Arrangement of Electrons in Atoms (Chapter 4) Notes

Part 1 Properties of Electrons

I. Properties of Light-Different types of electromagnetic radiation (x-rays, radio waves, microwaves, etc…) SEEM to be very different from one another. Yet they share certain fundamental characteristics. All types of electromagnetic radiation, also called radiant energy, move through a vacuum at a speed of 3.00 x l08 meters per second.

A. Wavelength – distance between identical points on successive waves; may be measured in any length unit but is usually dependent on how long the wave is (X-rays are usually measured in nanometers or Angstroms while the very long radio waves might be measured in meter. The Greek letter, , is used to depict wavelength (pg 92)

B. Frequency – the number of complete wave cycles that pass a given point in one second: the unit is cycles/second but is written as sec-1, or Hertz. The Greek letter , is used to depict frequency.

Wavelength and frequency vary inversely and are thus related as the product of frequency and wavelength equals the speed of light, c.

c = c = 3.00 X 108m/s

1. What is the wavelength of radiation whose frequency is 6.24 x l013 sec-1?

A: 4.81X10-6 m

2. what is the frequency of radiation whose wavelength is 2.20 x l0-6 nm? (2.20 X 10-15 m)

A: 1.36X1023 s-1 or Hz

3. The range of visible light is generally considered to be from 350 to 700 nm (3.50 X 10-7m to 7.00 X 10-7 m. What is the range of frequency of visible light?

A: 8.6X1014 s-1or Hz to 4X1014 s-1or Hz

Violet:   400 - 420 nm Indigo:   420 - 440 nm Blue:   440 - 490 nm Green:   490 - 570 nm Yellow:   570 - 585 nm Orange:   585 - 620 nm Red:   620 - 780 nm

When white light passes through or is reflected by a colored substance, a characteristic portion of the mixed wavelengths is absorbed. The remaining light will then assume the complementary color to the wavelength(s) absorbed. This relationship is demonstrated by the color wheel shown on the right. Here, complementary colors are diametrically opposite each other. Thus, absorption of 420-430 nm light renders a substance yellow, and absorption of 500-520 nm light makes it red

II. The Photoelectric Effect (pg 93) – refers to the emission of electrons from a metal when light shines on the metal. The wave theory of light (early 1900) could not explain this phenomenon. The mystery of the photoelectric effect involved the frequency of the light striking the metal. For a given metal, no electrons were emitted if the light’s frequency was below a certain minimum – regardless of how long the light was shone. Light was known to be a form of energy, capable of knocking loose an electron from a metal. But the wave theory of light predicted that light of any frequency could supply enough energy to eject an electron. Scientists couldn’t explain why the light had to be of a minimum FREQUENCY in order for the photoelectric effect to occur.

Energy Information – Radiation of different wavelengths affect matter differently – certain wavelengths (near infrared) may burn your skin with a heat burn, overexposure to X radiation causes tissue damage. These diverse effects are due to differences in the energy of the radiation. Radiation of high frequency and short wavelength are more energetic than radiation of lower frequency and longer wavelength. THE QUANTITATIVE RELATIONSHIP BETWEEN FREQUENCY AND ENERGY WAS DEVELOPED THROUGH THE QUANTUM THEORY OF MAX PLANCK.

The explanation of the photoelectric effect dates back to 1900 when Max Planck revised classical ideas of light by proposing that light, which before was thought of as a collection of waves, consisted of BUNDLES OF ENERGY called QUANTA. A quantum is the minimum quantity of energy that can be lost or gained by an atom. Planck proposed the following relationship between a quantum of energy and the frequency of radiation:

E = hvPlanck’s constant, h, is 6.63 x l0-34 Joules sec Many times, you will use this formula AND the

formula, c = , together.

