Name: ______________________________

CHAPTER 5 ELECTRONS IN ATOMS5.1 Models of the Atom

What did Bohr propose in his model of the atom?

REVISING THE ATOMIC MODEL

The Bohr Model of the AtomBohr proposed that an electron is magnitude the farther from the nucleus you go. The energy of the electron is greater when it is in orbits farther from the nucleus. found only in a specific circular path, or orbit, around the nucleus.

Each electron orbit has a fixed energy, and the fixed energies that an electron can have are called energy levels. The energy levels closest to the nucleus have the lowest energy. Energy levels increase in energy as they form farther from the nucleus.

Electrons can move from one energy level to another. Electrons gain energy to move from a lower to a higher level, and they lose energy when they drop from a higher to a lower level. A quantum of energy is the amount of energy required to move an electron from one energy level to another. In Bohr’s models, the energy of electrons is considered to be quantized.

The energy lost or gained as electrons move is not always the same. The energy levels in an atom are not evenly spaced – the higher energy levels are closer together – and it takes less energy to move from Level 6 to Level 7 than it does to move from Level 1 to Level 2.

The atom achieves the ground state when electrons occupy the closest possible positions around the nucleus. Electromagnetic radiation is emitted when electrons move closer to the nucleus

Bohr’s Model does not work for atoms larger than hydrogen (more than one electron) and does not explain the chemical behavior of atoms.

What does the quantum mechanical model determine about the electrons in an atom?

THE QUANTUM MECHANICAL MODEL

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How do sublevels of principal energy levels differ?

The Quantum Mechanical Model was developed by Irwin Schroedinger.

Like the Bohr Model, the quantum mechanical model restricts the energy of electrons to certain values, but it does not restrict electrons to a specific path around the nucleus. It uses a mathematical formula to determine the allowed energy that an electron can have and how likely it is to find that electron in various locations around the nucleus of an atom.

ATOMIC ORBITALS

Solutions to the Schroedinger equation give the energies, or energy levels, an electron can have. For each energy level the equation leads to a mathematical expression called an atomic orbital. An atomic orbital describes the probability of finding an electron at various locations around the nucleus of an atom.

The energy levels of electrons are labeled by principal quantum numbers (n). The principal quantum number corresponds to the main energy level in which the electron is likely to be found. On the periodic table each principal quantum number corresponds to a period.

The values for n are 1 Energy Level 1 Period 1 Row 12 Energy Level 2 Period 2 Row 23 Energy Level 3 Period 3 Row 34 Energy Level 4 Period 4 Row 45 Energy Level 5 Period 5 Row 56 Energy Level 6 Period 6 Row 67 Energy Level 7 Period 7 Row 7

For each principal energy level greater than 1, there are several orbitals with different shapes and different energy levels. These energy levels within a principal energy levels constitute energy sublevels. Each energy sublevel corresponds to one or more orbitals of different shapes. The orbitals describe where an electron is likely to be found.These orbitals are designated as s, p, d, and f. Each orbital has suborbitals, each of which can hold a maximum of 2 electrons.s 1 suborbital 2 electrons

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p 3 suborbitals 6 electrons d 5 suborbitals 10 electrons f 7 suborbitals 14 electrons

Summary of Principal Energy Levels and Sublevels

Principal Energy Leveln =

Number of

Sublevels

Type of Sublevel

Maximum Number of Electrons

1 1 1s 2

2 2 2s, 2p 8

3 3 3s, 3p, 3d 18

4 4 4s, 4p, 4d, 4f 32

5 4 5s, 5p, 5d, 5f 32

6 4 6s, 6p, 6d 32

7 2 7s, 7p 8

The numbers and types of atomic orbitals depends on the principal energy level.

The principal quantum number theoretically equals the number of sublevels that exist within the principal energy. This is seen in n = 1, n = 2, n = 3, and n = 4. The number of orbitals in a principal energy level is equal to n2, and the maximum number of electrons is equal to 2n2, where n is the principal quantum number.

The Heisenberg Uncertainty Principle states that it is impossible to know the velocity and the position of an electron at the same time.

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5.2 Electron Arrangement in AtomsWhat are the three rules that govern electron configurations in elements?

THE MEANING OF THE ELECTRON CONFIGURATION

There are 2 ways to represent the arrangement of electrons in an atom. The first is known as electron configuration. The word "configuration" means "the arrangement of the parts of something."

