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ATOMIC STRUCTURE &
PERIODICITY (Part 1; sec 1-8)
Light, Matter
Structure of the one-electron atom
Quantum Mechanics
STRUCTURE OF ATOM
(Pre-1900; Classical Science = CS)
• Electrons (-1 charge) and Protons (+1
charge) had been observed.
• Models of the Atom
– “Raisin Pudding”: J.J. Thomson
– Small positive nucleus surrounded by a lot of
empty space through which the electrons are
dispersed: Rutherford (1911)
• A third sub-atomic particle, the Neutron was
discovered by Chadwick (1932)
LIGHT or EM RADIATION:
WAVE
• CS considered electromagnetic radiation
(EM) or light as a wave based on
observations of diffraction, reflection,
interference, refraction.
• Form of energy, delocalized, no mass
• Wavelength, λ = c/ν
m
• Frequency, ν
Hz = 1/s
• Speed, c = λ ν
3.00E+08 m/s
Figure 7.1
The Nature
of Waves
ELECTROMAGNETIC
SPECTRUM
• Light or electromagnetic radiation spans
many orders of magnitude in E, ν, and λ.
• Figure 7.2
• Visible: ROY G. BIV
400-800 nm
• At lower E and ν , λ increases: Infrared,
microwave, radiowave
• At higher E and ν , λ decreases: Ultraviolet,
X-rays, gamma-rays
ELECTRONS, PROTONS,
NEUTRONS: PARTICLES
• CS considered these subatomic particles to
be particles with mass (m), velocity (v) and
momentum (mv)
• It was assumed that an object was either a
wave (light) or a particle (electron).
FROM CLASSICAL TO
QUANTUM THEORY
• From the late 1800’s to the 1920’s, many
experimental observations that could not be
explained by CS were recorded. These led
to the development of Quantum Mechanics
(QM) and a new structure of the atom.
– A heated solid (blackbody) absorbs or emits
quantized energy packets (not continuous
packets), ΔE = nhν (n = integer) (Planck, 1900)
FROM CS TO QM (2)
– Radiation is quantized and consists of particle waves
called photons: photoelectric effect, Eph = hν = hc/λ
(Einstein, 1905)
– Particles have wave properties: electron diffraction
– Atomic line spectra (Balmer,1885)
• As scientists worked to understand these and other
exptal results, several conclusions emerged:
– Electrons have WAVE and particle properties.
– Light has PARTICLE and wave properties.
– deBroglie Eqn expresses this: λ = h/mv; duality of
nature
PHOTOELECTRIC EFFECT
• Expt: Shine light on clean metal surface
and detect electrons ejected from metal.
– Vary Energy (E = hν = hc/λ) and Intensity of
light
– Measure number (#) and kinetic energy of
electrons (KE = 1/2 mv2).
PHOTOELECTRIC EFFECT (2)
• Observations ( conflicted with CS)
– Light must have a minimum energy value in order to
eject electrons; this is called the threshold energy = hνo .
(CS said no threshold energy exists).
– If Eph > hνo, then # of electrons increased with the
intensity of light. (CS said # electrons increased with
frequency of light).
– If Eph > hνo, then KE of electrons increased with the
frequency of light. (CS said # electrons increased with
intensity of light).
PHOTOELECTRIC EFFECT (3)
• Conclusions
– Energy of photon = hν = hνo + 1/2 mv2 if
hν>hνo Conservation of energy statement.
– If hν>hνo , then no electrons are ejected.
– Energy of light = mc2 means that light has
“mass” (apparent mass, relativistic mass)
m = E/c2 = h/ λc
– Light = wave AND particle (photon) with
quantized energy
ATOMIC LINE SPECTRA
• CS: Rutherford model of the atom.
• Expt: When atoms are excited, they return to their
stable states by emitting light. This light can be
recorded to produce an atomic spectrum. Early
experiments showed that the spectra consists of
lines and that atoms from different elements gave
different line spectra. Fig 7.6
• What do these spectra tell us about the structure of
the atom?
ATOMIC LINE SPECTRA (2)
• Balmer measured the emission spectrum of H and
fit the observed wavelengths of the emitted light to
an equation:
• ν = Rc (1/22 – 1/n2) where R = Rydberg constant =
1.097E-2 1/nm
• The emission lines of the H atom in other regions
of the EM spectrum fit the Balmer-Rydberg Eqn:
ν = Rc (1/m2 – 1/n2) for n > m; n and m are
integers or quantum numbers. (empirical eqn.)
• Each emission line is associated with an electron
going from state n to state m.
Figure 7.7 A Change Between Two
Discrete Energy Levels Emits a
Photon of Light
BOHR ATOM (Fig 7.8)
• The Rutherford model could not explain these results, but
Bohr’s “planetary” or quantum model could (1914).
• Bohr assumed quantized orbital angular momentum values
such that when centrifugal force out (merry-go-round) =
electrostatic attraction in, the electron was in a stable state.