1. If a certain light has 7.18 x l0-19 J of energy, what is the frequency of this light? A: 1.08X1015 s-1or Hz

b. what is the wavelength of this light? A: 2.75X10-7 m

2. If the frequency of a certain light is 3.8 x l014 Hz, what is the energy of this light? A: 2.5X10-19 J

3. The energy of a certain light is 3.9 x l0-19 J. What is the wavelength of this light? Is it visible? A: 510 nm – Yes visible light.

4. Calculate the smallest increment of energy that an object can absorb from yellow light, the color given off when sodium atoms are heated in a flame. The wavelength of this light is 589 nm. A: 3.36X10-19 J

Albert Einstein expanded on Planck’s theory by explaining that electromagnetic radiation has a dual wave-particle nature. While light exhibits many wavelike properties, it can also be thought of as a stream of particles. Each particle of light carries a quantum of energy. Einstein called these particles PHOTONS. A photon is a particle of electromagnetic radiation having zero mass and carrying a quantum of energy.

Einstein explained the photoelectric effect by proposing that electromagnetic radiation is absorbed by matter only in whole numbers of photons. In order for an electron to be ejected from a metal surface, the electron must be struck by a single photon possessing at least the minimum energy (Ephoton = hv) required to knock the electron loose, this minimum energy corresponds to a minimum frequency. If a photon’s frequency is below the minimum, then the electron remains bound to the metal surface. Electrons in different metals are bound more or less tightly, so different metals require different minimum frequencies to exhibit the photoelectric effect.

 

Example from problem 4: An atom or molecule emitting or absorbing radiation whose wavelength is 589 nm cannot lose or gain energy by radiation except in MULTIPLES OF 3.37x l0-19 J. It cannot, for example, gain 5.00 x l0-19 J from this radiation because this amount is not a multiple of 3.37 x l0-19.

5. In astronomy, it is often necessary to be able to detect just a few photons because the light signals from distant stars are so weak. A photon detector receives a signal of total energy 4.05 x l0-18 J from radiation of 540 nm wavelength. How many photons have been detected? 

A: 11 photons

6. Excited chromium atoms strongly emit radiation of 427 nm. What is the energy in kilojoules per photon?

A: 4.66X10-22 kJ

7. Light hitting certain chemical substances may cause rupture of a chemical bond. If a minimum energy of 332 kJ is required to break a carbon-chlorine bond in a plastic material, what is the longest wavelength of radiation that possesses the necessary energy? A: 5.99X10-31 m

 

III. The Hydrogen-Atom Line-Emission Spectrum

When investigators passed electric current through a vacuum tube containing hydrogen gas at low pressure, they observed the emission of a characteristic pinkish glow. When a narrow beam of the emitted light was shined through a prism, it was separated into a series of specific frequencies (and therefore specific wavelengths, c =) of visible light. The bands of light were part of what is known as hydrogen’s LINE-EMISSION SPECTRUM. (page 95)

The lowest energy state of an atom is its ground state.

A state in which an atom has a higher amount of energy is an excited state. When an excited atom returns to its ground state, it gives off energy.

IV. Bohr’s Model of Hydrogen – Neils Bohr incorporated Planck’s quantum theory to explain line-emission spectra. Bohr said the absorptions and emissions of light by hydrogen corresponded to energy changes within the atom. The fact that only certain frequencies are absorbed or emitted by an atom tells us that only certain energy changes are possible.

 Bohr’s model incorporated (l) Rutherford’s

Experiment, which established a nucleus and (2) Einstein’s theory that used Planck’s quantum theory to determine that light is discrete bundles of energy.

V. Bohr’s Theory of the Atom:Electrons cannot have just any energy; only

orbits of certain radii having CERTAIN energies are permitted.

Thus, when an electron absorbs quanta of energy, it will cause them to jump away from the nucleus to a higher orbit (energy level or n) and when the electron falls from a high orbit to a lower one, a photon of a particular wavelength is released, and a particular color will be given off. Bohr was able to calculate a set of allowed energies. Each of these allowed energies corresponds to a circular path of a different radius.

