Ch. 13 Quantum Mechanical Model

Ch. 13 Quantum Mechanical Model

Electron Configuration

Quantum Mechanical Model

• Quantum mechanics was developed by Erwin Schrodinger

• Estimates the probability of finding an e- in a certain position

• Electrons are found in an “electron cloud” or orbital

Radial Distribution CurveOrbital

Orbital (“electron cloud”)– Region in space where there is 90% probability of

finding an e-

Each orbital letter has a different shape.

“s” orbitalspherical shaped, and holds up to 2e-

“p” orbitalDumbbell shapedArranged x, y, z axes, and canhold up to 6e-

“d” orbitalclover shaped, and can hold upto 10e-

“f” orbital

f

• Orbitals combine to form a spherical shape.

• This orbital can hold up to

14e-

2s

2pz2py

2px

Hog HiltonYou are the manager of a prestigious new hotel in downtown

Midland—the “Hog Hilton”. It’s just the “snort of the town” and you want to keep its reputation a cut above all the other hotels. Your problem is your clientele. They are hogs in the truest sense.

Your major task is to fill rooms in your hotel. The Hog Hilton only has stairs. You must fill up your hotel keeping the following rules in mind:1) Hogs are lazy, they don’t want to walk up stairs!2) Hogs want to room by themselves, but they would rather room with another hog than walk up more stairs.3) If hogs are in the same room they will face in opposite directions.4) They stink, so you can’t put more than two hogs in each room.

Hog Hilton• Your hotel looks like the diagram below:

6th floor ______5th floor ______ ______ ______ 4th floor ______3rd floor ______ ______ ______2nd floor ______1st floor ______

Book 7 hogs into the rooms.

Hog HiltonYour hotel looks like the diagram below:

6th floor ______5th floor ______ ______ ______ 4th floor ______3rd floor ______ ______ ______2nd floor ______1st floor ______

Book 14 hogs into the rooms.

Let’s play Hog Hilton!!

Rules for e- configurations1. Aufbau principle: e- enter orbitals of lowest energy

level (Hogs are lazy, they don’t want to walk up stairs!)

2. Pauli exclusion principle: an atomic orbital may have at most 2 e-, e- in the same orbital will spin in opposite directions (They stink, so you can’t put more than two hogs in each room. & If hogs are in the same room they will face in opposite directions.)

3. Hund’s rule: when e- occupy orbitals of = energy, 1 enters each orbital until all the orbitals contain 1 e- w/parallel spins (Hogs want to room by themselves, but they would rather room with another hog than walk up more stairs.)

Now you will relate the “Hog Hilton” to electron orbitals. Electron orbitals are modeled by the picture on the left and are grouped into principal energy levels.

1. Compare their similarities and differences.2. To go between floors on the Hog Hilton did the hogs need to use energy? Would electrons

need to use the energy to go between orbitals.

3d ___ ___ ___ ___ ___ n=3(4s ____) n=43p ___ ___ ___ n=33s ___ n=32p ___ ___ ___ n=22s ___ n=21s ___ n=1

6th floor ___5th floor ___ ___ ___4th floor ___3rd floor ___ ___ ___2nd floor ___1st floor ___

A. The principle quantum numbers, (n)• Electrons are in designated energy levels.

Organization of e- in the Quantum Mechanical model

The ground state- the lowest energy state of the atom

B. Within the energy level are sublevels, designated by letters.

Principle energy level

(n)

Number of

sublevels

Type of Orbital

1st energy level

1 sublevel “s” (1 orbital)

2nd 2 sublevels

“s” (1) & “p” (3 orbitals)

3rd 3 sublevels

“s”(1) , “p” (3) & “d” (5 orbitals)

4th 4 sublevels

“s”(1), “p”(3) , “d”(5), and “f” (7)

