AP Chemistry: Chapter 7 - Atomic Structure & Periodicity

AP Chemistry

To: 2013-2014 AP Chemistry students From: Big Evergreen III, a past student of Mrs. Moses SUBJECT: Hints / strategies / review to survive AP Chemistry. Think categorically: know acid from base, strong from weak, metal from nonmetal,

ionic from covalent, etc. Know your nomenclature, you will need it for everything. When you are taught something, learn it: many concepts are reused within other

concepts so if you didn’t learn something in the first place it will hurt you later. Know your solubility rules: this will help so much on the reactions part of the exam! Learn the details and the relationships: How does temperature, pressure, etc. affect a

certain system? What does it mean if something is solid, liquid or gas? What are certain

numbers dependent upon?

Table of Contents 1. Atoms, Molecules, and Ions...........................................................................................................

2. Stoichiometry .................................................................................................................................

3. Reactions ........................................................................................................................................

4. Gases ..............................................................................................................................................

5. Thermochemistry ...........................................................................................................................

6. Atomic Structure & Periodicity .....................................................................................................

7. Fundamentals of Chemical Bonding ..............................................................................................

8. Theories of Chemical Bonding ......................................................................................................

9. Liquids & Solids ............................................................................................................................

10. Properties of Solutions .................................................................................................................

11. Kinetics ........................................................................................................................................

12. Chemical Equilibrium ..................................................................................................................

13. Acids and Bases ...........................................................................................................................

14. Aqueous Equilibria ......................................................................................................................

15. Spontaneity of Chemical Processes .............................................................................................

16. Electrochemistry ..........................................................................................................................

17. Nuclear Chemistry & Radiochemistry .........................................................................................

18. O-Chem aka Organic Chemistry ..................................................................................................

Atomic Structure and Periodicity Particles and Waves

Electromagnetic Radiation

Much information about atomic electronic structure was obtained from studies on

the interaction of electromagnetic radiation with matter.

• Electromagnetic radiation carries energy through space & has a wavelike

nature. E.g. light, x-rays, microwaves

• Each wave has a characteristic wavelength and frequency.

wavelength, λ: distance between wave peaks. Units: m

frequency, ν: # of cycles (complete waves) that pass a point in one second.

Units are hertz. 1 Hz = 1 s-1

In a vacuum, all electromagnetic radiation travels at a speed of 3.00 x 108

m/s. This is the speed of light, c.

c = νλ (speed of light = frequency X wavelength)

units: m/s = s-1 m

frequency and wavelength are inversely proportional

Practice Problems

*

1. Calculate the frequency of an X ray that has a wavelength of 8.21 nm.

(hint: 1nm = 10-9

m)

Step 1: Write the formula to find frequency if wavelength is given

c = νλ

Step 2: Manipulate the formula so that you’re solving for frequency

c = νλ c/λ = ν/λ ν = c/λ

Step 3: Convert 8.21nm to m so that we can cancel out the units in the

train-and-caboose (this is kind of a given, but I just added it as a step

anyway…)

8.21 nm x 10-9

m = 8.21 x 10-9

m

1 nm

Step 3: Plug in the values and chug

ν = (3 x 108 m/s) / (8.21 x 10

-9 m)

= 3.65 x 1016

1/s or 3.65 x 1016

s-1

Now, try the rest on your own!

2. Calculate the wavelength, in nm, of infra-red radiation that has a

frequency of 9.76 x 1013

s-1

(the answer should be in nm, not m)

3. Calculate the frequency, in hertz, of a microwave that has a wavelength

of 1.07 mm (that’s right, mm not nm!) Answers: 2) 3.1 x 103 nm 3) 2.8 x 1011 s-1

Electromagnetic Spectrum

A "continuum" of all possible wavelengths of electromagnetic radiation

Humans only see a small part of the whole EMS

The region we can see is called “visible light” (our colors)

What you need to know from the Electromagnetic Spectrum (EMS)

1. Memorize each type of wave and know how they are arranged from

lowest to highest energy (Radio, TV, Micro, Infra-red, Visible Light

(ROYGBIV), UltraViolet, X, Gamma) and their frequency

2. Know that low energy corresponds to long wavelengths and low

frequency, whereas high energy corresponds to short wavelengths and

high frequency

3. Wavelengths in the visible region range from about 400 nm to 700 nm

4. Left -> Right is from lowest energy to highest energy

Question:

1. Which light has a higher frequency: the bright red brake lights of an

automobile or the faint green light of a distant traffic signal?