Thus the larger the value of n, the farther the electron is from the nucleus and the higher energy it possesses.

 The success of Bohr’s model of the hydrogen

atom is explaining observed spectral lines led many scientist to conclude that a similar model could be applied to all atoms. It was soon recognized, however, that Bohr’s approach did not explain the spectra of atoms with more than one electron. Nor did Bohr’s theory explain the chemical behavior of atoms.

Part 2 Quantum Model of the Atom

So, where are the electrons of an atom located?

A. Various Models of the Atom

Dalton’s Model

Thompson’s Plum Pudding Model

Rutherford’s Model

Bohr’s ‘Solar System’ Model – electrons rotate around the nucleus

Quantum Mechanics Model – modern description of the electron in atoms, derived from a mathematical equation (Schrodinger’s wave equation)

B. In 1926, the Austrian physicist Erwin Schrodinger used the hypothesis that electrons have a dual wave/particle nature to develop an equation that treated electrons in atoms as waves.

Schrodinger’s equation results in a series of so called wave functions, represented by the letter (psi). Although has no actual physical meaning, the value of 2 describes the probability distribution of an electron. (Same concept you learned in Algebra II when you were doing linear regressions and finding the best fit line.)

We cannot know both the location and velocity of an electron (Heisenberg’s uncertainty principle), thus Schrodinger’s equation does not tell us the exact location of the electron, rather it describes the probability that an electron will be at a certain location in the atom.

1.      Waves are confined to a space and can only have certain frequencies.

2.      Electrons are considered to be waves confined to the space around an atomic nucleus. Electrons can only exist at specific frequencies. And according to E=hv (Planck’s hypothesis), these frequencies correspond to specific energies (or quantified amounts of energy.)

3.      Electrons, like light waves, can be bent or diffracted.

C. Heisenberg’s Uncertainty Principle: says that there is a fundamental limitation on just how precisely we can hope to know both the location and the momentum of a particle. It turns out that when the radiation used to locate a particle hits that particle, it changes its momentum. Therefore, the position and momentum cannot both be measure exactly. As one is measured more precisely, the other is known less precisely.

Today we say that the electrons are located in a region outside the nucleus called the electron cloud.

I. Electron Cloud – Energy Levels

Electrons are found in various energy levels around the nucleus. The energy levels are analogous to the rungs of a ladder. The lowest rung of the ladder corresponds to the lowest energy level. A person can climb up or down a ladder by going from rung to rung. Similarly, an electron can jump from one energy level to another. A person on a ladder cannot stand between the rungs, similarly, the electrons in an atom cannot exist between energy levels.

A. Quantum: To move from one rung to another, a person climbing a ladder must move just the right distance. To move from one energy level to another, an electron must gain or lose just the right amount of energy. The exact amount of energy required to move from one energy level to another is called a quantum of energy.

B. Photon: When electrons move from one energy level to another energy level we see light – going from one energy level to another energy level gives off an exact amount of light (called a photon).

II. Quantum Mechanics Model of the Atom and Quantum Numbers

Quantum Numbers – a series of numbers which describe several properties of an energy level (or orbit)

A. Principal Quantum Number, “n” (Energy Levels): energy levels (represented by the letter n) are assigned values in order of increasing energy: n=1,2,3,4, and so forth…. which correspond to the periods in the periodic table. The principle q. n. is related to the size and energy of the orbital. n=1, n=2, n=3, n=4, n=5, etc… Which energy level is furthest away from the nucleus and has electrons with the highest energy - 1, 2,3, or 4?