An electron configuration describes "the arrangement of electrons in space around a nucleus."

The electron configuration of an atom is a form of notation shows how the electrons are distributed among the various atomic orbital and energy levels.consists of a series of numbers, letters and superscripts as shown 1s2

This electron configuration provides us with the following information: 1s2

The large number "1" refers to the principle quantum number "n"n stands for the energy level in which the element is foundn stands for the period in which the element is foundn tells us that the electrons of helium occupy the first energy level of the atom.

The letter "s" stands for the angular momentum quantum number.It tells us that the two electrons of the helium electron occupy an "s" or spherical orbital.

The superscript (IT IS NOT AN EXPONENT) "2" refers to the total number of electrons in that orbital.In this case, we know that there are two electrons in the spherical orbital at the first energy level.

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Electrons generally do not orbit the nucleus as scientists used to think. Rather, they hover, wiggle and jiggle, vibrate back and forth, and move in certain patterns based on three factors:

their energies their orientations in space (in other words,

exactly where they fit in space relative to the other electrons in the atom)

the angular momentum. Angular momentum may be thought of as describing how wildly electrons swing about in a circular path around some center point.

ELECTRON CONFIGURATIONS AND THE PERIODIC TABLE

The elements of the periodic table are organized by number from 1 - 118.The number of the element is called the atomic number.

It is the number of protons found in the nucleus of exactly one atom of that element.

The atomic number is also the number of electrons an atom has WHEN THE ATOM IS NEUTRAL.

We use the number of protons to identify elementsThe number of electrons that an atom has can change from moment to moment. The protons are found deep inside the atom's nucleus; protons CANNOT come and go. Therefore, the number of protons in an atom fixes the identity of the element, regardless of the number of electrons an atom has from one moment to the next.

The next thing that you need to recall is the fact that the energy sublevels are filled in a specific order that is shown by the arrow diagram seen below:

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Remember to start at the beginning of each arrowFollow it all of the way to the end, filling in the sublevels that it passes through.

The order for filling in the sublevels becomes: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.

STEPS FOR WRITING ELECTRON CONFIGURATIONS

Determine the number of electrons the atom has.

On the periodic table, the atomic number is the number of protons of the atom, and thus equals the number of electrons in an atom with zero charge.

Refer to the Aufbau diagram for the order of orbital filling

Put one electron into the highest energy orbital available, starting with 1s (holds a maximum of two electrons).

Once you've put every electron into an orbital (according to the order), write the configuration.

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ORBITAL NOTATION

The second system used to represent the arrangement of electrons in an atom is known as orbital notation. Orbital notations use a series of up and down arrows to represent individual electrons in each sublevel.

Rules Governing Electron Configurations and Orbital Notations

The Aufbau Principle “Aufbau” in German translates

loosely to “building out” The Aufbau principle is named for its actual

meaning It states that orbitals with lower energy are

filled before those with higher energy.

Pauli's Exclusion Principle The Pauli exclusion principle is a

quantum mechanical principle formulated by Wolfgang Pauli in 1925

It states no two electrons in the same atom can have the same set of 4 quantum numbers

It is one of the most important principles in physics

the three types of particle from which ordinary matter is made - electrons, protons, and neutrons - are all subject to it.

To meet this rule one electron in each orbital is said to be spinning to the right (all 'up' arrows) and one electron is said to be spinning to the left (all 'down' arrows)

The electrons spinning to the right have a +1/2 spin quantum number and the electrons spinning to the left have a -1/2 spin quantum number

In consecutive orbitals of equal

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energy, the right spinning (up) arrows are placed into individual orbitals first, followed by the down arrows.

Hund’s Rule: Orbitals of equal energy are occupied

by one electron before any orbital is occupied by a second electron

All electrons in singly occupied orbitals must have the same spin.

This arrangement minimizes electron-electron repulsions.

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Rules Governing Orbital Notation

The Aufbau Principle “Aufbau” in German translates loosely to “building out” The Aufbau principle is named for its actual meaning It states that orbitals with lower energy are filled before those with higher energy.