Green light has a higher frequency than Red light, which means it has

more energy

Just like an atom is the smallest piece of an element, a

“quantum” is the smallest amount of energy you can

gain or lose

Quantized Energy

1900 - Max Planck introduced the theory of “quantum packets of energy”. This

theory states that energy can only be absorbed or released from atoms in discrete

quantities or “bundles.” He called the smallest bundle of energy a “quantum.”

Thus, E is quantized, not continuous.

And since c = λ ν,

h = Planck’s constant = 6.63 x 10-34

J-s

hν = smallest amount of energy

Practice Problems

A “quantum” of energy

(E) = hv

A “quantum” of energy

(E) = h times c

λ

1. Calculate the energy (in Joules) and the frequency (in Hertz) of

electromagnetic radiation that is given off by a sodium vapor lamp if the

wavelength of the radiation that is 515 nm.

Step 1: Write the correct formula to find frequency

c = λ ν

Step 2: Manipulate the formula so that you’re solving for frequency

ν = c / λ

Step 3: Calculate frequency

= 5.83 x 1014

sec-1

or 5.83 x 1014

Hz

Step 4: Write the correct formula to find Energy of electromagnetic radiation

E = hv

Step 5: Use Planck’s constant and the calculated frequency to find Energy

E = hv = (6.63 x 10-34

J.s)(5.83 x 10

14 / s) = 3.87 x 10

-19 J

*

The Photoelectric Effect

1905 - Einstein used Plank’s theory to explain the

photoelectric effect. He assumed light traveled in

energy packets called photons.

1 photon = smallest increment of radiant energy

• Energy of 1 photon: E = hν

• Thus light has both wave-like characteristics

(EM studies) & particle nature (Planck &

Einstein) a.k.a wave-particle duality of light

•More intense light would have more photons and

thus eject more electrons, whereas higher

frequency light would have more energy and give

the ejected electrons more energy

Here are some super awesome flashcards ~ http://www.funnelbrain.com/fc-14325-line-spectrum.html

Try these on your own.

2. Calculate the smallest increment of energy that can be emitted or

absorbed at a wavelength of 645 nm.

3. What frequency and wavelength of radiation has photons of energy 8.23

x 10-20

J? What type of electromagnetic radiation is this (refer to the EM

spectrum). Hint: find frequency first from the Energy formula(E = hv) and

then plug the calculated frequency into the wavelength and frequency

formula(c = λν).

Answers: 2) 3.08 x 10-19 J 3)2.41 x10-6 m, infrared radiation

Line spectra

• When white light is passed through a prism, it separates into a continuous

spectrum of all wavelengths of visible light. (ROYGBIV)

• When the light from a heated element passes through a prism, a line spectrum

with distinct lines is observed. Each line corresponds to a specific wavelength

of visible light.

• Each atom has its own unique line spectrum.

BOHR MODEL ~1913

• Bohr tried to explain observed line spectra based on

movement of electrons.

• Niels Bohr used the "planetary model” of the atom

in which electrons orbit the nucleus like planets

orbiting the sun to explain the phenomenon of "line

spectra" (at least for hydrogen)

• charged electrons travel rapidly in orbits around the

tiny + charged nucleus

• Based on Planck's and Einstein's research, Niels Bohr proposed that the energy

possessed by electrons was also "quantized". Therefore, an electron can only be

located in specific orbits (energy levels) and not just anywhere within the electron

cloud

1. Electrons are contained in specific energy levels called orbits. These energy

levels are quantized which means only certain energies are allowed. An e- in

a permitted orbit has a specific energy.

Energy levels are designated by the principal quantum number, n.

n = 1,2,3…

n = 1 is ground state level - this is level closest to nucleus

(lowest in E).