B. Angular Momentum or Azimuthal Quantum Number, “l” (Sublevels): Within each energy level, the electrons are located in various sublevels – there are 4 different sublevels s, p, d, and f. “l” defines the shape of the orbital (s, p, d, & f). The possible values of “l” are limited by the value for “n”. If n = 3, “l” can be 0, 1, or 2, but not 3 or higher. This q.n. is related to the shape of the orbital.

l = 0, is referring to the s sublevel

l = 1, is referring to p sublevel

l = 2, is referring to d sublevel

l = 3, is referring to f sublevel

1s 2s 2p 3p

C. Orbital’s: Where are the electrons in the various sublevels located in relation to the nucleus? Electrons are NOT confined to a fixed circular path, they are, however, found in definite regions of the atoms – these regions are called atomic orbital’s! Each orbital can only hold 2 electrons at a time (Pauli exclusion principle).

Within the s sublevel (l=0) there is only 1 orbital (which is spherical) it is called the s orbital.http://www.shef.ac.uk/chemistry/orbitron/AOs/1s/index.html

Within the p sublevel (l=1) there are 3 orbital’s (which are dumbbell shaped) called the px, py, pz orbital’s.

Within the d sublevel (l=2) there are 5 orbital’s (4 of which are cloverleaf shaped) called the dxy, dxz, dyz, dx2-y2, dz2 orbital’s.

Within the f sublevel (l=3) there are 7 orbital’s - which are too complex to draw

The magnetic quantum number, ml,

refers to the position of the orbital (plane) in space relative to other orbital’s. It may have integral numbers ranging from 0 in the s sublevel, 1 to –1 in the p sublevel, 2 to –2 in the d sublevel and 3 to –3 in the f sublevel.

ml = 0, is referring to the s orbital

ml = -1, 0, +1, are referring to the three p orbital’s (px, py, and pz)

ml = -2, -1, 0, +1, +2, are referring to the five d orbital’s

ml = -3, -2, -1, 0, +1, +2, +3, are referring to the seven f orbital’s

Examples:What are the values of n, l, and ml for the orbital’s in the 3 d sublevel?2. What are all possible values of n, l, and ml in the n = 3 energy level?3. Which of the following sets of quantum numbers are NOT allowed in an atom? For each incorrect set, state why it is incorrect.

A. n = l, l = 0, ml = lB. n = 2, l = 2, ml = lC. n = 5, l = 3, ml =2D. n = 6, l = -2, ml =2E. n = 6, l = 2, ml = -2

D. D. How many electrons can go into each energy level?

Each orbital can hold two electrons. (2n2 = number of electrons per energy level)

The 1st energy level (n=1) only has 1 sublevel called 1s. s only has 1 orbital called the s orbital, so only 2 electrons will be found in the 1st energy level. (2n2 = 2)

The 2nd energy level (n=2) has 2 sublevels called 2s and 2p. s only has 1 orbital called the s orbital, p has 3 orbital’s called px, py, and pz orbital’s, so 8 electrons will be found in the 2nd energy level. (2n2 = 8)

The 3rd energy level (n=3) has 3 sublevels called 3s, 3p, and 3d. s only has 1 orbital called the s orbital, p has 3 orbital’s called px, py, and pz orbital’s, and d has 5 orbital’s, so 18 electrons will be found in the 3rd energy level. (2n2 = 18)

How about the 4th energy level?

It has 4 sublevels called 4s, 4p, 4d, and 4f. s only has 1 orbital, p has 3 orbital’s, d has 5 orbital’s, and f has 7 orbital’s, so 32 electrons will be found in the 4th energy level. (2n2 = 32)

E. Lets put it all together:

Example of neon atom:

Fourth Quantum Number, ms, refers to the magnetic spin of an electron within an orbital. Each orbital can hold two electrons, both with different spins. Clockwise spin is represented with a value of +1/2 and counterclockwise spin is represented with a value of –1/2. Electrons fill the orbital’s one at a time with the same spin (+1/2), then fill up the orbital(s) with electrons of the opposite spin (-1/2).

ms = +1/2 or –1/2

Example: Which of the following sets of quantum numbers are not allowed? For each incorrect set state why it is incorrect.

