AP Chemistry Unit 7 Atomic Structure and Periodicity

Unit 7: Atomic Structure and Periodicity You should be able to: Characteristics of waves Light Spectrum order 3 light equations Atomic Spectrum Bohr’s Model Rydberg equation Schrodinger model/quantum mechanical model o Compare and contrast between the two Heisenberg uncertainty principle Quantum #’s Orbital shapes and energies Electron configuration o Short hand - "Noble Gas Configuration" Reading the periodic table o Long hand - Complete Electron Configuration Arrows - Orbital Notation History of the periodic table Periodic groups Representative vs. transition elements Periodic Trends o Ionization Energy o Electronegativity o Atomic Size o Ionic Size o Shielding o Electron Affinity Know what a metalloid is

7.1 Electromagnetic Radiation Read and outline 7.1

Define:

• Electromagnetic Radiation

• Wavelength

• Frequency

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• Amplitude

• Trough

• Crest

How does frequency and wavelength relate to each other? How fast does light travel? How does a microwave work? 7.1 Notes One way energy travels thought space is by electromagnetic radiation. Wavelength (λ) is the distance between two consecutive peaks. Frequency () is the amount of wave cycles per second that pass a given point. The unit for frequency is hertz (Hz) which are inverse seconds.

Short wavelengths have high frequencies and high energy

Long wavelengths have low frequencies and low energy

“c”—the speed of light; 2.99792458 [just call it 3] × 108 m/s;

ALL EM RADIATION TRAVELS AT THIS SPEED!

c=λν c = 2.99 x 108

m/s λ = Wavelenght (m) ν = Frequency (1/s)

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7.2 The Nature of Matter Read and outline 7.2 Define: Planck’s Constant

Quantized

Photons

Dual Nature of Light

Diffraction

Diffraction Pattern

What are particles described as?

What are waves described as?

Example 7.1a

The brilliant red colors seen in fireworks are due to the emission of light with wavelengths around 650 nm when strontium salt such as strontium nitrate and strontium carbonate are heated. Calculate the frequency of this red light with a wavelength of 6.50 x 102 nm.

υ = 4.61 × 1014 Hz

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What did “old physics” say about matter and energy?

How can a system transfer energy according to Planck?

If a beam of light can be consider to be a stream of particles, do photons have mass? Why or why not?

How does white light’s diffraction grading and Hydrogen’s spectrum differ?

What does all matter exhibit?

What are the conclusions of Planck’s and Einstein’s experiments?

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7.2 Notes At the end of the 19th century, physicists were feeling rather smug. All of physics had been explained [or so they thought]. Matter and Energy were distinct: Matter was a collection of particles and Energy was a collection of waves. Enter Max Planck stage left… Max Planck solved the "Ultraviolet catastrophe" problem - the fact that a glowing hot object did not emit UV light as predicted. He made an incredible assumption: There is a minimum amount of energy that can be gained or lost by an atom, and all energy gained or lost must be some integer multiple, n, of that minimum. (As opposed to just any old value of energy being gained or lost.) Energy is in fact is quantized and can occur only in discrete units of h. where h is a proportionality constant, Planck's constant, h = 6.6262 x 10-34 J*s . This ν is the lowest frequency that can be absorbed or emitted by the atom, and the minimum energy change, hν, is called a quantum of energy. Think of it as a “packet” of E equal to hυ. There is no such thing as a transfer of E in fractions of quanta, only in whole numbers of quanta.

de Broglie’s equation:

You know Einstein for the famous E = mc2 from his second “work” as the special theory of relativity published in 1905. Such blasphemy, energy has mass?! That would mean:

2CE

m =

therefore,

mx Ch

or...... Ch

C

hC/ 2 ==== λ

λλ

2CE

m

Light can have wave like properties, and have certain characteristics of particulate matter.

∆Energy = n(hν)

Example The blue color in fireworks is often achieved by heating copper (I) chloride to about 1200OC. Then the compound emits a blue light having a wavelength of 450. nm. What is the increment of energy that is emitted?

= 4.41 × 10-19 J

Example What is the energy of the red light that has a wavelength of 675 nm?

= 2.94 × 10-19 J

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Example Compare the wavelength for an electron (mass = 9.31 x 10-31 kg) traveling at a speed of 1.0 x 107 m/s with that for a ball (mass = 0.10 kg) traveling at 35 m/s. Worksheet 7.01 Light Equations

1. Calculate the wavelength of a wave whose frequency is 6.4 × 1022 s−1. 2. Find the energy of a light beam that has a frequency of 5.4 × 1022 Hz. 3. Find the frequency of a particle that has an energy of 1.6 × 10−19 J. 4. Calculate the frequency of a wave that has a wavelength of 3.4 × 107 m. 5. A beam of light has a wavelength of 4.3 × 10−7 m. Find the energy of the light beam.

