AP Chapter 6

Electronic Structure of AtomsHW: 5 7 29 35 63 67 69 71 73 75

-Electromagnetic Radiation = Emission and transmission of energy in the form of waves

-examples: visible light, infrared, UV, X-Rays-Electromagnetic wave = Travels at the speed of light = 3.0x108 m/s in a vacuum

6.1 – Wave Nature of Light

Electromagnetic Spectrum = (display of electromagnetic radiation by wavelength)

6.1 – Wave Nature of Light-Wavelength = l = Distance between identical points on successive

waves. Unit = Angstrom (A), nm, mm-Frequency = n = # of waves passing a point in a given unit of time

(typically 1 second). Unit = Hz = 1/s-Speed of the wave = c = ln

-Amplitude = Height-Node = Amplitude = 0

A high frequency wave must have a short wavelengthA low frequency wave must have a long wavelength

6.1 – Wave Nature of Light

Calculate:The yellow light given off by a sodium vapor lamp

used for public lighting has a wavelength of 589 nm. What is the frequency of this radiation?

(answer = 5.09 x 1014 s-1)

• Wave nature alone cannot explain all behaviors of light– Emission of light from hot objects

(blackbody radiation)

– Emission of electrons from metal surfaces on which light shines (photoelectric effect)

– Emission of light from electronically excited gas atoms (emission spectra)

6.2 – Quantized Energy and Photons

6.2 – Quantized Energy and Photons• He concluded that energy of a single quantum is equal

to a constant times the frequency of the radiation:E = h

where h is Planck’s constant, 6.63 10−34 Js.• Max Planck explained it by assuming that energy

comes in “chunks” called quanta.• Quantum = The smallest quantity of energy that can

be emitted or absorbed• Quantum Theory – Atoms and molecules emit and

absorb energy in discrete quantities only• Photon = A quantum of light energy

• Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light:

c = E = h

6.2 – Quantized Energy and Photonsa) A laser emits light with a frequency of 4.69 x 1014 s-1.

What is the energy of one photon of the radiation from this laser?

b) If the laser emits a pulse of energy containing 5.0 x 1017 photons, what is the total energy of that pulse?

c) If the laser emits 1.3 x 10-2 J of energy during a pulse, how many photons are emitted during the pulse?

Answers:d) 3.11 x 10-19 Je) 0.16 Jf) 4.2 x 1016 photons

6.3 – Line Spectra and the Bohr Model

When observing the emission spectra of atoms/molecules, only a line spectrum of discrete wavelengths is observed.

Emission Spectrum = Spectrum of radiation emitted by a substance/energy source – can be continuous or line spectrum depending on the substance

(continuous spectrum)

(line spectrum)

6.3 – Line Spectra and the Bohr ModelThe energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation:

E = -RH ( )1nf

2

1ni

2-

where RH is the Rydberg constant, 2.18 10−18 J, and ni and nf are the energy levels of the electron-If nf is smaller than ni, then the e- moves closer to the nucleus and DE is negative-If nf is larger than ni, then the e- moves farther from the nucleus and DE is positive-Each line on the line spectrum of Hydrogen can be calculated using this equation.

6.3 – Line Spectra and the Bohr Model

Ground State = Lowest energy state for the electron

Excited State = A higher energy state

• Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:

1. Electrons in an atom can only occupy certain orbits (corresponding to certain energies).

2. Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.

3. Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by

E = h

6.3 – Bohr’s Model of the Hydrogen Atom

Quantum Mechanics Preview:

6.4 - The Wave Behavior of Matter

• Louis de Broglie posited that if light can have material properties, matter (electrons in atoms) should exhibit wave properties.

• He demonstrated that the relationship between mass and wavelength was:

=hmn

This equation relates the wave ( ) l and particle (m) natures

6.4 – The Wave Behavior of Matter• Heisenberg Uncertainty Principle:

Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely its position known

It is impossible to know both the momentum and the position of an electron

6.5 - Quantum Mechanics

• Erwin Schrödinger developed a mathematical treatment (Schrodinger Wave Equation) into which both the wave and particle nature of matter could be incorporated.

• It is known as quantum mechanics.

6.5 -Quantum Mechanics• Uses advanced calculus• The wave equation is

designated with a lower case Greek psi ().

• The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time = electron density

Orbitals and Quantum Numbers

• Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies.

• Each orbital describes a spatial distribution of electron density.

• An electron is described by a set of four quantum numbers.

Principal Quantum Number, n

• The principal quantum number, n, describes the energy level on which the orbital resides.