Aufbau Diagram of Nitrogen's OrbitalConfiguration

2px 2py 2pz 2px 2py 2pz

NON 2s 2s

N

1s

1s

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Pauli's Exclusion Principle The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang

Pauli in 1925 It states no two electrons in the same atom can have the same set of 4 quantum numbers

It is one of the most important principles in physics the three types of particle from which ordinary matter is made - electrons, protons, and

neutrons - are all subject to it.

To meet this rule one electron in each orbital is said to be spinning to the right (all 'up' arrows) and one electron is said to be spinning to the left (all 'down'arrows)

The electrons spinning to the right have a+1/2 spin quantum number and the electrons spinning to the left have a -1/2 spin quantum number

In consecutive orbitals of equal energy, the right spinning (up) arrows are placed into Individual orbitals first, followed by the down arrows.

1 4 2 5 3

2px 2py 2pz

1 2+1/2 Right

2s

-1/2 Left

Cl

1 2

1s

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Hund’s Rule: Orbitals of equal energy are occupied by one electron before any orbital is occupied by a

second electron All electrons in singly occupied orbitals must have the same spin. This arrangement minimizes electron-electron repulsions.

1 4 2 5 3

2px 2py 2pz

1 2+1/2 Right

2s

-1/2 Left

Cl

1 2

1s

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5.3 Atomic Emission Spectra and the Quantum Mechanical ModelWhat causes atomic emission spectra? LIGHT AND ATOMIC EMISSION SPECTRA

Light was originally thought of as made of small fast moving particles; it was not until later that light as a wave was accepted. Today physicists view light as a wave and a particle (photon).

According to the wave model, light consists of a small portion of the electromagnetic spectrum. The electromagnetic spectrum starts with very long radio waves(10-7m-300kHz), goes to radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, gamma rays and finally cosmic rays(10-14m – 3x1022Hz). All electromagnetic radiation travels at 3.0 x 108m/s, in a vacuum and moves slightly slower through air, glass, water, etc.

A wave consists of two principle parts – wavelength and amplitude

Amplitude is the height of the wave from where it crosses a zero point, mid way between the crest and the trough

The wavelength (λ) of a wave is the distance between two identical points of a wave

The frequency (ν) of a wave is the number of wave cycles to pass a given point per unit of time (typically per second)

The SI unit for frequency is the Hertz (Hz) and is cycles/second. Frequency can also be thought of as a reciprocal second (s-1), and is typically used this way in problems

The product of frequency and wavelength equals a constant – the speed of light (c) c=λν Wavelength is inversely proportional to the frequency (shorter wavelengths have higher frequency – longer wavelengths have lower frequency)

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How did Einstein explain the photoelectric effect?

Sunlight is the most common light source we have. It covers the visible wavelengths in a continuous spectrum (ROYGBIV) (400 nm – 700 nm).

Newton discovered that white light could be broken down into the spectrum – yet mankind had been seeing it for thousands of years with the rainbow – sunlight is refracted by rain drops acting as a prism.

The longer wavelengths are bent the least by a prism. This is what causes red sunsets and sunrises.

Every element emits light when heated by the passage of electricity through its gas or vapor. The atoms first absorb energy and then release it the form of light. The light emitted is of a specific wave length(s), unlike the continuous spectrum of white light. Thus each wavelength corresponds to a specific amount of energy being emitted. The spectrum of such a light is called an emission spectrum of the element and is unique to each element

Wavelengths of light can also be absorbed by a hot gas when it is cooler than the light source – such as the sun or other stars.

THE QUANTUM CONCEPT AND THE PHOTOELECTRIC EFFECT

In the early 1900’s German physicist Max Planck was trying to describe why a piece of metal that was being heated would change colors while being heated (from black to red to yellow to blue to white).

Planck’s explanation involved energy of a body changed in small discrete units Planck described this mathematically by stating that the amount of radiant energy (E) absorbed or emitted by a body is proportional to the frequency of the radiation E ∝ v or E = h v

h is another fudge factor called Planck’s constant and

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has a value of 6.6262x10-34J·s, where J is joule, the SI unit for energy.

The energy of a quantum then is h v, and any attempt to increase the energy of a system by less than h v will fail

The size of 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

Prior to Plank’s discovery, people thought that you add any small amount of energy to a system. For example, heating water – by the thermometer the temperature rose continuously – not it small jumps. The problem is that the thermometer is unable to detect such small changes – thus we have no experience with energy that is quantized.

