The Quantum Model of the Atom

Section 4:2

Modern Chemistry (2009)

5-2020

L. Blanchard Byrne

Target 04-02 I can describe the location of electrons. (4 quantum numbers)

The Atomic Model

Ernest Rutherford

The Rutherford Model

(Peach Pit Model)

protons & neutrons are located at the center of the atom while electrons orbit about the nucleus freely

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J.J. Thomson

The Plum Pudding Model

an atom is composed of electrons surrounded by a soup of positive charge that is evenly distributed

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Niels Bohr

The Planetary Model

electrons are found in specific orbits of defining energy levels that circle the positively charged nucleus

The Atomic Model

Werner Heisenberg (1901-1976)

The Electron Cloud Model

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• Similar to Bohr, electrons are restricted to specific energy levels (n levels)

when electrons move to a lower energy level, a quantum of energy is released (vice versa)

• BUT 🡪 electrons do NOT have exact circular orbits in which they follow – he stated that the location of the electron is all based off of probability

He described the probability as a “fuzzy cloud” – where it’s more dense = a higher probability of finding an electron

• Heisenberg Uncertainty Principle

The Atomic Model

Erwin Schrodinger (1887-1961)

Electron Wave Model

The Quantum Mechanical Model

• Electrons can be both particles and waves
• Each energy level is given a quantum number (n) with an assigned value – EX: n = 1, n = 2, etc.
• Atomic orbitals: the region of space where there’s a high probability of finding an electron around its nucleus in a wave function shape
• 90% of the time electrons are found here
• each energy level has one or more atomic orbitals
• each atomic orbital holds two electrons

Quantum Numbers

Address a single electron in an atom.

Given by four parts to an address:

State:

City:

Street:

House number:

Superior Bathroom

1

2

3

4

5

6

7

Superior

Pretty Good

Dumpy

Freaky!

balcony

Pretty Good Bathroom (Church)

Dumpy Bathroom (school)

Freaky School Bathrooms!

Typical in Tanzania, Africa

These are the school bathrooms at Masame Village on Mt. Kilimanjaro,

Tanzania, Africa, where my daughter taught math with the Peace Corps.

The bucket is for “flushing” as well as hand washing. There is no toilet paper.

A new way to think about “pop a squat”. Your feet are positioned on the raised area over the hole.

A good home style Tanzanian Bathroom

FREAKY!

This is the toilet in her cottage. Your feet go on the sides of the white porcelain part while you squat. Peace Corps issued her two rolls of toilet paper a month.

It flushed by turning the faucet to fill the tank and then pulling the lever. If the water wasn’t running in the village that day, it was flushed by carrying a pail of water from the stream a km away from the village.

4 Quantum Numbers and the “Bathroom Building”

• Principal Quantum Number = Floor number
• Angular Momentum Quantum Number = Bathroom type
• Magnetic Quantum Number = Which of the bathrooms of that type
• Spin Quantum Number = First or second stall

x

y

z

xy

xz

yz

x²-y²

z²

4d

5d

6d

Balcony

4 Quantum Numbers and the Periodic Table

Principal Quantum Number = How far the electron is from the nucleus –

Main Energy Level– row number

Angular Momentum Quantum Number = Shape or type of orbital - Block on the table

Magnetic Quantum Number = Position in the orbital –

Which orientation in space for that orbital type

Spin Quantum Number = First or second electron in the orbital

Principal Quantum Number

• Energy level n

Seven current

possibilities

n = 1

n = 2

n = 3 ….

or n = K, L, M, N… 1 to infinity possible orbitals

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• The larger the number, the farther from the nucleus and the more energy the electron has.
• Periodic Table – Periods 1 - 7

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Principal Quantum Number

What is the principal quantum number for each of these atoms?

n = 4

n = 6

Principal Quantum Number

What is the principal quantum number for the outermost electron for the element Iron?

n = 3

the last six electrons have been filling the 3d sublevel

Angular Momentum Quantum Number

• There are four main sublevels: s, p, d, and f
• Symbolized by a lowercase L (l = )

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s – spherically shaped;

1 atomic orbital – holds 2 electrons

p – dumbbell-shaped;

3 atomic orbitals – holds 6 electrons

d – clover-shaped;

5 atomic orbitals – holds 10 electrons

f – flower shaped:

7 atomic orbitals – holds 14 electrons

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Schrodinger’s notation uses numbers. These are the mathematical answers to his wave functions.