The equation below shows how much energy an electron will have

based on its location in the electron cloud (the energy level it is on)

where...

electrons would have quantized amounts of energy so they could

either be in the first energy level (n = 1) or the second energy level (n

= 2) or the third energy level (n =3 )... and so on but they could not

exist between these levels.

Practice Problem

E = energy of an electron

RH = Rydberg constant = 2.178 x 10-18

J

n = the energy level of the electron

Calculate the amount of energy an electron must have a) to be in the 1st

energy level of a hydrogen atom and b) to be in the third energy level

of a hydrogen atom

a) E =

=

= -2.18 x 10

-18 J

b) E =

=

= -2.42 x 10

-19 J

2. Electrons circle the nucleus at specific radii. (r α n2)

3. Electrons can jump from one level to another by absorbing or emitting

photons of specific frequencies. (e- must gain energy from heat, radiation,

etc. to jump to higher level.)

An electron at n=1 is in its “ground” state.

In order to jump to a higher energy level (an

“excited” state), the electron must absorb

energy in the form of photons of light.

Since everything wants to be low energy, an

excited electron will eventually transition

from an excited state to a lower energy level

(moves closer to the nucleus). To do this,

the electron must release/emit energy in the

form of photons of light.

This emission is the cause of line spectra!

The emitted energy has a specific

frequency(E=h ) and wavelength(c = λν)

that corresponds to a specific part of the

electromagnetic spectrum. If it falls in the

visible portion of the spectrum, we see it as

a colored spectral “line”. Mystery Solved!

Bohr's theory explains 4 observed lines in line spectra for hydrogen.

Lines correspond to emitted radiation in visible portion of the EM

spectrum when e- jumps from 1 level to another.

This process is responsible for colors of fireworks & neon signs.

Electrons are excited by heat or electricity and electrons jump to

higher energy levels. Light is emitted when electrons lose energy and

drop back down to lower energy levels. The colors correspond to

wavelengths of emitted light waves.

• Calculating ΔE (the transition energy)

This tells you how much energy must be absorbed or emitted to move

from one level to another

1. ΔE = Efinal – Einitial =

2. (-) J means that energy was released/emitted

Practice Problem

How does Bohr’s model of the atom explain the concept of line spectra?

Planck said energy is quantized

Einstein said light is energy so it must also be quantized (photons)

Bohr said the amount of energy an electron has must also be quantized

So when excited electrons move to a level that is closer to the nucleus by

emitting energy, the energy they emit is represented by

ΔE = hv

which shows the frequency of the emitted energy. With a known frequency,

the wavelength can be calculated (using c = λν) and we can use the

electromagnetic spectrum to determine what type of energy was emitted. If it

is in the visible region, we can see a color (a spectral line).

Practice Problem

***So, excited electrons transitioning from higher to lower energy levels will

emit/release/lose photons of specific wavelengths and frequencies that are often

visible as "colored lines" (line spectra) when viewed through a prism.

Calculate ΔE when an electron moves from n=5 to n=2.

Step 1: Write out the formula you’re going to use

ΔE = Efinal – Einitial =

Step 2: Plug & Chug

ΔE = Efinal – Einitial =

= -4.58 x 10

-19 J

Calculate the frequency and wavelength of light emitted in a hydrogen atom

when an electron goes from n=5 to n=2.

Step 1: Find change in energy

ΔE = Efinal – Einitial =

= -4.58 x 10

-19 J

Step 2: Find frequency

ΔE = hv

V =

= 6.90 x 10

14 s

-1

Step 3: Find wavelength

c = λν

λ =

= 4.3 x 10

-7 m

Step 4: Convert meters to nanometers

4.3 x 10-7

m x 1 nm = 430 nm

10-9

m

These are the known transitions that

can be made by electrons in a

hydrogen atom. You DO NOT need

to memorize them, but be aware of

the scientist’s names that were used

to name them.

