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ARC / Chemistry / Chem 400 / Which orbitals do not exist based on the rules of quantum mechanics?

Which orbitals do not exist based on the rules of quantum mechanics?

Which orbitals do not exist based on the rules of quantum mechanics?

Description

School: American River College
Department: Chemistry
Course: General Chemistry
Professor: Victoria wheaton
Term: Fall 2017
Tags: General Chemistry
Cost: 50
Name: Chem 400 Study Guide Exam 3
Description: Electrons in Atoms, Electromagnetic Radiation, Quantum Mechanics, Electron Configurations, Orbital Diagrams, Periodic Table Trends, Born-Haber Cycle
Uploaded: 03/18/2018
9 Pages 155 Views 2 Unlocks
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Chem 400 Study Guide Exam 3 HIGHLIGHT AND SHARE


Which orbitals do not exist based on the rules of quantum mechanics?



Electrons in Atoms, Electromagnetic Radiation, and Quantum Mechanics ● The Bohr Model of the Atom was inspired by light from excited gases that comes out in specific colors, not a continuous spectrum

● Balmer​: Equation of a Wavelength

○ = Constant λ1 (122 −1n2 )

● Rydberg’s Wavelength Equation​ (more generalized): ​this equation gives the wavelengths of light from excited atoms, but the n values have no physical meaning ○ = R where R= 1.097 x 10 1λ (7m


What is the element represented by this electron configuration?



n l2 −1n2u )

● Bohr later came up with the energy levels of electrons in a hydrogen atom from Rydberg’s equation

● Only certain n values are allowed (n=1, n=2...n=8,n=9) only whole #’s, no decimals ● It was discovered that particles that are fast moving have wave-like behavior ● DeBroglie Wavelength: λ =hmv

○ λ = wavelength

○ h= planck’s constant (6.626 x 10-34 J · s)

○ m= mass in kg

○ v= velocity in m/s


What are the steps of the born haber cycle?



● DeBroglie stated that electrons can be thought of as particles that can exhibit wave-like behavior We also discuss several other topics like When do circadian rythms occur?

● Heisenberg:​ Presented the Uncertainty Principle. You cannot simultaneously locate a fast moving particle and know its velocity without a significant error

● Bohr Model of the Atom​: It is an inaccurate representation of the atom because it violates the uncertainty principle

● Although the Bohr Model of the Atom is invalid, here are some things we can learn from the model:

○ Energy levels of the electrons are quantized

○ There is a ground state, where the electron cannot go any lower. Bohr’s calculation of the distance between the electron and nucleus is correct

○ Electrons do not absorb or release energy without making transitions to other levels

Quantum Mechanics

● Quantum Mechanics: ​Gives us volumes in space where the electron is likely to be found. To honor Bohr, we call these volumes, orbitals We also discuss several other topics like What is the purpose of retrenchment?

● The meaning of n

○ The First Orbital is a spherical shaped volume in space that is more dense with probability near the nucleus

■ We say that the the principle quantum number of the first orbital is n=1 ○ The Second Orbital (n=2) has two possible shapes. The second orbital is shaped like a dumbbell

○ The Third Orbital (n=3) has three possible shapes. The third orbital is shaped like a propellor

● The meaning of L

○ L is the shape quantum number, technically the azimuthal quantum number ○ The first spherical orbital n=1 is represented by L=0

○ The second dumbbell orbital n=2 is represented by L=1, and so on… ○ Each of the l orbitals is given a letter designation

L = 0

S-orbital

L = 1

P-orbital

L = 2

D-orbital

L = 3

F-orbital

Don't forget about the age old question of How were the storming of the bastille and the women's march?

● The meaning of mL If you want to learn more check out How proteins and carbohydrates are digested and absorbed by the body?

○ ml gives the direction of the orbital in space

○ Each L value has its own set of ml values (the magnetic quantum)

Table of mL Values

L = 0

mL= 0 (the s-orbital can only have 1 direction because it is a sphere)

L = 1

mL= -1, 0, or 1 (the p-orbital has 3 possible directions)

L = 2

mL = -2, -1, 0, 1, or 2 (the d-orbital has 5 possible directions

L = 3

mL = -3, -2, -1, 0, 1, 2, or 3 (the f-orbital has 7 possible directions)

● The meaning of ms 

○ The fourth quantum number (ms) denotes the “spin”

○ All elements with have a ms = ± 21 If you want to learn more check out Why do monkeys with parietal lesions find it difficult to finish landmark tasks?

Table of Quantum Numbers

Quantum Number

What it represents

How to Calculate it

n

Size (principle quantum number)

row

L

Shape (shape quantum)

n-1

ml

Direction (magnetic quantum)

± l

ms

Spin (spin quantum)

± 21

● Energy Diagram: Filling order is increasing energy in multielectron atom. Based on the n+L value

● For multielectron atoms a splitting occurs and the following energy diagram allows us to fill in electrons

● This diagram is based on energy

● The energy of an orbital in a hydrogen atom is based only on n, but in a multielectron atom it is based on n + L Don't forget about the age old question of What are stored in the semantic memory?

● Each orbital has 2 e- and no 2 e- have the same four quantum #’s

● Reason for difference in energy

○ Other electrons are present in the multielectron atom

○ Multielectron means more than one electron

○ This leads to:

■ Electron-electron repulsion

■ Higher charge in the nucleus

■ Shielding of nucleus

■ Penetration of orbitals

● Every orbital has 3 quantum numbers to define it (n, L, mL)

● E.g. which orbital(s) do not exist based on the rules of quantum mechanics?