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We will use the letter representations for l.

l = s

l = p

Angular Momentum Quantum Number

What is the angular momentum quantum number for the last electron in the element nitrogen?

l = p

Angular Momentum Quantum Number

What is the angular momentum quantum number for the last electron in the element copper?

l = d

Magnetic Quantum Number

• Orientation of the orbital around the nucleus m =

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• For l = s s is a sphere and has no x, y, z orientation

m = s (for sphere)

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(superior bathrooms)

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​

​

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m = s

Magnetic Quantum Number

l = p dumbbell shaped wave patterns

m = p_x, p_y, p_z (pretty good bathrooms)

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m = -1

m = 0

m = 1

Magnetic Quantum Number

• Where l = d There are 5 orientations in space.

(dumpy bathrooms)

Magnetic Quantum Number

• Where l = f there are 7 possible orientations

(freaky bathrooms)

Magnetic Quantum Number Wave Shapes

m =

Magnetic Quantum Number

What is the magnetic quantum number for the last electron in the element carbon?

m=p_y

Magnetic Quantum Number

What is the magnetic quantum number for the last electron in the element cobalt?

m=d_xz

Spin Quantum Number

• Indicates the two possible spin states of an electron in an orbital symbolized by s
• Two possible values +1/2 and -1/2

(two toilets to a school bathroom)

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• A single orbital can hold a maximum of two electrons which must have opposite spins.

Spin Quantum Number

What is the spin quantum number for the last electron in the element carbon?

s= +1/2

Spin Quantum Number

What is the spin quantum number for the last electron in the element copper?

s = -1/2

Why does 3d fill after 4s?

Putting the 4 Together

n =

l =

m =

s =

Hydrogen n= 1 (1^st period)

l = s or 0 (spherical)

m = s or 0 (no orientation)

s = +1/2

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Helium n= 1 (1^st period)

l = s or 0 (spherical)

m = s or 0 (no orientation)

s = -1/2

Lithium n= 2 (2nd period)

l = s or 0 (spherical)

m = s or 0 (no orientation)

s = +1/2

Beryllium n= 2 (2nd period)

l = s or 0 (spherical)

m = s or 0 (no orientation)

s = -1/2

Boron n= 2 (2nd period)

l = p or 1 (dumbbell)

m = p_x or -1 (oriented on the x axis)

s = +1/2

Carbon n= 2 (2nd period)

l = p or 1 (dumbbell)

m = p_y or 0 (oriented on the y axis)

s = +1/2

Nitrogen n= 2 (2nd period)

l = p or 1 (dumbbell)

m = p_z or +1 (oriented on the z axis)

s = +1/2

Oxygen n= 2 (2nd period)

l = p or 1 (dumbbell)

m = p_x or -1 ( oriented on the x axis)

s = -1/2

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Fluorine n= 2 (2nd period)

l = p or 1 (dumbbell)

m = p_y or 0 (oriented on the y axis)

s = -1/2

Neon n= 2 (2nd period)

l = p or 1 (dumbbell)

m = p_z or +1 (oriented on the z axis)

s = -1/2

Sodium n= 3 (3rd period)

l = s or 0 (sphere)

m = s or 0 (No orientation)

s = +1/2

Magnesium n= 3 (3rd period)

l = s or 0 (sphere)

m = s or 0 (No orientation)

s = -1/2

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Aluminum n= 3 (3rd period)

l = p or 1 (dumbbell)

m = p_x or -1 (oriented on the x axis)

s = +1/2

Quiz

Write the four quantum numbers for the outermost electron in each of the following elements:

Li

Al

Mg

P

K

Br

Ga

Ba

Ar

N

Quiz

Li n=2

l=s

m=s

s= +1/2

Al n=3

l=p

m=p_x

s= +1/2

Mg n=3

l=s

m=s

s= -1/2

Br n=4

l=p

m=p_y

s= -1/2

Ga n=4

l=p

m=p_x

s= +1/2

Ba n=6

l=s

m=s

s= -1/2

P n=3

l=p

m=p_z

s= +1/2

K n=4

l=s

m=s

s= +1/2

Ar n=3

l=p

m=p_z

s= -1/2

N n=2

l=p

m=p_z

s= +1/2

Fin