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Worksheet7.02 Name______________________________ Light Equations

Solve the following problems using the de Broglie equation:

1. If a particle has a mass of 0.0045 kg, and is traveling at a velocity of 35.5 m/s, find its wavelength, in meters. 2. A 0.200 kg baseball has a wavelength of 1.0 × 10−34 m. Find its velocity, in m/s. 3. A rock has a wavelength of 3.4 × 10−35 m. It is moving at 56 m/s. Find its mass, in kg. 4. What is the wavelength of an electron that has a mass of 9.11 × 10−31 kg and is traveling at a velocity of

4.4 × 106 m/s? 5. If a proton has a mass of 1.67 × 10−27 kg, and is traveling at a velocity of 4.2 × 104 m/s, find its frequency, in Hz.

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7.3 The Atomic Spectrum of Hydrogen Read and outline 7.3 Define:

• Continuous Spectrum

• Line Spectrum What is significant of the line spectrum of hydrogen? 7.3 Notes

Diffraction results when light is scattered from a regular array of points or lines. A continuous spectrum is made from white light shined through a prism, and a diffraction grating is made from exciting electrons. Emission spectrum—the spectrum of bright lines, bands, or continuous radiation that is provided by a specific emitting substance as it loses energy and returns to its ground state OR the collection of frequencies of light given off by an "excited" electron. Absorption spectrum—a graph or display relating how a substance absorbs electromagnetic radiation as a function of wavelength Line spectrum--isolate a thin beam by passing through a slit then a prism or a diffraction grating which sorts into discrete frequencies or lines What is the significance of the line spectrum of hydrogen? It indicates that only certain energies are allowed for the electron in the hydrogen atom. In another words, the energy of the electron in the hydrogen atom is quantized. The discrete line spectrum of hydrogen shows that only certain energies are possible; that is, the electron energy levels are quantized, in contrast, if any energy level were allowed, the emission spectrum would be continuous. Niels Bohr connected spectra, and the quantum ideas of Einstein and Planck: the single electron of the hydrogen atom could occupy only certain energy states, stationary states

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7.4 The Bohr Model Read and outline 7.4 Define:

• Quantum Model

What is significant of the line spectrum of hydrogen? What quantum number did Bohr find to fit his model? What are two important points to the Bohr Model? Why does Bohr’s Model only work for Hydrogen? 7.4 Notes

An electron in an atom would remain in its lowest E state unless otherwise disturbed.

• Energy is absorbed or emitted by a change from this ground state

• an electron with n = 1 has the most negative energy and is thus the most strongly attracted to the positive nucleus. [Higher states have less negative values and are not as strongly attracted to the positive nucleus.]

• ground state--n = 1 for hydrogen

λγ hC

h ==photonE

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• To move from ground level to n = 2 the electron/atom must absorb no more or no less than

0.75 Rhc. [that’s a collection of constants]

• So, a move of n = 2 to n = 1 emits 985 kJ of energy. • What goes up must come down. Energy absorbed must eventually be emitted. • The origin or atomic line spectra is the movement of electrons between quantized energy states. • IF an electron moves from higher to lower E states, a photon is emitted and an emission line is observed. • Bohr’s equation for calculating the energy of the E levels available to the electron in the hydrogen atom:

= 2

218-

nZ

J10x 2.178- E

• where n is an integer [larger n means larger orbit radius, farther from nucleus], Z is the nuclear charge • The NEGATIVE sign simply means that the E of the electron bound to the nucleus is lower that it would be if the

electron were at an infinite distance [n = ∞] from the nucleus where there is NO interaction and the energy is zero.

• ΔE is simply the subtraction of calculating the energy of two different levels, say n=6 and n=1. If the difference is negative, E was lost. If the difference is positive, E was gained.

• As the electron becomes more tightly bound, its energy becomes more negative related to the zero-energy reference state (corresponding to the electron being at infinite distance from the nucleus). As the electron is brought closer to the nucleus, energy is released for the system.

• TWO Major defects in Bohr's theory: 1) Only works for elements with ONE electron. 2) The one, lonely electron DOES NOT orbit the nucleus in a fixed path!!

Example Calculate the energy required to excite the hydrogen electron from level n = 1 to level n=2. Also calculate the wavelength of light that must be absorbed by a hydrogen atom in its ground state to reach this excited state.

ΔE = 1.633 × 10-18 J λ = 1.216 × 10-7 m

Example Calculate the energy required to remove the electron for a hydrogen atom in its ground state.

