Chapter 13 Electrons in Atoms



Chapter 4 Electrons in Atoms

1. How are the wavelength and frequency of light related?

Wavelength

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4 The amplitude of a wave is the wave’s height from zero to the crest.

5 The wavelength, represented by ( (the Greek letter lambda), is the distance between the crests. It is often measured in meters or nanometers.

Frequency

Frequency ν (nu) is the number of waves that pass a given point per second.

Frequency units are cycles/sec or hertz (Hz) or s-1.

Frequency and wavelength are inversely related. As one goes up the other goes down.

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2. At what speed do all types of electromagnetic waves travel?

Electromagnetic radiation includes many kinds of waves of energy.

All types of EM waves travel at a speed of 3.0 x 108 m/s in a vacuum.

C = 300 million meters per second. This is called the speed of light

MEMORIZE:

c = λ ν

(where C is speed of light, λ is wavelength in meters or nm and ν is frequency in Hz or s-1)

Remember that 1 m = 1x109 nm.

Be able to solve for frequency or wavelength by rearranging the formula and using the speed of light. Your units must agree before solving.

3. Electromagnetic Radiation

A traveling wave motion that results from changing electric and magnetic fields.

Includes radiowaves, microwaves, infrared, visible light, UV waves, X-rays, and gamma rays.

The electromagnetic spectrum consists of radiation over a broad band of wavelengths.

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Know the order on the spectrum including the energy, frequency, and wavelength trends.

4. New Ideas About Light

In the early 1900s experiments involving light and matter could not be explained by wave theory of light. Max Planck studied the emission of light by hot objects. He proposed that a hot object does not emit electromagnetic energy continuously as would be expected from waves. Instead, he suggested that the object emits energy in small packets of energy called quanta.

A quantum is the amount of energy required to move an electron from one level to the next level.

Planck found that energy lost or gained is proportional to the frequency. The higher the energy, the higher the frequency.

The constant h , is known as Planck’s constant, and has a value of 6.626 x 10-34 J/Hz

He proposed that the energy, E , of a single quantum equals a constant times the frequency.

MEMORIZE

E = h(

Where E is energy in joules, h is Planck’s constant (see above) and ( is frequency in Hz.

Example:

The wavelength of an X-ray is 0.10 nm. Give the frequency.

3.0 x 1018 Hz

What is the energy of this X-ray?

2.0 x 10-15 J

Example:

The yellow light given off by a sodium vapor lamp used for public lighting has a wavelength of 589 nm. What is the frequency of this radiation?

5.09 x 1014 Hz

What is the energy of this radiation?

3.37 x 10-19 J

Example:

A laser used in eye surgery to fuse detached retinas produces radiation with a frequency of 4.69 x 1014 Hz. What is the wavelength of this radiation?

6.40 x 10-7m

Example:

An AM radio station broadcasts at 1440 kHz, and its FM partner station broadcasts at 94.5 MHz. Calculate and compare the energy of quanta emitted by these radio stations. How do the wavelengths compare of the AM and FM waves?

AM station has energy of 9.54 x 10-28 J while the FM station is 6.26 x 10-26 J. The FM station has higher energy. The wavelength of the AM waves is 208 m while the FM waves are 3.17 m.

Example:

[pic] Answer: 6.00 x 1015 Hz Ultraviolet

5. The Dual Wave-Particle Nature of Light

In 1905 Albert Einstein expanded on Planck’s theory by introducing the idea that electromagnetic radiation exhibits both wave properties and also particle

properties. It can be thought of as a stream of particles. Each particle of light carries a quantum of energy. Einstein called these particles photons.

Example: Cobalt-60 is an artificial radioisotope that is produced in a nuclear reactor and is used as a gamma-ray source in the treatment of certain types of cancer. If the wavelength of the gamma radiation from a cobalt-60 source is 1.00 x 10-3 nm, calculate the energy of a photon of this radiation.

1.99 x 10-13 J

6. What causes atomic emission spectra?

When atoms absorb energy, electrons move into higher energy levels. These electrons then lose energy by emitting light when they return to lower energy levels.

Excited State and Ground State

Energy added to an atom causes electrons to move out away from the nucleus

The farther from the nucleus, the higher the energy. This is called the “excited state.”

Energy absorbed is then released as photons of light as electrons fall back to their original “ground state.”

White light is made up of all the colors of the visible spectrum.

Passing it through a prism or spectroscope separates it into its components called a continuous spectrum (a rainbow)

Atomic Emission Specta

By heating a gas with electricity or a solid compound with a flame we can see a color.

