 # AP Chapter 6 Electronic Structure of Atoms HW: 5 7 29 35 63 67 69 71 73 75.

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AP Chapter 6 Electronic Structure of Atoms HW: 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 = 3.0x10 8 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 = = Distance between identical points on successive waves. Unit = Angstrom (A), nm,  m -Frequency = = # of waves passing a point in a given unit of time (typically 1 second). Unit = Hz = 1/s -Speed of the wave =  c  -Amplitude = Height -Node = Amplitude = 0 A high frequency wave must have a short wavelength A 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 10 14 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

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 Photons a)A laser emits light with a frequency of 4.69 x 10 14 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 10 17 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: a)3.11 x 10 -19 J b)0.16 J c)4.2 x 10 16 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 Model The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation:  E = -R H ( ) 1nf21nf2 1 n i 2 - where R H is the Rydberg constant, 2.18  10 −18 J, and n i and n f are the energy levels of the electron -If n f is smaller than n i, then the e- moves closer to the nucleus and  E is negative -If n f is larger than n i, then the e- moves farther from the nucleus and  E 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: = h m This equation relates the wave (  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 Momentum Quantum Number, l Value of l0123 Type of orbitalspdf

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 – m s + ½, - ½ – Two “allowed” values and corresponds to direction of spin

6.6 – Representation of Orbitals The 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, m s Valence electrons: 3s 2 Electron 1 = 3,0,0, Electron 2 = 3,0,0,-

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 Anomalies Group 6: Ex - Chromium is [Ar] 4s 1 3d 5 rather than the expected [Ar] 4s 2 3d 4. Group 11: Ex - Copper is [Ar] 4s 1 3d 10 rather than the expected [Ar] 4s 2 3d 9.

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)

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