WEAKNESS IN BOHR’S THEORY

Bohr’s calculations fell apart when applied to atom others than hydrogen

(atoms with more than one electron)

Bohr did not take into consideration the interactions that take place when

other electrons are present

o Electrons repel other electrons

o Electrons “shield” each other from nuclear attraction

Interactions with other electrons alter the amount of energy required by

electrons to transition from one level to another

The Particles and Waves section is done

Do these in order to reinforce what you just learned:

1. https://staff.rockwood.k12.mo.us/grayted/apchemistry/Documents/U5%20At

omic%20Structure/PROBSET%201%20Transition%20Energy.pdf (only 2

problems!! )

2. https://docs.google.com/viewer?a=v&pid=sites&srcid=bHNuZXBhbC5jb21

8YXAtY2hlbWlzdHJ5fGd4Ojc4NTlkYjFjNzNmYjUwMzc (only do

questions # 6 and 48(part a- i and ii, part b- i, ii, and iii(you’re smart, I know

you can think of a plausible reason for part iii!!))

3. https://staff.rockwood.k12.mo.us/grayted/apchemistry/Documents/U5%20At

omic%20Structure/PROBSET%205%20Test%20Prep%20Atomic%20Struct

ure.pdf (do #1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, and 23(if you want but I’ll

explain how to do this at the tutoring sesh) you can do the other ones too, but

some of them are a bit redundant)

I’ll post a review key for these questions when I get a chance.

By the end of the semester, you’ll be able to answer all the question on the

review don’t let these questions intimidate you!

Quantum Numbers

THE QUANTUM-MECHANICAL MODEL OF THE ATOM

This is how we envision the atom today

Planck noted that excited matter emits energy

Einstein showed that energy acts like both a wave (it has frequency and

wavelength) and a particle (bundled into packets called photons)

Louis DeBroglie wondered, “If light waves can act like particles of matter,

could particles of matter act like waves?”

o DeBroglie discovered that electrons could behave like waves… a

standing wave (like a vibrating guitar string). The particle and wave

properties are related by:

λ =

where h = Planck’s constant

m = mass of particle

v = velocity

Erwin Schrodinger developed an equation that describes electron behavior

as both a particle and a wave (the equation has a wave function, Ψ)

1. When you square the wave function, Ψ, you get a 3-dimensional

probability map that describes regions in space (the electron cloud)

where electrons are likely to be. We call these regions “orbitals”

(This relates to QUANTUM NUMBERS!!! I really liked

quantum numbers obvs)

2. He also set-up and solved a series of complex equations that took into

account:

KE (kinetic energy) of an electron

Wavelength of an electron

Attraction of electron for nucleus

Repulsions between electrons

Heisenberg Uncertainty Principle

Both the position and the

momentum of an electron cannot be

exactly known at the same time (ask

Moses to give her example about the

speed ticket for this principle, it’ll help

you remember)

1. In order to known either

the location or momentum of an

electron, light must hit the electron and

bounce back to your eye or measuring

device… however, the light that hits the

electron will cause it to change

momentum and/or location… it’s a no-

win situation

QUANTUM NUMBERS (eep, i’m so excited! i loved quantum numbers last year!)

Mathematical solutions to Schrodinger’s equation are associated with a set

of 3 quantum numbers

1. Principal quantum number, n

2. Azimuthal quantum number, m

3. Magnetic quantum number, ml

They are kind of like an “address” that tells us where each electron lives

within a given atom

Every electron within an atom has a unique set of quantum numbers

Principal Quantum Number (n)

Generally referred to as the “shell”

Tells the average distance from the nucleus an electron is

1. As “n” becomes larger, the radius that the electron can travel away

from the nucleus gets larger

2. Think of “n” as similar to the Bohr energy levels

Each shell can hold a max of electrons equal to 2n2

1. The first four shells can hold 2, 8, 18, and 32 electrons, respectively

Angular Momentum Quantum Number (l)

Generally referred to as the “sublevel” or “subshell” (i’m going to call them

the sublevel)

Tells the shape of the orbital

Allowed values of l = 0, 1, 2, 3, …

o The number of sublevels possible in each shell is equal to the value of

n for that subshell

The 3rd

subshell (n = 3) may contain a maximum of three

sublevels

o The value of l can never be greater than n – 1

Sublevels in the Atom

Principal Level / Shell (n) Sublevel Number, l Sublevel Letter

1 0 s

2 0,1 s, p

3 0,1,2 s, p, d

4 0,1,2,3 s, p, d, f

Problem: If n=3, what are the allowed values of l

Answer: 0, 1, 2 (s, p, d)

