# l is lambda n is nu Inverse Relationship! Units: Wavelength m or nm

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l is lambda n is nu Inverse Relationship! Units: Wavelength m or nm
Properties of Light (Wavelength (l) and Frequency (n)) l is lambda longer wavelength lower frequency n is nu What is the relationship between wavelength and frequency? Inverse Relationship! As one increases, the other decreases. Units: Wavelength m or nm Frequency 1/s or s-1 or Hz higher frequency shorter wavelength

Electromagnetic Spectrum: all types of “light”-colored light is only a small portion of the spectrum. Blue Green Yellow Orange Red High Frequency Short Wavelength High Energy Low Frequency Long Wavelength Low Energy What does ROY G BIV mean?

Converting from Wavelength to Frequency
c = ln c is the speed of light c = 3.00X108 m/s What is the frequency (n) of light that has a wavelength (l) of 7.32X10-6 m? Start with: c = ln then divide both sides by l to get n by itself. What is the wavelength of light that has a frequency of 7.32X105 1/s?

Demonstration: Atomic Emission
When atoms are “excited”, have extra energy, they can lose some of the energy in the form of light, but only very specific wavelengths of light are given off from a particular element-not all wavelengths are given off. If electrons can be anywhere in the atom, then all wavelengths of light should be seen-since only certain wavelengths are seen, electrons must be restricted to certain energies. Balmer Series: n6 → n2 n5 → n2 n4 → n2 n3 → n2 Highest Energy (violet) Lowest Energy (red)

Highest Energy (ultraviolet)
Lyman Series: n7 → n1 n6 → n1 n5 → n1 n4 → n1 n3 → n1 n2 → n1 Highest Energy (ultraviolet) Higher energy than visible light (longer drop) Lowest Energy (ultraviolet) The larger the “drop”, the higher the energy of the light emitted. Paschen Series: n7 → n3 n6 → n3 n5 → n3 n4 → n3 Highest Energy (infrared) Lower energy than visible light (shorter drop) Lowest Energy (infrared) Visible light (Balmer Series) is in between Lyman and Paschen

Energy of Light: Units of energy are joules (J)
E = hn c = speed of light = 3.00X108 m/s c = ln h = Plank’s Constant = X10-34 J·s What is the energy of light that has a frequency of 3.92X107 1/s? What is the energy of light that has a wavelength of 3.92X10-6 m? What is the wavelength of light having an energy of 8.93X10-20 J?

Orbitals: orbitals are the shapes that result from solving the wave equations of quantum mechanics. The shape represents a 90% probability of finding an electron within the orbital. The shape of an orbital depends upon the energy of the electrons in it. The energy of an electron primarily depends upon two quantum numbers: n is the principle quantum number (like the energy level) l is the angular momentum quantum number n determines the size of an orbital (larger values of n mean higher energy electrons and larger orbitals) l determines the shape of an orbital (larger values of l mean higher energy and more complex shapes for the orbitals)

There is only ONE “s” orbital in a given energy level.
When “l” = 0, the shape of an orbital is a sphere These orbitals are called “s” orbitals. The value of “n” determines the size of the sphere There is only ONE “s” orbital in a given energy level. A single orbital (of any type) can hold a maximum of two electrons.

There are THREE “p” orbitals in a given energy level.
When “l” = 1, the shape of an orbital is a “dumbbell” These orbitals are called “p” orbitals and there are three of them for each energy level. px py pz There are THREE “p” orbitals in a given energy level.

There are FIVE “d” orbitals in a given energy level.
When “l” = 2, the shape of an orbital is a “ double dumbbell” These orbitals are called “d” orbitals and there are three of them for each energy level. dxz dyz dxy dx2 – y2 dz2 There are FIVE “d” orbitals in a given energy level.

There are SEVEN “f” orbitals in a given energy level.
When “l” = 3, the shape of an orbital is a “ quadruple dumbbell” These orbitals are called “f” orbitals and there are three of them for each energy level. There are SEVEN “f” orbitals in a given energy level.

B1B3B4B5B7B8 Begin Key elements with last electron in an “s” orbital elements with last electron in an “p” orbital elements with last electron in an “d” orbital elements with last electron in an “f” orbital n 1 2 3 4 5 6 7 n is the principle energy level n - 1 n - 2

Example: Sulfur S 1s2, 2s2, 2p6, 3s2, 3p4
Electron Configuration Practice Example: Sulfur S s2, 2s2, 2p6, 3s2, 3p4

Valence Electrons: Electrons in the outermost orbitals-highest energy electrons in the atom. The valence electrons are the electrons that are taking part in chemical reactions of an element. Electron Dot Structures: Diagrams showing the number of electrons in the valence shell using an element symbol and “dots” to represent electrons. Note: electrons in “d” or “f” orbitals are not shown in dot structures. Examples: See Table 5-5 on page 140 for dot structures of 2nd period elements.

