Quantum Numbers

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# Quantum Numbers - PowerPoint PPT Presentation

Quantum Numbers. Bohr model- required that electrons be confined to specific orbits which had specific corresponding energy. Bohr equation: n represents the number of each orbit, starting closest to the nucleus

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## PowerPoint Slideshow about 'Quantum Numbers' - nehru-calhoun

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### Quantum Numbers

Bohr model- required that electrons be confined to specific orbits which had specific corresponding energy

Bohr equation:

• nrepresents the number of each orbit, starting closest to the nucleus
• His theory was widely accepted because the constants ended up to be equal to the Rydberg constant! And produced a model of the atom

The energy difference between two given orbits is constant

• The same amount of energy needed to promote an electron to a higher orbit, will be released when the electron drops back
Wave mechanical model
• Describing the motion of an electron- very complicated wave equations- Schroedinger Equation
6 new ideas….
• 1. The wave equations require 3 numbers-quantum numbers-in order to solve the equations
Quantum numbers
• n- principal quantum number
• l- azimuthal quantum number
• ml –magnetic quantum number
• ms- spin quantum number

2. Changed the picture of the atom

• Bohr’s fixed orbits replaced by a “cloud”
• Modern orbit is a region of space in which the probability of finding the electron is the highest

3. Wave equations provide a shape for each of the clouds

• 4. arrangements of electrons agrees with element arrangement of the periodic table
• Deeper understanding of chemical properties based on shapes of clouds

5. Results of the wave equation agree completely with the Bohr model calculations

• 6. Heisenberg Uncertainty Principal
• Position and momentum of an electron cannot be exactly known at the same time
Electron Configuration
• Principal energy level – n (principal quantum number)
• Energy level increases in size and energy the farther the electron is from the nucleus- can hold more electrons
• Maximum number of electrons an energy level 2n2
Sublevels - l- azimuthal quantum number (room type)
• Each principal quantum energy level contains sublevels
• # of sublevels = to the value of nfor that energy level
• Ex: for the third principal energy level (n=3) contains a maximum of 3 sublevels
• Sublevels 5, 6, and 7 are theoretically possible but not currently needed

Sublevels are numbered with consecutive whole numbers starting with 0

• The value of l can never be greater than n-1
• Each number corresponds to a letter s,p,d, or f (room type s,p,d,f)
Orbitals
• Each sublevel can contain one or more electron orbitals
• Orbital-region of space that has high electron density and each orbital may contain a MAXIMUM of 2 electrons
Orbitals
• To share an orbital the 2 electrons must have opposite spins (Pauli Exclusion Principle)
• ms - values for spin can be +1/2 or -1/2
• When 2 electrons share an orbital they are “paired”
• Orbitals have the same designation as the sublevel they are in (s,p,d,f)

The number of orbitals that a sublevel can have depends on the azimuthal quantum number, l

• Can have 2l + 1 orbitals
ml magnetic quantum number (room number)
• Each orbital is given a number that range from

- l to +l including 0

Electron Configurations

A list of all the electrons in an atom (or ion)

• Must go in order (Aufbau principle)
• 2 electrons per orbital, maximum
• We need electron configurations so that we can determine the number of electrons in the outermost energy level. These are called valence electrons.
• The number of valence electrons determines how many and what this atom (or ion) can bond to in order to make a molecule

1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14…etc.

Electron Configuration Rules
• The ways in which electrons are arranged in various orbitals around the nuclei of atoms are called electron configurations.
• Three rules—the aufbau principle, the Pauli exclusion principle, and Hund’s rule—tell you how to find the electron configurations of atoms.
Aufbau Principle
• electrons occupy the orbitals of lowest energy first. In the aufbau diagram below, each box represents an atomic orbital.
Pauli Exclusion Principle
• an atomic orbital may describe at most two electrons. To occupy the same orbital, two electrons must have opposite spins; that is, the electron spins must be paired.
Hund’s Rule
• states that electrons occupy orbitals of the same energy in a way that makes the number of electrons with the same spin direction as large as possible.

8A

1A

1

2A

3A

4A

5A

6A

7A

2

3

3B

4B

5B

6B

7B

8B

8B

8B

1B

2B

4

s

d

p

5

6

7

f

6

7

group # = # valence (outside) e-

Row

=

# shells

Why are d and f orbitals always in lower energy levels?
• d and f orbitals require LARGE amounts of energy
• It’s better (lower in energy) to skip a sublevel that requires a large amount of energy (d and f orbtials) for one in a higher level but lower energy

This is the reason for the diagonal rule! BE SURE TO FOLLOW THE ARROWS IN ORDER!

8A

1A

1

2A

3A

4A

5A

6A

7A

2

3

3B

4B

5B

6B

7B

8B

8B

8B

1B

2B

4

d

5

6

7

f

6

7

Subshells d and f are “special”

group # = # valence e-

3d

period # = # e- shells

4d

5d

6d

4f

5f

Electron Configuration

1s1

# of electrons

in that subshell

row # (on periodic table)

Also known as shell #

(principal quantum # n)

possibilities are 1-7

7 rows

subshell

possibilities are

s, p, d, or f

4 subshells

Diagonal Rule
• Must be able to write it for the test! This will be question #1 ! Without it, you will not get correct answers !
• The diagonal rule is a memory device that helps you remember the order of the filling of the orbitals from lowest energy to highest energy
• _____________________ states that electrons fill from the lowest possible energy to the highest energy

1s2

2s2

2p6

3s2

3p6

3d10

4s2

4p6

4d10

4f14

5s2

5p6

5d10

5f14

6s2

6p6

6d10

7s2

7p6

1s2

2s2

2p6

3s2

3p6

4s2

3d10

4p6

5s2

4d10

5p6

6s2

4f14

5d10

6p6

7s2

5f14

6d10

7p6

Shorthand Notation
• A way of abbreviating long electron configurations
• Since we are only concerned about the outermost electrons, we can skip to places we know are completely full (noble gases), and then finish the configuration
Paramagnetic Atoms
• Lone atoms with one or more unpaired electrons and are attracted by magnetic fields
• _____ _____ ____ ____ ____

1s 2s 2p

Diamagnetic Atoms
• Lone atoms with NO unpaired electrons are repelled by magnetic fields
• _____ _____ ____ ____ ____

1s 2s 2p

• Ex: Neon