1s

2s2p

3p3s

4s3d

4p5s

4d5p

6s4f

5d6p7s

7s 7p6s 6p 6d 6f 6g5s 5p 5d 5f 5g4s 4p 4d 4f3s 3p 3d2s 2p1s

Filling in orbitals then writing the electron configuration

4p _ ↑↓ _ _ ↑↓ _ _ ↑↓ _3d _ ↑↓ _ _ ↑↓ _ _ ↑↓ _ _ ↑↓ _ _ ↑↓ _4s _ ↑↓ _3p _ ↑↓ _ _ ↑↓ _ _ ↑↓ _3s _ ↑↓ _2p _ ↑↓ _ _ ↑↓ _ _ ↑↓ _ 2s _ ↑↓ _ 1s _↑↓_ 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6

1. Noble Gases – outermost s & p sublevels filled

Because they have their s2 & p6 orbitals filled they

follow the:2 + 6 = OCTET RULE

D. According to their e- configs, elements can be classified into 4 main groups

2. Representative Elements – outermost s or p sublevel is only partially filled, energy level same as period #The pink elements excluding the Noble Gases.s1 s2

p1 p2 p3 p4 p5

3. Transition metals – outermost s sublevel & nearby d sublevel contain e- , energy level is the same as the period # minus 1

d1 d2 d3 d4 d5 d6 d7 d8 d9 d10

4. Inner Transition metals - outermost s & nearby f generally contain e-

f1 f14

d1 d2 d3 d4 d5 d6 d7 d8 d9 d10

f1 f14

s1 s2

p1 p2 p3 p4 p5 s2

p6

Your Periodic Table should look like this.

How many electrons are present in the d sublevel of a neutral atom of Manganese?

Learning Check

1 2 3 4 5

5 electrons

What element has the electron configuration 1s22s22p63s23p4?

Add together all the exponents, then find that atomic number. = Sulfur 16

E. Using the Noble Gases to write Shorthand

• Write the noble gas that is in the previous row. • Use the symbol of the noble gas, put it in brackets,

then write the rest of the configuration.

• Write the e- config for Tin (Sn). • [Kr] 5s2 4d10 5p2

Write the e- config using Noble Gas notation for Cobalt.It would be written [Ar] 4s2 3d7

Learning CheckUsing the Noble Gas Shorthand write the e- configuration

1. Cr

2. Br

3. Te

4. Ba

[Ar] 4s2 3d4

[Ar] 4s2 3d10 4p5

[Kr] 5s2 4d10 5p4

[Xe] 6s2

Electromagnetic Spectrum• The electromagnetic spectrum (see p. 373) includes radio

waves, microwaves, infrared waves, visible light, ultraviolet waves, x-rays, and gamma rays.

• Visible light is in the middle of the spectrum.• The speed of light is 3.0 X 108 m/s.

• The formula for light is c =ƛʋ• C = speed of light, ƛ = wavelength, ʋ = frequency– Visible light has many wavelengths of light that can be

separated into red, orange, yellow, green, blue, indigo, and violet (ROY G BIV)

Atomic Emission Spectrum

• Every element gives off light when it is excited by the passage of an electric current through its gas or vapor.

• The atomic emission spectrum occurs when the light that is given off by an element in its excited state is passed through a prism. It consists of a few lines called a line spectra or discontinuous spectra. Each line on the spectra corresponds with a frequency.

• See page 374.• Work problems # 11 and 12 on page 375.

Planck’s Constant

• In 1900, German Physicist Max Planck used math to explain why objects, such as iron, that are heated change color.

• He said energy can be quantized. The size of an emitted or absorbed quantum depends on the size of the energy change. A small energy change involves the emission or absorption of low frequency radiation. A large energy change involves the emission or absorption of high frequency radiation.

Planck’s constant cont.

• The math formula used is:

E = h x vE = radiant energy of a unit (quantum)h = Planck’s constant = 6.6262 x 10 -34

v = frequency of radiation

Planck’s constant cont.

• In 1905, Albert Einstein used Planck’s work to call quanta of light photons. He then used this information to explain the photoelectric effect (metals eject/emit electrons called photoelectrons when light shines on them).

• Work problems 13 and 14 on p. 379.