Orbital Diagrams: box diagrams used to record where electrons are located in an atom.
Use the number of boxes to identify which type of orbital is being filled A single box is “s” Three boxes is “p” Five boxes is “d” Seven boxes is “f”

Orbital Diagrams: Put arrows into boxes for each electron of a given type that is present in an orbital. For example: C has an electron configuration of 1s2, 2s2, 2p2 A total of 6 electrons need to be placed in the orbital diagram. Electrons must fill the lowest energy orbital before a higher energy orbital can be filled. Each box (orbital) can only contain up to 2 electrons and must have opposite spin (Pauli Exclusion Principle). If two or more orbitals are of equal energy, then electrons can not pair up until each orbital has one electron in it (Hund’s Rule). 1s 2s 2p

Fill in the orbital diagram for the valence shell of sulfur.
3p S is 1s2, 2s2, 2p6, 3s2, 3p4 outer shell Fill in the orbital diagram for the valence shell of bromine. Br is 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p5 outer shell 4s 3d 4p

Noble-Gas Configurations:
Noble-Gases: He, Ne, Ar, Kr, Xe, Rn Each of these elements has an entirely full outer shell of electrons. This makes them very stable-unreactive. To shorten electron configurations of other elements, we can replace part of the electron configuration with a noble-gas symbol in brackets and then show just the outer shell electrons. For example: Br: 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p5 electrons in Ar Therefore: Br: [Ar] 4s2, 3d10, 4p5

Orbital energies in single electron system.
Bohr Model Orbital energies in multi electron systems. Quantum Model Bohr’s theory did not predict different energies within the same principle energy level for multi electron systems. Quantum mechanics does!

Quantum Numbers: n is the principle quantum number and is related to the major energy levels of the electron. n must be a positive integer! As n increases, the size of the orbital increases and the electron spends more time farther from the nucleus. Farther from the nucleus is higher energy. Consequence of “n”: periods (horizontal rows or energy levels) on the periodic table. These currently range from 1 to 7.

Quantum Numbers l is the angular momentum quantum number and is related to shape of the atomic orbital. l must be a whole number which can range from 0 to (n-1)! For example: when n = 1, l must be 0 when n = 2, l is either 0 or 1 when n = 3, l is either 0, 1, or 2 when n = 4, l is either 0, 1, 2, or 3 When l = 0, the shape is a sphere (s orbital). When l = 1, the shape is a dumbbell with 2 lobes (p orbital). When l = 2, the shape is a dumbbell with 4 lobes (d orbital). When l = 3, the shape is a dumbbell with 8 lobes (f orbital). Consequence of “l”: number of types of orbitals in a given period of the periodic table (only 1 in period 1, 2 in period 2, etc….).

Consequence of “ml”: number of orbitals for each type of orbital
Quantum Numbers ml is the magnetic quantum number and is related to the orientation in space of the atomic orbital. ml must be an integer which can range from -l through 0 to +l For example, when l = 0, ml = 0 when l = 1, ml = -1, 0, 1 when l = 2, ml = -2, -1, 0, 1, 2 when l = 3, ml = -3, -2, -1, 0, 1, 2, 3 1 value (only one s orbital) 3 values (three p orbitals) 5 values (five d orbitals) 7 values (seven f orbitals) Consequence of “ml”: number of orbitals for each type of orbital

Quantum Numbers ms is the spin quantum number and is related to the direction of “spin” of the electron. ms must be either + ½ or - ½ Two values for each set of three other quantum numbers. This means that 2 electrons can only occupy an orbital if they have opposite “spin”. Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers. Another way of saying this is that two electrons can only occupy the same orbital if they have opposite spin. Two electrons in the same orbital must have the same first three quantum numbers and ms must be + ½ for one and - ½ for the other. Consequence of “ms”: only 2 electrons allowed in any single orbital

One way of thinking about “spin”
The gold arrows represent magnetic fields created by the “spinning” electrical charge. Notice that the arrows point in opposite directions-therefore the electrons are spinning in opposite directions (one clockwise and one counterclockwise).

General Rule: electrons must have lowest possible energy
First electron in an atom Quantum Numbers n = l = ml = 0 ms = +½ Quantum Numbers are like addresses for the electrons in an atom. Each electron needs to have its own unique address.

