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. BIV400-800 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 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

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 Balmer-Rydberg 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 Three-Dimensional 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