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

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

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3 Converting from Wavelength to Frequency c = c is the speed of lightc = 3.00X10 8 m/s What is the frequency ( ) of light that has a wavelength ( ) of 7.32X10 6 m? What is the wavelength of light that has a frequency of 7.32X10 5 1/s? Start with: c = then divide both sides by to get by itself.

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4 Demonstration: Atomic Emission Balmer Series: n6 n2 n5 n2 n4 n2 n3 n2 Highest Energy (violet) Lowest Energy (red) 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.

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

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Energy of Light: Units of energy are joules (J) E = h h = Planks Constant = 6.626X10 34 J·s What is the energy of light that has a frequency of 3.92X10 7 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? c = c = speed of light = 3.00X10 8 m/s

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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)

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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.

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pxpx pypy pzpz 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. There are THREE p orbitals in a given energy level.

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d xz d yz d xy d x 2 – y 2 dz2dz2 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. There are FIVE d orbitals in a given energy level.

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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.

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n - 1 n - 2 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 n is the principle energy level B1B3B4B5B7B8 Begin

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Electron Configuration Practice Example: Sulfur S 1s 2, 2s 2, 2p 6, 3s 2, 3p 4

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14 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. See Table 5-5 on page 140 for dot structures of 2 nd period elements. Examples:

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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

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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 1s 2, 2s 2, 2p 2 1s2s2p 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 (Hunds Rule).

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17 3d Fill in the orbital diagram for the valence shell of sulfur. S is 1s 2, 2s 2, 2p 6, 3s 2, 3p 4 3s3p outer shell Fill in the orbital diagram for the valence shell of bromine. Br is 1s 2, 2s 2, 2p 6, 3s 2, 3p 6, 4s 2, 3d 10, 4p 5 4s 4p outer shell

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18 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. Br: 1s 2, 2s 2, 2p 6, 3s 2, 3p 6, 4s 2, 3d 10, 4p 5 For example: Br: [Ar] 4s 2, 3d 10, 4p 5 electrons in Ar Therefore:

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

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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.

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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….).

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Quantum Numbers m l is the magnetic quantum number and is related to the orientation in space of the atomic orbital. m l must be an integer which can range from - l through 0 to + l For example, when l = 0, m l = 0 when l = 1, m l = -1, 0, 1 when l = 2, m l = -2, -1, 0, 1, 2 when l = 3, m l = -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 m l : number of orbitals for each type of orbital

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Quantum Numbers m s is the spin quantum number and is related to the direction of spin of the electron. m s 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 m s must be + ½ for one and ½ for the other. Consequence of m s : only 2 electrons allowed in any single orbital

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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).

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25 Quantum Numbers First electron in an atom General Rule: electrons must have lowest possible energy n = 1 l = 0 m l = 0 m s = +½ Quantum Numbers are like addresses for the electrons in an atom. Each electron needs to have its own unique address.

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

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27 n = 2 l = 0 m l = 0 m s = +½ n = 2 l = 0 m l = 0 m s = ½ 3 rd 4 th 5 th n = 2 l = 1 m l = 1 m s = +½ 6 th n = 2 l = 1 m l = 0 m s = +½ 7 th n = 2 l = 1 m l = 1 m s = +½ 8 th n = 2 l = 1 m l = 1 m s = ½ 9 th n = 2 l = 1 m l = 0 m s = ½ 10 th n = 2 l = 1 m l = 1 m s = ½ since l = 0, s orbital being filled No 2 electrons have the same set of quantum numbers! since l = 1, p orbitals being filled 2s 1 then 2s 2 2p 1, then 2p 2, and so on … 2p 3, 2p 4, 2p 5, 2p 6 If we keep adding electrons to an atom:

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

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30 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. 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. 5) Electrons can not move into higher energy suites until the lower energy suites are full. 4) Electrons will not share a bedroom until each bedroom in that suite has one electron in it. 2) The maximum number of electrons in a bedroom is 2. 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.

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31 1 st floor 2 nd floor 3 rd floor 4 th floor 5 th floor 6 th floor A diagram of our electron hotel

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32 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

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

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34 Designation for last electron of each of the first 18 elements. Notice: Elements in the same group have the same type of electron as the last electron (except He). s1s1 s2s2 p1p1 p2p2 p3p3 p4p4 p5p5 p6p6 He is in the last group because it has a full outer shell!

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

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Orbital Diagrams: In the first energy level ( n = 1), l can only be 0 and m l 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 m l 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 m l 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.

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

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Why two columns of elements in the s block? Each orbital can contain up to two electrons (m s 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 (m s 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 (m s 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 (m s can only be +½ or ½) and there are seven f orbitals in any energy level.

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