Passing this light through a prism does something different. Each element gives off its own characteristic lines of color called the atomic emission spectrum. These can be used to identify the atom.

Heat or electricity or light can move the electron up to higher energy levels (excited state electron)

As the electron falls back down to ground state it gives the absorbed energy back as photon of light

Each photon of light corresponds to a specific wavelength, frequency, energy and color of light.

The further they fall, the greater the energy associated with that change of the electron.

The light emitted by an electron moving from a higher to a lower energy level has a frequency directly proportional to the energy change of the electron.

The three groups of lines in the hydrogen spectrum correspond to the transition of electrons from higher energy levels to lower energy levels.

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In 1924, De Broglie developed an equation that predicts that all moving objects have wavelike behavior. Today, the wavelike properties of beams of electrons are useful in magnifying objects. The electrons in an electron microscope have much smaller wavelengths than visible light. This allows a much clearer enlarged image of a very small object, such as this mite.

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7. Why are the electrons so important?

The chemical properties of atoms, ions, and molecules are due to the arrangement of the electrons within them.

Recall Thomson’s Plum Pudding model of the atom.

Then Rutherford showed that most of an atom’s mass is concentrated in a small, positively charge region called the nucleus.

Later experiments showed that the nuclei of atoms are composed of protons and neutrons.

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8. Bohr’s Planetary Model

Electrons travel in definite orbits or circular paths around the nucleus like the planets orbiting the sun.

These electrons in a particular path have a fixed energy, they do not lose energy and cannot fall into the nucleus.

9. Quantum Model of the Atom

• The quantum mechanical model of the atom was developed mathematically by Schrodinger (and DeBroglie) in1926.

• It describes the location of electrons in certain regions of space based upon probability. Schrodinger’s equation describes areas in space where electrons can exist. These areas in space are called orbitals which indicate the probable location (90%) of a electron. An orbital is the space occupied by 2 electrons of opposite spin.

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Energy Levels

1 The fixed energy levels are like rungs of a ladder. The lowest rung corresponds to the lowest energy level. The highest rung is the highest energy level.

2 Electrons can jump from one level to another by gaining or losing energy.

3 The energy levels are not equally spaced. They become more closely spaced the farther they are from the nucleus.

4 The region of space surrounding the nucleus where the probability of finding an electron is greatest is represented as a fuzzy probability cloud or electron cloud. Within the electron cloud, electrons are moving at high speed.

10. Heisenberg Uncertainty Principle

It is impossible to know exactly the position and velocity of an electron at the same time

11. What are the Four Quantum Numbers

Principal quantum number (n)

Angular momentum quantum number (l)

Magnetic quantum number (m )

Electron spin quantum number (s)

They are the ADDRESS OF THE ELECTRON

No 2 electrons have the same address. It’s sort of like the state, city, street, and apartment number

Principal quantum number (n)

refers to the energy level – distance from the nucleus

size and energy of an orbital

has integer values (n=1, n=2 etc.) As they increase in distance from the nucleus they increase in energy.

MEMORIZE

12. The maximum # of electrons allowed in an energy level = 2n2 (where n is the level number)

Ex: level 1 2(1) 2 = 2 electrons max

level 2 2(2) 2 = 8 electrons max

13. Sublevels: s,p,d,f some people don’t forget

s sublevel and orbitals

s sublevels have 1 orbital

Each orbital can hold 2 electrons

Spherical shaped orbital

Every energy level has an s sublevel which is an s orbital where 2 electrons can be found.

The orbitals get larger as the energy levels get larger

[pic]

p sublevel and orbitals

p sublevels have 3 different orbitals

Each p orbital can hold 2 electrons for a maximum of 6 electrons in the p sublevel

p orbitals are peanut (dumbbell) shaped

[pic]

d sublevel and orbitals

• d sublevels have 5 different orbitals

• Each d orbital can hold 2 electrons for a maximum of 10 electrons in the d sublevel

• d sublevels are mostly double peanut/dumbell shaped

[pic][pic]

f sublevel and orbitals

f sublevels have 7 different orbitals

2 electrons per orbital for a maximum of 14 electrons in an f sublevel

f orbitals are mostly “flower” shaped (ok…that’s a stretch)

[pic][pic]

[pic]

This is a composite of the orbitals of the element magnesium.

14. Filling Order of Electrons

In the “Atom Hotel”, the floors represent sublevels within a level.

Each room represents an orbital.

Each room can hold 2 electrons maximum

s floor has 1 room, p floor has 3 rooms, d floor has 5 rooms, and the f floor has 7 rooms

Within a floor, people will fill rooms 1 per room then pair up before choosing the next floor.