In 1905 Albert Einstein was studying Newton’s idea that light was made of particles. From this Einstein stated that light could be described as quanta of energy that behaved as particles. These particles he called photons. As described by Plank, the energy of photons is quantized according to E = h v

Most classical trained scientists (Newton’s theories) found the duality of light to be a bit much to handle – but when it solved several problems they had been facing, the duality of light was easier to accept. Case in point – it was known that when light struck certain metals that electrons (called photoelectrons) were released. But the reaction was not present for all wavelengths of light – potassium would not react to red light no matter how strong, but a weak yellow light would work. Classical physics and it’s “light is a wave” thought that any wavelength of light should work – even if it was weak, it should build up enough to eventually knock an electron loose.

Einstein recognized that there was a threshold below

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How are the frequencies of light emitted by an atom related to changes of electron energies?

which the photoelectric effect would not take place – if the frequency, and therefore the energy, of the photons is too low then no photoelectrons will be ejected. This photoelectric effect is the basis for solar cells today.

An example of a similar situation would be a ping pong ball hitting a billiard ball – it is not likely to have much effect. But a golf ball (same size as a ping pong ball with more mass) were to strike a billiard ball, traveling at the same speed as the ping pong ball, the billiard ball would move – the golf ball has more energy – enough to move the billiard ball.

AN EXPLANATION OF ATOMIC SPECTRA

Bohr’s model of the atom (planetary model) is often used to explain the atomic spectra of atoms. Recall that Bohr stated that electrons exist on energy levels. When enough energy is added to an atom to cause a quantum leap, an electron jumps to a higher energy level.

This is an unstable situation that is remedied by the electron dropping back to its former energy level. The energy that was absorbed is now released in the form of light. The light emitted depends on what energy level an electron is dropping to.

There are three principle groups of lines observed in the emission spectrum for hydrogen atoms

If the electron is dropping from the 2-7 energy levels to n=1 (ground level), then emission spectra is produced in the ultraviolet wavelengths – these are the Lyman series

If the electron is dropping from the 3-7 energy levels to n=2, then emission spectra is produced in the visible wavelengths – these are the Balmer series

If the electron is dropping from the 4-7 energy levels to n=3, then emission spectra is produced

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How does quantum mechanics differ from classical mechanics?

in the infrared wavelengths – these are the Paschen series

QUANTUM MECHANICS

Bohr’s explanation for the model of an atom was good for some things (such as atomic spectra) but it was lacking in helping to understand how atoms bond to form molecules – quantum mechanics to the rescue!

In 1924, a French graduate student Louis de Broglie wondered if light could behave as a wave and a particle, could matter (which we think of as particles) behave as a wave? De Broglie derived an equation that described the wavelength of a moving particle - λ= h , where h is Planck’s constant, m is the mass of the particle and v is the velocity of the particle.

So an electron with a mass of 9.11 x 10-28g, moving near the speed of light would have a wavelength of 2x10 -8m, which is about the size of an atom

De Broglie’s equation predicts that all particles exhibit wavelike motion – so why don’t we see it? Depends on the mass and the speed of the object o A basketball (200g) moving at 30m/s would have a wavelength of 10-30m. This is twice a short as a cosmic wave and we do not have a way to measure or detect it.

An electron moving at the same speed would have a wavelength of 2x10-1m, which is measurable.De Broglie’s prediction of the duality of matter (particle and wave) opened the door to a new branch of science called quantum mechanics.

The major difference between classical and quantum mechanics are-

Classical mechanics the motions of bodies much larger than the atoms that make it up – energy seems to be absorbed and emitted in any amount

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Quantum mechanics describes the motions of subatomic particles and atoms as waves – energy is absorbed or emitted in packages called quanta.

A last taste of quantum mechanics is the uncertainty principle: German Werner Heisenberg speculated in 1927 that it was impossible to know both the position and the velocity of a particle at the same time. This idea works better with very small objects (subatomic) than with large objects (baseballs). When you try to determine the position of an object, you add energy to the object thus changing its speed. When you try to determine the speed of an object then you cannot determine its speed. For a baseball traveling at 30m/s, the uncertainty is only 10-19m, which is too small to be measured. Where as for an electron with a mass of 9.11x10-28g, the uncertainty is almost 10 million meters.

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