A. n = 3, l = 3, ml = 0 ms = -1/2

B. n = 4, l = 3, ml = 2, ms = -1/2

C. n =4, l = l, ml = l, ms = +1/2

D. n = 2, l – 1, ml = -l, ms = -1

E. n = 3, l = 1, ml = -2, ms = -1/2

Quantum Numbers AnalogyEnergy Levels (n) or Principal Q.N.n=1 (Georgetown) n=2 (Austin) n=3 (San Antonio) n=4 (Laredo)

Sublevels (l) or Azimuthal Q.N.l=0 – s shape 1 bedrooml=1 – p shape 3 bedrooml=2 – d shape 5 bedrooml=3 – f shape 7 bedroom

Orbital’s (ml) or Magnetic Q.N.If l=0 then ml=0 (Represents the 1 bed/orbital in the s sublevel)If l=1 then ml= -1, 0, 1 (Represents the 3 bed’s/orbital’s in the p

sublevel) If l=2 then ml= -2, -1, 0, 1, 2 (Represents the 5 bed’s/orbital’s in the p

sublevel)If l=3 then ml= -3, -2, -1, 0, 1, 2, 3 (Represents the 7 bed’s/orbital’s in

the p sublevel)Magnetic Spin – Fourth Q.N. (ms)

ms = +1/2 - 1st electron in orbitalms = -1/2 – 2nd electron in orbital

Part III: Electron Configurations

I. Electron Configuration:

Definition of electron configuration: An electron configuration is a written representation of the arrangement of electrons in an atom.

Rules for writing Electron Configurations:

Aufbau Principle – electrons fill in order from lowest to highest

energy.

Aufbau Diagram

The Pauli Exclusion Principle – An orbital can only hold two electrons.Two electrons in the same orbital must have opposite spins.

How many electrons can occupy each sublevel (s, p, d, f)?

s = 1 x 2 = 2 e-

p = 3 x 2 = 6 e-

d = 5 x 2 = 10 e- f = 7 x 2 = 14 e-

Hund’s rule – the lowest energy configuration for an atom is the one having the maximum number of unpaired electrons for a set of degenerate orbital’s. By convention, all unpaired electrons are represented as having parallel spins with spin “up”.

Hund’s Rule

One electron enters each orbital until all the orbitals contain one electron with spins parallel.

Ex. Nitrogen

1s 2s 2p

II. What? How do we write an electron configuration?

A. 1st rule - electrons occupy orbital’s that require the least amount of energy for the electron to stay there. So always follow the vertical rule (Aufbau Principle):

You notice, for example, that the 4s sublevel requires less energy than the 3d sublevel; therefore, the 4s orbital is filled with electrons before any electrons enter the 3d orbital!!!! So just follow the above chart and you can’t go wrong!!!!)

Diagonal Rule

B. 2nd rule – only 2 electrons can go into any orbital, however, you must place one electron into each orbital in a sublevel before a 2nd electron can occupy an orbital. Orbital’s with only 1 electron in the orbital are said to have an unpaired electron in them.

III. Writing Electron Configurations (3 ways): A. Orbital Notation: an unoccupied

orbital is represented by a line______, with the orbital’s name written underneath the line. An orbital containing one electron is written as _____, an orbital with two electrons is written as ____. The lines are labeled with the principal quantum number and the sublevel letter.

Examples: (Remember that you must place one electron into each orbital before a second

electron in placed into an orbital.)Hydrogen ____ Helium __

1s 1s

Lithium ___ ____

1s 2s

Carbon ____ ____ ____ ____ _____ 1s 2s 2p 2p 2p

You try to write the notation for Titanium

B. Electron Configuration Notation: eliminates the lines and arrows of orbital notation. Instead, the number of electrons in a sublevel is shown by adding a superscript to the sublevel designation. The superscript indicates the number of electrons present in that sublevel.

Examples:

Hydrogen: 1s1 Helium: 1s2

Lithium: 1s22s1

Carbon: 1s22s22p2

You try to write the notation for Titanium

C. Short Hand or Noble Gas Notation: Use the noble gases that have complete inner energy levels and an outer energy level with complete s and p orbital’s. Use the noble gas that just precedes the element you are working with.

