three postulates to explain
  this contradiction.
• Only orbits of certain radii, corresponding to
  certain definite energies, are permitted for the
  electron in a hydrogen atom.
• An electron in a permitted orbit has a specific
  energy and is in an allowed energy state. An
  electron in an allowed energy state will not
  radiate energy and therefore will not spiral into
  the nucleus.
• Energy is emitted or absorbed by the electron
  only as the electron changes from one allowed
  energy state to another. This energy is emitted
  or absorbed as a photon, Ehv

9
Energy States of Hydrogen Atom

• Bohr calculated the energies corresponding to
  each allowed orbit for the electron in the
  hydrogen atom using the following formula
• E(-hc/RH)(1/n2)
• In this equation, h is Plancks constant, c is
  the speed of light and RH is the Rydberg
  constant, which means they can all be multiplied
  together to simplify the equation to
• E(-2.18 X 10-18J)(1/n2)
• Where n is called the principle quantum number or
  energy level from 1 to infinity. Each orbit has a
  different number for n increasing out from the
  nucleus with 1 being closest to the nucleus.
• The energies of the electron of a hydrogen atom
  given by the above equation are negative for all
  values of n. The lower (more negative) the energy
  is, the more stable the atom will be. Since the
  energy is lowest for n1, when the electron is
  there, the atom is the most stable. This is why
  n1 is called the ground state.
• When the electron is in a higher energy orbit it
  is said to be in an excited state.
• In his third postulate, Bohr assumed that the
  electron could jump from one allowed energy
  state to another by either absorbing or emitting
  photons whose radiant energy corresponds exactly
  to the energy difference between the two states.
  Energy must be absorbed for an electron to go to
  a higher energy state and be emitted to fall to a
  lower state, so only specific energies of light
  can be absorbed and emitted by the electron in
  the hydrogen atom. Animation
• Therefore, the existence of discrete spectral
  lines are due to the quantized jumps of electrons
  between energy levels.

10
Results of Bohrs Model

• Model worked great to explain the hydrogen atom,
  but not for any other atom.
• Avoided problem of why the electron didnt fall
  into the nucleus.
• Became an important step to the excepted model
  today, as two ideas are also incorporated into
  our current model
• Electrons exist only in certain discrete energy
  levels, which are described by quantum numbers
• Energy is involved in moving an electron from one
  level to another.

11
Wave Behavior of Matter

• In the years following Bohrs model, the dual
  nature of light became a familiar concept, which
  says that light appears to have either wavelike
  or particle-like characteristics. It was thought
  then that if light could behave as a stream of
  particles then maybe matter could have properties
  of a wave.
• Louis de Broglie suggested that as the electron
  moves about the nucleus, it is associated with a
  particular wavelength, and that the
  characteristic wavelength of the electron depends
  on its mass, m and on its velocity, v, by the
  equation ?h/mv.
• Within a few years, the wave properties of the
  electron were demonstrated experimentally. As
  electrons passed through a crystal, they were
  diffracted by the crystal, just as x-rays are
  diffracted. Thus, a stream of electrons exhibits
  the same kinds of wave behavior as
  electromagnetic radiation and has both particle
  and wavelike characteristics.
• The technique of electron diffraction has been
  highly developed to produce such things as the
  electron microscope which can obtain images at
  the atomic level.

Spider
Pollen
Atoms
12
Uncertainty Principle

• German physicist Werner Heisenberg proposed that
  the dual nature of matter places a fundamental
  limitation on how precisely we can know both the
  location and the momentum of any object.
• This is only significant for things as small as
  an electron as a small change in its position
  often due to the measuring device is more
  significant than a small change in our positions.
  
• When applied to electrons it is impossible to
  know both the momentum of the electron and its
  exact location in space at the same time.

13
Quantum Mechanics and Atomic Orbitals

• In 1926, Austrian physicist Erwin Schröndinger
  proposed a wave equation that incorporates the
  wavelike and particle like behavior of the
  electron.
• We wont go into the equation but look at the
  results he obtained that led to the current view
  of the atom.
• Just like when a guitar string is plucked and
  creates a fuzz showing where the string is most
  likely located. An electron that is moving around
  a nucleus at a rapid wavelike speed forms a cloud
  where there is a high probability that the
  electron can be found.
• The solution to Schrödinger's equation for the
  atom yields a set of wave functions and
  corresponding energies. These wave functions are
  called orbitals and each orbital describes a
  specific distribution of electron density in
  space.
• There are three quantum numbers that describe the
  orbitals where the electrons in an atom are
  found.