• This model led to quantized electronic energy levels and to
an eqn consistent with the Balmer-Rydberg Eqn.
• The energy of an electron in the nth energy level is
quantized and equals En = - hcRZ2/n2 = -2.178E-18 Z2/n2 J
where n = 1, 2, 3...; note energies of bound states < 0
BOHR ATOM (2)
• Then when an electron goes from one quantized
level (n) to another (m), light is emitted or
absorbed.
• The energy of this light is ΔE = hc/ λ = hν = Rhc
(1/m2 – 1/n2). (based on theory of atom)
• The wavelength of the light is 1/λ = R(1/m2 -1/n2 )
• The Bohr atom is the basis for the modern theory
of the atom but it has limitations. For example, it
is only accurate for 1-electron atoms and ions.
Figure 7.8
Electronic
Transitions
in the Bohr
Model for
the
Hydrogen
Atom
•QUANTUM MECHANICS
(Schrodinger, 1926)
• The QM model of the atom replaced the
Bohr model. This model is based on
electron’s wave properties.
• The stable states of the electron in an atom
are viewed as standing waves around the
nucleus. (Fig 7.10)
• These standing waves (Ψ) are called wave
functions and are interpreted as the allowed
atomic orbitals for electrons in an atom.
Figure 7.10
The
Hydrogen
Electron
Visualized
as a
Standing
Wave
Around the
Nucleus
QUANTUM MECHANICS (2)
• The goal of QM is to solve the Schrodinger Eqn,
H Ψ = E Ψ; i.e. find Ψ = atomic orbital plus the
associated (quantized) energy for these stable
states of the electron in the hydrogen atom.
• Ψ2 is related to the probability of finding an
electron at a particular (x,y,z) location. Ψ2 is called
the probability distribution. (Fig 7.11)
• Ψ2 4πr2 is the radial probability distribution (Fig
7.12); probability of finding electron at a
particular r value and any angular values.
Figure 7.11 a&b (a)
The Probability
Distribution for the
Hydrogen 1s
(GROUND STATE)
Orbital in ThreeDimensional Space
(b) The Probability
of Finding the H 1s
Electron at Points
Along a Line Drawn
From the Nucleus
Outward in Any
Direction
Figure 7.12 a&b Cross Section of the Hydrogen
1s Orbital Probability Distribution Divided into
Successive Thin Spherical Shells (b) The Radial
Probability Distribution (max = ao = 5.29E-2 nm)
QUANTUM MECHANICS (3)
• Heisenberg Uncertainty Principle (1927)
states that we cannot know the position and
momentum of an electron (considered a
wave) exactly. (vs CS)
• Δx Δ(mv) ≥ h/4 π
• Neither Δx nor Δ(mv) can be zero.
QUANTUM MECHANICS (4)
• The Ψ = wave function = orbital for a stable
state of the electron.
• Each Ψ is defined by 3 quantum numbers
that are related to each other; a set of Ψs
lead to atomic electronic configurations.
• QM is the basis for understanding chemical
bonding, molecular shapes (Chap.8 and 9),
chem reactions, phys. and chem. properties.
ATOMIC ORBITALS AO) and
QUANTUM NUMBERS (QN)
• Principal QN, n = 1, 2, 3…(K, L, M...shell);
determines energy (quantized) and size of
atomic orbital.
• Angular momentum QN, ℓ = 0, 1, 2…n-1
(s, p, d… subshell); determines shape of
atomic orbital. For each n value, there are n
ℓvalues. Fig 7.14-17)
Figure 7.13 Two
Representations of
the Hydrogen 1s,
2s, and 3s Orbitals
(a) The Electron
Probability
Distribution (b)
The Surface
Contains 90% of
the Total Electron
Probability (the
Size of the Oribital,
by Definition)
Figure 7.14 a&b Representation of the 2p
Orbitals (a) The Electron Probability Distribution
for a 2p Oribtal (b) The Boundary Surface
Representations of all Three 2p Orbitals
Figure 7.16 a&b Representation of the 3d
Orbitals (a) Electron Density Plots of Selected 3d
Orbitals (b) The Boundary Surfaces of All of the
3d Orbitals
Figure 7.17 Representation of the 4f Orbitals in
Terms of Their Boundary Surfaces
AOs and QNs (2)
• Magnetic, mℓ = - ℓ, …-2, -1, 0, +1, +2, …+
ℓ; determines spatial orientation of orbital.
For each ℓ value, there are 2ℓ + 1 mℓ values.
• Spin, ms = +1/2, -1/2; determines
orientation of electron spin axis.
AOs and QNs (3)
• There are relationships (limitations)
between four quantum numbers (Table 7.2)
• For the H atom and other one-electron
atoms, all AOs with the same n value have
the same energy. This is called energy
degeneracy. (Fig 7.18)
Figure 7.18 Orbital Energy Levels
for the Hydrogen Atom