ΔE = 2.178 × 10-18 J

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Worksheet 7.03 Name______________________________ Bohr’s Orbitals 1. Calculate the wavelengths of the light emitted when each of the following transitions occur in the hydrogen

atom. a. n = 3 → n = 2 b. n = 4 → n = 2 c. n = 5 → n = 3

2. Using vertical lines, indicate the transition form the above problem on an energy – level diagram for the hydrogen atom (see fig 7.8)

3. An excited hydrogen atom emits light with a frequency of 1.141 x 1014 Hz to reach the energy level for which n = 4. In what principle quantum level did the electron begin?

4. From the Heisenberg uncertainty principle, calculate Δx for a baseball (mass = 145g) with Δv 0.100m/s. How

does this Δx compare to the size of the baseball?

5. Calculate the maximum wavelength of light capable of removing an electron for a hydrogen atom form the energy state characterized by n = 4 to n = 10.

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7.5 The Quantum Mechanical Model of the Atom Read and outline 7.5 Define:

• Standing Wave

• Wave Function

• Orbital

• Quantum Mechanical Model

• Heisenberg Uncertainty Principle

• Probability Distribution

• Radial probability distribution 7.5 Notes Quantum Mechanics--- to Schrodinger and de Broglie the electron bound to the nucleus seemed similar to a standing wave. Standing waves can be looked at like playing an instrument. The wave is kept between two or more nodes. We can have a whole number of half wavelengths. Only certain circular orbits have a circumference into which a whole number of wavelengths of the standing electron wave will fit.

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THE WAVE MECHANICAL VIEW OF THE ATOM

Schrodinger equation: ĤΨ = EΨ Schrodinger equation Ψ is the wave function. Each solution consists of a wave function that is characterized by a particular value of E (energy). A specific wave function is often called an orbital. The wave function does not know the pathway of the electron.

• solutions are called wave functions--chemically important. The electron is characterized as a matter-wave

• sort of standing waves--only certain allowed wave functions

(symbolized by the Greek letter, ψ, pronounced “sigh”)

• Each ψ for the electron in the H atom corresponds to an allowed energy (−Rhc/n2). For each integer, n, there is an atomic state characterized by its own ψ and energy En.

• In English? Points 1 & 2 above say that the energy of electrons is quantized.

The hydrogen electron is visualized as a standing wave around the nucleus [above right]. The circumference of a particular circular orbit would have to correspond to a whole number of wavelengths, as shown in (a) and (b) above, OR else destructive interference occurs, as shown in (c). This is consistent with the fact that only certain electron energies are allowed; the atom is quantized. (Although this idea encouraged scientists to use a wave theory, it does not mean that the electron really travels in circular orbits.) Heisenberg uncertainty principle - There is a fundamental limitation to just how precisely we can know both the position and momentum of a particle at a given time.

Δx is the uncertainty of the position

Δ(mv) is the uncertainty of the momentum h is Planck’s constant.

The more accurately we know the position of an electron the less accurately we know the momentum.

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7.6 Quantum Numbers Read and outline 7.6 Define:

• Quantum Numbers

• Principle Quantum Number

• Angular Momentum Quantum Number

• Magnetic Quantum Number

• Subshell (Sublevel)

• Magnetic Spin Quantum Number

7.6 Notes

• Quantum numbers o Orbitals made for the Schrödinger equation.

• Principle quantum number (n)

o Energy level o Related to the size and the energy of

the orbital.

• Angular momentum quantum number (l) o Integers from 0 to n-1 o Related to the shape of the orbital

s = 0 p = 1 d = 2 f = 3

• Magnetic quantum number (ml)

o Integer value between l and –l o Related to the orientation of the orbital

• Magnetic Spin (ms)

o Electrons need to spin opposite ways o ms = -½ or ½

Example For principle quantum level n = 4, determine the number of allowed subshells (l), and the given designation of each

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Worksheet 5.04 Name______________________________ Quantum numbers 1. Circle the following designations that are incorrect : 1s, 1p, 7d, 9s, 3f, 4f, 2d.

2. Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets that are

incorrect, state which is wrong in the set.

a. n = 2 l = 1 ml = -1

b. n = 1 l = 1 ml = 0

c. n = 8 l = 7 ml = -6

d. n = 1 l = 0 ml = 2

3. Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets that are

incorrect, state which is wrong in the set. a. n = 3 l = 2 ml = 2

b. n = 4 l = 3 ml = 4

c. n = 0 l = 0 ml = 0

d. n = 2 l = -1 ml = 1

4. Give the maximum amount of electrons in an atom that can have their quantum numbers: a. n = 4 b. n = 5 ml = +1

c. n = 5 ms = +1/2

d. n = 3 l = 2

e. n = 2 l = 1

f. n = 0 l = 0 ml = 0

g. n = 2 l = 1 ml = -1 ms = +1/2

h. n = 3

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7.7 and 7.8 Orbital Shapes and Energies and Electron Spin and the Pauli Exclusion Principle Read and outline 7.7 and 7.8 Define:

• Nodal Surfaces

• Nodes

• Degenerate

• Electron Spin

• Electron spin quantum number

• Pauli Exclusion Principle

Summarize the Hydrogen Atom: 1. 2. 3. 4.