• It is a measure of the distance from the nucleus.

• The values of n are integers ≥ 0. • Now 1-7

Angular Momentum Quantum Number, l

• This quantum number defines the shape of the orbital.

• Allowed values of l are integers ranging from 0 to (n − 1).

• We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.

Angular MomentumQuantum Number, l

Value of l 0 1 2 3

Type of orbital s p d f

Magnetic Quantum Number, m l

• Describes the three-dimensional orientation of the orbital.

• Values are integers ranging from - l to l :

− l ≤ m l ≤ l• Therefore, on any given energy level, there can

be up to– s = 0 = one s orbital– p = -1, 0, 1 = three p orbitals– d= -2,-1,0,1,2 = five d orbitals,– f=-3,-2,-1,0,1,2,3 = seven f orbitals

Magnetic Quantum Number, m l

• Orbitals with the same value of n form a shell.– Ex – The n=3 shell has an s orbital, three p orbitals and

five d orbitals

• The set of orbitals with the same shape within a shell form a subshells.– Ex = there are three orbitals in a p subshell)

Spin Quantum Number

• Each e- in one orbital must have opposite spins• Symbol – ms

• + ½ , - ½– Two “allowed” values and corresponds to

direction of spin

6.6 – Representation of OrbitalsThe s Orbital

• Value of l = 0.• Spherical in shape.• Radius of sphere

increases with increasing value of n.

• Radius of sphere increases with increasing energy of the electron(s).

p Orbitals

• Value of l = 1.• Have two lobes with a node (no probability of

finding electron) between them.

d Orbitals• Value of l is 2.• Four of the five

orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.

f Orbitals

Higher than f not currently needed…

AP EXAM QUESTIONS:

List the four quantum numbers for the valence electrons in magnesium.

List in order – n, l, m l , ms

Valence electrons: 3s2

Electron 1 = 3,0,0,Electron 2 = 3,0,0,-

1

21

2

AP EXAM QUESTIONS:List the four quantum numbers for the valence

electrons in Nitrogen.

Energies of Orbitals

• For a one-electron hydrogen atom, orbitals on the same energy level have the same energy.

• That is, they are degenerate.

6.7 – Many Electron Atoms• As the number of electrons

increases, though, so does the repulsion between them.

• Therefore, in many-electron atoms, orbitals on the same energy level (principle quantum number) are no longer degenerate.

• This is the order we use from the periodic table to fill orbitals = Aufbau Principle = electrons fill from low to high energy

Pauli Exclusion Principle

• No two electrons in the same atom can have exactly the same energy.

• Also means that no two electrons in the same atom can have identical sets of quantum numbers.

6.8 - Electron Configurations

• Shows the distribution of all electrons in an atom

• Consist of – Number denoting the

energy level

Electron Configurations

• Distribution of all electrons in an atom

• Consist of – Number denoting the

energy level– Letter denoting the type of

orbital

Electron Configurations

• Distribution of all electrons in an atom.

• Consist of – Number denoting the

energy level.– Letter denoting the type of

orbital.– Superscript denoting the

number of electrons in those orbitals.

Practice: N, Zr, Bi

Orbital Diagrams

• Each box represents one orbital.

• Half-arrows represent the electrons.

• The direction of the arrow represents the spin of the electron.

Practice: B, Si

Hund’s Rule

“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”

(In a p, d or f subshell, fill each orbital with ONE electron before pairing any)

• Diagmagnetism = Repelled by a magnet = Has all paired electrons with opposite spins

• Paramagnetism = Attracted to a magnet = has at least one unpaired electron

• Shielding = Inner electrons block outer electrons from the electrostatic force of the nucleus

• Valence electrons = Outer-shell electrons involved in bonding

Condensed Electron Configurations

• Begin at the NOBLE GAS (Has full valence shell) before the element. Write that symbol in [brackets]

• Continue on with the rest of the configuration

Practice: Na, As, Ag, At

Periodic Table

• Different blocks on the periodic table, then correspond to different types of orbitals.

Some Anomalies

Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row.

Some AnomaliesGroup 6:

Ex - Chromium is[Ar] 4s1 3d5

rather than the expected[Ar] 4s2 3d4.Group 11:

Ex - Copper is[Ar] 4s1 3d10

rather than the expected[Ar] 4s2 3d9.

Some Anomalies

• This occurs because the 4s and 3d orbitals are very close in energy and a half-filled d is more stable than “missing” 1 e-.

• These anomalies occur in f-block atoms, as well (Sm and Pu and Tm and Md)