5s

n=5

L=0

exists

2d

n=2

L=2

Does not exist

3p

n=3

L=1

exists

4f

n=4

L=3

exists

Electron Configurations

● E.g. Electron Configuration for Bromine

○ Br: 1s22s22p63s23p64s23d104p5 

● Give a full set of quantum numbers for the highest energy electron in bromine ○ n=4, L=1, mL= -1, 0, or 1, ms= ± 1/2

● E.g. Electron Configuration Exceptions for Chromium

○ Cr: 1s22s22p63s23p64s13d5(Chromium tries to make 2 half-filled orbitals) ○ The exceptions to electron configurations include: Chromium, Molybdenum, Tungsten, Copper, Silver, Gold

● E.g. Electron Configurations for the Exceptions

○ Cu: 1s22s22p63s23p64s13d10 

○ Mo: 1s22s22p63s23p64s23d104p65s14d5 

○ Ag: 1s22s22p63s23p64s23d104p65s14d10 

Noble Gas Configurations

● Another way to write electron configurations is called the noble gas core configuration ● E.g. Write the full and noble gas configuration of Phosphorus

○ P: 1s22s22p63s23p3 

○ P: [Ne] 3s23p3(find the closest noble gas prior to the element)

Orbital Diagrams

● E.g. Oxygen

● Paramagnetic​: Atoms with at least 1 unpaired electron

● Diamagnetic: ​Atoms with no unpaired electrons

● Excited state configurations also exist

● E.g. What is the element represented by this electron configuration? Answer: Mg

● Valence​: The word valence corresponds to the outermost electrons of an atom (aka those outside the noble gas core)

Electron Configurations for Ions

● S2-: 1s22s22p63s23p6(ADD electrons for ANIONS)

● K+: 1s22s22p63s23p6(SUBTRACT electrons for CATIONS IN THE MAIN GROUP) ● Ti2+: 1s22s22p63s23p63d2(For cations of transition metals, remove electrons from the highest n value)

● Zn2+: 1s22s22p63s23p63d10 

Trends

● Isoelectric​: having the same number of electrons (i.e. Ca+ and K are isoelectric) ● Atomic Radius​: ​The distance between the nucleus and the outermost electrons of an atom

● Ionization Energy​: The energy required to remove an electron from an atom ○ Always endothermic, always measured in the gas phase, implied to be the first ionization energy, but successive ionization energies exist

● E.g.

○ Chemical Equation for 1st Ionization Energy:

■ A(g) → A+(g) + e-(You are taking an electron away)

○ Chemical Equation for 2nd Ionization Energy

■ A+(g) → A2+(g) + e- 

○ Chemical Equation for 6th Ionization Energy

■ A5+(g) → A6+(g) + e- 

● Successive energies are always higher than the previous one for Ionization Energy ● Electron Affinity​: ​The energy released or absorbed when an additional electron is added to an atom (measured in the gas phase)

● E.g.

○ Chemical Equation for 1st Electron Affinity

■ A(g) + e-→ A-(g)

○ Chemical Equation for 2nd Electron Affinity

■ A-(g) + e- → A2-(g)

● The energy of electron affinity is positive when the atom doesn’t want any more electrons (full outer orbital or level)

● Most atoms have a negative first electron affinity because energy is released when electrons are added to atoms

● We are adding an electron to an atom by placing an additional e-the orbital close to the nucleus

● Periodic Trend for Radius of Atom

● Periodic Trend for Ionization Energy

● Periodic Trend for Electron Affinity

○ Electron affinity is not as easy to generalize, Alkaline Earth metals and Noble Gases are positive

● Successive I.E. (Ionization Energies) get larger

● E.g. What element does this list come from? (2nd period)

○ 1st I.E. 1.086 x 106 J/mol

○ 2nd I.E. 2.353 x 106 J/mol

○ 3rd I.E. 4.621 x 106 J/mol

○ 4th I.E. 6.223 x 106 J/mol

○ 5th I.E. 37.831 x 106 J/mol

○ 6th I.E. 47.227 x 106 J/mol

○ Because there is a big jump to take the 5th electron out, this atom must have 4 valence electrons. Therefore, the answer is Carbon

● E.g. draw valence orbital diagrams to show how Li2O forms

● Metallic Behavior: ​To act like a metal (Cesium is the most metallic element) ○ Shiny

○ Conducts heat

○ Conducts electricity

○ Malleable

○ Ductile

● Acid-Base Behavior of Oxides​: Metal oxides are basic (think CuO react with Acid). Non-metal oxides are acidic (think pollutants of nitrogen oxides and sulfur oxides causing acid rain)

● Demonstration: Sulfur burns in oxygen to produce sulfur dioxide. Sulfur dioxide dissolves in water to make H2SO3 (aq)(sulfurous acid)

● Ionic bonds form when electrons are lost by metals to make cations and electrons are gained by nonmetals to make anions. Positive and negative ions form a lattice

Born-Haber Cycle

● Energy to form ionic bonds are represented by the Born-Haber Cycle ● We use a large enthalpy diagram to show the formation of ionic bonds like NaCl

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