General Rule: electrons must have lowest possible energy
1st electron in an atom Quantum Numbers n = l = ml = 0 ms = +½ Only Electron in H (1s1) First Electron in He (1s1) 2nd electron in an atom n = l = ml = 0 ms = -½ Second Electron in He (1s2) Helium has 2 electrons and each electron must have a different set of quantum numbers. This is an expression of the Pauli Exclusion Principle.

since l = 0, “s” orbital being filled
If we keep adding electrons to an atom: 3rd 4th n = l = ml = 0 ms = +½ n = l = ml = 0 ms = -½ 2s1 then 2s2 since l = 0, “s” orbital being filled No 2 electrons have the same set of quantum numbers! 5th 6th 7th 8th 9th 10th n = l = ml = -1 ms = +½ n = l = ml = 0 ms = +½ n = l = ml = 1 ms = +½ n = l = ml = -1 ms = -½ n = l = ml = 0 ms = -½ n = l = ml = 1 ms = -½ since l = 1, “p” orbitals being filled 2p1, then 2p2, and so on … 2p3, 2p4, 2p5, 2p6

Summary of Quantum Number meanings.
2 2 6 2 6 10 2 6 10 14 # e- when full Each orbital can contain up to two electrons One will be spin (+½) and one will be spin (-½)

Imagine that electrons live in a fancy hotel with the following rules.
1) Electrons must go the lowest energy bedroom available. Lower floors are lower in energy. 2) The maximum number of electrons in a bedroom is 2. 3) Smaller suites are lower in energy than larger suites on the same floor. There are four types of suites: 1 bedroom, 3 bedrooms, 5 bedrooms, and 7 bedrooms. 4) Electrons will not share a bedroom until each bedroom in that suite has one electron in it. 5) Electrons can not move into higher energy suites until the lower energy suites are full. 6) The 5 bedroom suites are so much higher in energy than the 3 bedroom suites, that they appear one floor above their real floor number. The 7 bedroom suites appear 2 floors above their real floor number for the same reason.

A diagram of our electron “hotel”
1st floor 2nd floor 3rd floor 4th floor 5th floor 6th floor

Electron Configurations: like a bookkeeping system for where electrons will be located in an atom in its ground state. Electrons fill into the lowest possible energy orbitals using rules much like those we used for the electron “hotel”. The pattern can easily be remembered by using the periodic table to full effect. Start at element 1 and follow the atomic numbers. Fill in all electrons according to the Period Number (principle quantum number “n”) and the number of electrons in the orbital type (s, p, d, and f are the orbital types-from the angular quantum number (l)). The technical name for this is called the aufbau principle

d block (n-1) (n) p block s block (n-2) f block

Designation for last electron of each of the first 18 elements.
p1 p2 p3 p4 p5 p6 Notice: Elements in the same group have the same type of electron as the last electron (except He). He is in the last group because it has a full outer shell!

Designation for last electron of each of elements 19 through 36.
Notice the two exceptions to normal electron configurations.

Orbital Diagrams: In the first energy level ( n = 1), l can only be 0 and ml must also be 0. Therefore, there is only an “s” orbital in the first energy level. In the second energy level ( n = 2), l can be 0 or 1 and ml can be -1, 0, or 1. When l is 0, an “s” orbital is present, and when l is 1, three “p” orbitals are present. In the third energy level ( n = 3), l can be 0, 1, or 2 and ml can be -2, -1, 0, 1, or 2. When l is 0, an “s” orbital is present, when l is 1, three “p” orbitals are present, and when l is 2, five “d” orbitals are present.

s p d f Why only one “s” orbital in any energy level?
When l = 0, ml must also = 0 (only value), so one “s” orbital. Why three “p” orbitals in any energy level above 1? When l = 1, ml can be -1, 0, or 1 (three values), so three “p” orbitals. Why five “d” orbitals in any energy level above 2? When l = 2, ml can be –2, -1, 0, 1, or 2 (five values), so five “d” orbitals. Why seven “f” orbitals in any energy level above 3? When l = 3, ml can be –3, –2, -1, 0, 1, 2, or 3 (seven values), so seven “f” orbitals. s p d f

Why two columns of elements in the “s” block?
Each orbital can contain up to two electrons (ms can only be +½ or -½) and there is only one “s” orbital in any energy level. Why six columns of elements in the “p” block? Each orbital can contain up to two electrons (ms can only be +½ or -½) and there are three “p” orbitals in any energy level. Why ten columns of elements in the “d” block? Each orbital can contain up to two electrons (ms can only be +½ or -½) and there are five “d” orbitals in any energy level. Why fourteen columns of elements in the “f” block? Each orbital can contain up to two electrons (ms can only be +½ or -½) and there are seven “f” orbitals in any energy level.

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