15. The Atom Hotel: You filled this out in class…remember the order!

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16. Electron Arrangement Rules

In atoms, electrons and the nucleus interact to make the most stable (lowest energy) arrangement possible.

The arrangement of electrons in the orbitals f the atom is called the electron configuration.

Ex: 1s2 2s2 2p4

There are rules that must be followed when filling the orbitals.

Aufbau principle- electrons enter (fill) orbitals of the lowest energy first.

Pauli Exclusion Principle: no two electrons in the sma eatom can have the same set of four quantum numbers. The principal, angular momentum, and magnetic quantum numbers specify the energy, shape, and orientation of an orbital. Two electrons in the same orbital must have opposite spins (+1/2 and -1/2).

So how do you know the correct filling order?

Learn how to draw the following diagonal arrow diagram on your paper to remind yourself of the correct electron filling order.

There are a few exceptions, but it will work most of the time!

17. Hund’s Rule

Electrons take an empty orbital within a sublevel if possible, rather than pair with each other.

18. How to Write Orbital Filling Diagrams

Draw a line or a box for each orbital.

Follow the rules as you draw arrows to represent electrons until the correct number of electrons is reached.

Remember the atomic number is equal to the number of electrons in a NEUTRAL atom.

Ex: Carbon

[pic]

1s 2s 2p

19. Writing Electron Configurations

You must account for every electron of the atom. Use the diagonal arrow diagram to help you with the filling order of sublevels. Be able to sketch this out on your paper. Practice drawing it a couple of times!

[pic]

Add up the superscripts to check that they add up to the atomic number of the neutral atom. Remember that s has a max of 2 electrons, p has max of 6 electrons, d has max of 10 electrons, and f has max of 14 electrons.

Ex: Scandium has 21 electrons

1s22s22p63s23p64s23d1

20. Order of Stability

Full levels are most stable.

Full sublevels are more stable than partially filled sublevels.

Half full sublevels are more stable than no special arrangement.

You might predict the configuration of chromium to be 1s22s22p63s23p64s23d4

The actual configuration of chromium is 1s22s22p63s23p64s13d5

Exceptions

Half filled d orbitals (see chromium)

Cu 1s22s22p63s23p64s13d10

Fully filled d orbitals

21. Noble Gas Shorthand Configurations

The periodic table can be divided into sublevel blocks s,p,d,f.

The number of electrons in each sublevel is determined by counting over to the element.

Transition elements are a level number lower and inner transition elements are 2 level numbers lower.

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Neon 1s2 2s2 2p6

Sodium 1s2 2s22p6 3s1

You can abbreviate configurations by referring so the noble gas that comes before each element. Put the noble gas symbol in brackets then write the remaining configuration. Ex: Since the electron configuration of sodium (see above) is just like neon’s electron arrangement plus a little bit more, write the noble gas shorthand:

[Ne] 3s 1

Ex: Clorine’s configuration would be [Ne]3s23p5

Krypton’s configuration would be [Ar] 4s23d104p6

22. The Quantum Numbers of Electrons

Angular Momentum Quantum Number (l)

Indicates the shape of the orbital.

|s |p |d |f |

|0 |1 |2 |3 |

Magnetic quantum number (m )

Orientation in space of orbital relative to the other orbitals in the atom

Has values between l and –l including zero.

This is what the room number is in the atom hotel! The room in the middle is always 0.

|l values |# of orbitals |m values |

|0 or s |1 orbital |0 |

|1 or p |3 orbitals |-1, 0, 1 |

|2 or d |5 orbitals |-2,-1,0,1,2 |

|3 or f |7 orbitals |-3,-2,-1,0,1,2,3 |

Draw an orbital filling diagram to figure this one out! Remember 0 is the middle box.

Electron spin quantum number (s)

There are two values for electron spin: +1/2 or -1/2

Quantum Numbers of

Level 1 Electrons

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Quantum Numbers of

Level 2 Electrons

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And so on and so on……

Ex: Which element has a final electron with the following set of quantum numbers?

3, 1, -1, - ½

sulfur

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1s

2s

3s

4s

5s

6s

7s

2p

3p

4p

5p

6p

7p

3d

4d

5d

6d

7d

4f

5f

6f

7f

s

m

l

n

- 1/2

0

0

1

+ 1/2

0

0

1

- 1/2

1

1

2

- 1/2

0

1

2

- 1/2

-1

1

2

+ 1/2

1

1

2

+ 1/2

0

1

2

+ 1/2

-1

1

2

- 1/2

0

0

2

+ 1/2

0

0

2

s

m

l

n

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