Magnetic Quantum Number

Generally referred to as the “orbital”

Tells the orientation of the orbital in space

Any orbital can hold a maximum of two electrons

YOU MUST KNOW HOW MANY ORIENTATIONS ARE POSSIBLE

FOR EACH ORBITAL

o 1 for s

o 3 for p

o 5 for d

o 7 for f

The number of orbitals that a sublevel may have depends on the azimuthal

quantum number, l, of the sublevel and is equal to 2l + 1

Orbitals in the Atom

Sublevel

number, l

Sublevel letter Number of

orbitals, 2l + 1

Number of

electrons per

sublevel

0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14

Allowed values ml = -l… -3, -2, -1, 0, 1, 2, 3, … l

o Orbital s = 0

o Orbital p = -1, 0 +1

o Orbital d = -2, -1, 0, +1, +2

o Orbital f = -3, -2, -1, 0, +1, +2, +3

Problem: If l = 2, what are the allowed values ml?

Answer: -2, -1, 0, 1, 2

Note that when l = 2 that corresponds to a “d” orbital. There are 5 possible

orientations of “d” orbitals, right? When l = 2, there are also 5 possible values for

ml. See the relationship?

Electron Spin Quantum Number (ms)

Generally referred to as the “spin”

This quantum number is NOT part of a solution to Schrodinger’s equation. It

was later added to ensure that each electron (even those paired up in the

same orbital) has its own unique set of quantum numbers to identify it

o Pauli Exclusion’s Principle: no two electrons in the same atom may

have the same four quantum numbers

Tells the spin of the electron within the orbital

Spinning charges produce a magnetic field. In order for two electrons to

exist in the same orbital, they must spin in opposite directions thereby

creating opposite magnetic fields that cancel each other out. This minimizes

electron-to-electron repulsion and thus creates a lower energy state that is

more stable

Allowed values of ms = +1/2 or -1/2

A Summary of Schrodinger’s “Quantum-Mechanical” Model of the Atom

1. Electrons don't just move around the nucleus of

the atom in simple circular "orbits" as Bohr had

predicted. Schrodinger developed complex equations

that describe 3-dimensional regions within the atom

where electrons are likely to be found. These regions

are called "orbitals", and 90% of the time, electrons

will be found somewhere within that region.

2. Possible solutions to Schrodinger's equations

result in a set of 3 quantum numbers (n, l, ml) that describe the size, shape, and

orientation of the orbitals, respectively. They are sort of like an "address" for each

electron within an atom.

3. According to Heisenberg's Uncertainty Principle, the more you know about an

electron's location, the less you know about its momentum and vice versa.

Schrodinger’s Quantum Mechanical Model > Bohr’s Model

Problem: Write all possible sets of quantum numbers for an electron in a 3p orbital

n = 3; l = 1 since it is a “p” orbital; there are three orbitals, so ml = -1, 0, 1

(3, 1, -1, ½) (3, 1, -1, -1/2)

(3, 1, 0, ½) (3, 1, 0, -1/2)

(3, 1, 1, ½) (3, 1, 1, -1/2)

The Quantum Numbers section is done

Do these in order to reinforce what you just learned:

1. https://staff.rockwood.k12.mo.us/grayted/apchemistry/Documents/U5%20At

omic%20Structure/PROBSET%202%20Quantum%20Numbers.pdf (only 15

questions) 2. https://staff.rockwood.k12.mo.us/grayted/apchemistry/Documents/U5%20At

omic%20Structure/PROBSET%205%20Test%20Prep%20Quantum%20Nu

mbers.pdf (only do a few problems from the first 5 pages) 3. http://www.pwista.com/Midterm%20Review.pdf (there are A LOAD of

questions on here. But just do #1-12 or just #7-12)

I’ll post an answer key for these questions when I get a chance. If I don’t

post ‘em fast enough, bring the questions to tutoring and I’ll give you the

answers then.

By the end of the semester you’ll be able to answer all the question on the

review don’t let these questions intimidate you!