What does 2px1 mean?

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7.7 Notes

The electron probability distribution for a 1s orbital Node is an area that the electron has no probability of being in.

THE SHAPES OF ATOMIC ORBITALS

There is no sharp boundary beyond which the electrons are never found!! • s--spherical; the size increases with n. The nodes you see at left represent

ZERO probability of finding the electron in that region of space. The number of nodes equals n-1 for s orbitals.

• p--have one plane that slices through the nucleus and divides the region of

electron density into 2 halves. Nodal plane--the electron can never be found there!!

• 3 orientations: px, py, and pz.

• d--2 nodal planes slicing through the nucleus to create four sections; 5 orbitals. - The dz2 orbital is really strange!

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7.9 Polyelectronic Atoms and 7.10 The History of the Period Table Read and outline 7.9 and 7.10

Define: • Polyelectronic Atoms

• Degenerate Orbitals What are the three energy contributions that must be considered when describing a helium atom? 1.

2.

3.

The repulsions of the electrons cause ______________________ (more/less) of an uncertainly in the pathway and they ________________________ (can/cannot) be calculated exactly. This is called the electron correlation problem.

Es < Ep < Ed < Ef

"Penetrates" closest to the nucleus

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THE HISTORY OF THE PERIODIC TABLE in the 1800's Johann Dobereiner arranged the periodic table by _____________________________ In 1864 John Newlands arranged the periodic table by _____________________________ In 1870--Dmitrii Mendeleev & Julius Lothar Meyer arranged the periodic table according to ___________________ __________ and in 1913, Mosley arranged the elements by _______________________ The modern Periodic table of the elements contain ______________ groups (families) and _____________ periods.

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7.11 Electron Configuration Read and outline 7.11 Define: • Aufbau Principle

• Hund’s Rule

• Core electrons

• Valence electrons

• Transistion Metals

• Lanthanide series

• Actinide series

• Representative elements

ATOMIC ORBITAL ENERGIES AND ELECTRON ASSIGNMENTS

So How do we do that? Order of Orbital Assignments:

"Long hand" electron configuration

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Orbital Notation: "Short hand" (Noble Gas) electron configuration Electron configuration for ions: Isoelectronic species -- contain the same number of electrons

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7.12 Periodic Trends in Atomic Properties Read and outline 7.12 Define:

• First ionization energy

• Second ionization energy

• Electron affinity

• Atomic Radii

On page 309 there are ionization energies for Aluminum. Look at the I values, how can you tell that the stable Aluminum ion has a 3+ charge? What are the trends for:

Atomic Radii -

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Ionic Radius Ionization energy Successive Ionization energies

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Electron Affinity Electronegativity Summary of period trends. Add the ones that are not on this chart.

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Worksheet 7.07 Name______________________________ Periodicity For each of the following pairs, circle the atom or ion that is larger. Use the periodic table to assist you.

Magnesium atom or Sodium atom Cs1+ ion or Ca2+ ion

Iodine atom or Chlorine atom Silicon atom or Fluorine atom

Positive Sr2+ ion or Neutral Sr atom Selenium atom or Gold atom

Fluorine atom or Sulfur atom Aluminum atom or Helium atom

Sodium atom or Barium atom Xenon atom or Silver atom

Neutral Co atom or Positive Co2+ ion N3− ion or S2− ion

P3− ion or Al3+ ion Cobalt atom or Cesium atom

For each of the following pairs, circle the element that has the larger ionization energy. Use the periodic table to assist you.

Li or N Cl or Se

Li or K Cl or B

Li or Sc Br or Pd

Mg or Rb F or Fe

Mg or C F or Na

Mg or Cl V or Mo

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Worksheet 7.08 Name______________________________ Periodicity

Answer the following questions.

1. Restate in one or two words: “The amount of energy required to remove the first electron from the valence shell of a neutral atom.”

2. Restate in one or two words: “The tendency of an atom to hold on to its valence electrons while engaged in a chemical bond.”

3. Restate in one or two words: “The actions of the non-valence electrons, diluting the force of the attraction between nucleus and valence electrons.”

4. Which atom has a greater shielding, Au or Cu? Why?

5. Which has a larger atomic eadius, Au or Cu? Why?

6. Which has greater first ionization energy, Cu or Ag? Why?

7. Which has greater shielding, Xe or Ar? Why?

8. Which is a larger ion, sulfur ion or phosphorus ion? Why?

9. Which has greater shielding, Ge or Ra? Why?