Boron is ls22s22p1

The noble gas preceding Boron is He, so the short way is [He]2s22p1.

Sulfur is ls22s22p63s23p4

Short way: [Ne]3s23p4

Example: Titanium

               

               

               

                                   

                                   

                                   

                                   

                       

                           

                           

Using the Periodic Table

More Practice Problems: Write electron configurations for each of the following

atoms:1. boron2. sulfur3. vanadium4. iodineDraw orbital diagrams for these:5. sodium6. phosphorus7. chlorineWrite shorthand electron configuration for the following:8. Sr9. Mo 10. Ge

IV. Electron Configurations and Quantum Numbers – When writing the quantum numbers for a given element, keep the following in mind:

1. The highest energy electron is the LAST one you write in the electron configuration.

1s22s22p63s23p5 -- the 3p5 electron is the last written. Remembering Aufbau’s Principle, electrons fill from the lowest to the highest energy.

2. The outermost electron is the one with the LARGEST principle quantum number. It may be the last one you write: 1s22s22p63s23p64s23d104p2. The 4 p2 is the farthest from the nucleus. OR(2) 1s22s22p63s23p64s23d10. Here, it is the 4s2 electron, because it has the largest principle q.n.

To write the quantum numbers for the first example above, the 3p5 electron:

n = 3, l = 1, ml = 0, ms = -1/2

For the second example, the 4p2 electron: n = 4, l = 1, ml = 0, ms = +1/2

For the third example, the 4s2 electron is the outermost electron (but not the one with the highest energy) so the q.n.’s for the outermost electron would be: n = 4, l = 0, ml = 0, ms = -1/2

You try it: Write the electron configuration and the quantum numbers for the following:

1. outermost electron in bromine

2. outermost electron in copper

3. highest energy electron in vanadium

4. Write the electron configuration and the quantum numbers for the 35th electron in rubidium

Irregular Electron configurations – sometimes the electron configuration is NOT what we would predict it to be. Sometimes electrons are moved because (l) it will result in greater stability for that atom or (2) for some unknown reason??

It is very important to define “stable” here. STABLE means:

1. all degenerate (equal energy) orbital’s are FULL

2. all degenerate orbital’s are half-full

3. all degenerate orbital’s are totally empty.

Examples – draw the orbital’s (lines or boxes) and fill each orbital with the predicted number of electrons. Predict the electron configuration for Cr #24: [Ar]4s23d6

However, the real E. C. is [Ar]4s13d5. The 4s1 electron has been moved to achieve greater stability.

ALWAYS USE THE ACTUAL E. C. AND NOT THE PREDICTED ONE. YOU WILL HAVE THESE ATOMS WITH IRREGULAR E. C. HIGHLIGHTED OR MARKED ON YOUR PERIODIC TABLE.

Electron configurations for Ions-First, determine if the element will lose or gain electrons. Secondly, what number of electrons will be gained or lost? It is recommended that you write the e.c. for the atom and then determine what will happen.

For cations (positive ions) – look at the element and decide how many electrons will be lost when it ionizes and keep that in mind when writing the E. C. The last number in the E. C. will now be LESS than what is written on your periodic table.Ex. Write the electron configuration for magnesium ion: [Ne]3s2 is for the atom. Mg is a metal and will lose its valence (outer) electrons, so the e.c. for Mg2+ is 1s22s22p6

Practice: 1. #32. #123. #194. #13

For anions (negative ions) – look at the element and decide how many electrons that element will GAIN when it ionizes. The last number in the E. C. will be MORE than what is written on the periodic table.Ex. Sulfide ion: Sulfur atom is 1s22s22p4. Sulfur is a nonmetal with 6 valence electrons (2s2 and 2p4) and will gain 2 electrons: 1s22s22p6 is for the sulfide ion.Practice:

1. #172. #73. #164. #30