Transcript ATOMIC STRUCTURE & PERIODICITY (Part 1; sec 1-8) Light, Matter

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
• Based on observations of diffraction,
reflection, interference, refraction, CS
considered electromagnetic radiation (EM)
or light as a wave.
• Light=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.
• What were these observations?
FROM CS TO QM (2)
• A heated solid (blackbody) absorbs or emits
quantized energy packets (not continuous
packets), ΔE = nhν (n = integer) (Planck, 1900)
• 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)
FROM CS TO QM (3)
• As scientists worked to understand these
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.
– Recall λ = property of light and mv = property
of particle
– Note equivalency of wave and particle (duality)
Problems
• 34, 38, 42
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 = quantized = 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 (fingerprint). Fig 7.6
ATOMIC LINE SPECTRA (2)
• What do these spectra tell us about the
structure of the atom?
• 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 ≠ gas constant
ATOMIC LINE SPECTRA (3)
• The emission lines of the H atom in other
regions of the EM spectrum fit the BalmerRydberg 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
ATOMIC LINE SPECTRA (4)
• These eqns were a valuable tool to explain
the exptal observations of sharp line spectra
and also to predict other lines.
• But these eqns were not associated with the
structure of the atom. And the Rutherford
atom (existing theory) model was not
consistent with these eqns.
BOHR ATOM (Fig 7.8)
• Bohr proposed a “planetary” or quantum model of
the atom (1914) that was consistent with the eqns
• 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 BalmerRydberg Eqn.
Figure 7.8
Electronic
Transitions
in the Bohr
Model for
the
Hydrogen
Atom
BOHR ATOM (2)
• 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
• When an electron goes from one quantized
level (n) to another (m), light is emitted or
absorbed.
BOHR ATOM (2)
• 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.
Problems
• 46, 48, 50, 54
•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)
Figure 7.10
The
Hydrogen
Electron
Visualized
as a
Standing
Wave
Around the
Nucleus
QUANTUM MECHANICS (2)
• These standing waves (Ψ) are called wave
functions and are interpreted as the allowed
atomic orbitals for electrons in an atom.
• 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.
QUANTUM MECHANICS (3)
• 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 (4)
• 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 (5)
• 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
Problems
• 55, 60