Greatest probability of finding the electron
14
Quantum Numbers

• 1. The principle quantum number, n, has numerical
  values of 1-7. As n increases, the orbital
  (distribution of electron density) becomes
  larger. And the electron spends more time farther
  from the nucleus. An increase in n also mean that
  the electron has a higher energy and is therefore
  less tightly bound to the nucleus.
• 2. The angular momentum quantum number, ? , has
  numerical values from 0 to (n-1) for each value
  of n. This quantum number defines the shapes of
  the orbital and is more often described by the
  letters s p d f instead of the numerical values
  (s0, p1, d2, f3).
• The magnetic quantum number, m?, has numerical
  values between ? and -? including 0. this quantum
  number describes the orientation of the orbital
  in space.
• The collection of orbitals with the same value of
  n is called an electron shell. All orbitals that
  have n3, for example, are said to be in the
  third shell. Each subshell is designated by a
  number (the value of n) and a letter (s, p, d or
  f).
• Review all with Table 6.2 on page 227.

s
p
d
f
15

• The principle quantum number also states the
  number of subshells in the whole shell. For
  example, when n1 then there is only 1 subshell
  (1s) in the 1st shell and when n2 then there are
  2 subshells (2s and 2p) in the 2nd shell.
• Every s subshell contains 1 orbital (only one
  orientation in space), every p subshell contains
  3 orbitals (3 orientations in space x,y,z), every
  d subshell contains 5 orbitals (5 orientations in
  space xy, xz, yz,x2-y2, z2), and every f subshell
  contains 7 orbitals (7 orientations in space).
• In hydrogen, no matter what subshell the electron
  is in within one shell, it will have the same
  energy such as 3s, 3p or 3d.
• In many electron atoms, however, the
  electron-electron repulsion causes the different
  subshells to be at different energies but the
  orbitals within a subshell to be equal.

16
Electron Spin

• We know where the electron that hydrogen has
  resides in the ground state (1s) but where do the
  electrons in the many electron atoms reside.
• When scientists studied the line spectra of many
  electron atoms in great detail, they noticed that
  lines that were originally thought to be single
  were actually closely packed pairs. This meant
  that there were twice as many energy levels as
  there were supposed to be.
• In 1925, George Uhlenbeck and Sam Goudsmit
  proposed that electrons have an intrinsic
  property, called electron spin, that causes each
  electron to behave as if it were a tiny sphere
  spinning on its own axis.
• This observation led to the fourth and final
  quantum number for the electron, the spin
  magnetic number, ms. The two numerical values for
  are ½ and ½, which was first interpreted as
  indicating the two opposite directions in which
  the electron can spin.
• A spinning charge produces a magnetic field so
  the two opposite directions of spin therefore
  produce oppositely directed magnetic field. These
  two opposite magnetic fields lead to the
  splitting of spectral lines into closely spaced
  pairs.

17
Pauli Exclusion Principle

• Electron spin is crucial for the electron
  structure of atoms.
• In 1925, Wolfgang Pauli discovered the principle
  that governs the arrangements of electrons in
  many electron atoms.
• The Pauli Exclusion Principle states that no two
  electrons in an atom can have the same four
  quantum numbers, n, ? , m?, ms.
• Following this principle, an orbital can hold a
  maximum of two electrons and they must have
  opposite spins.
• Now we can look at how electrons are arranged in
  the various orbitals for many electron atoms,
  which is called the electron configuration.
• The most stable electron configuration of an
  atomthe ground state-is that in which the
  electrons are in the lowest possible energy
  states.
• Thus orbitals are filled in order of increasing
  energy with no more than two electrons in each
  orbital.
• Finally Hunds rule says that for orbitals with
  equal energies, the lowest energy is attained
  when the number of electons with the same spin is
  maximized (1 in each first then the second ones
  go in with opposite spins).