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Schrödinger’s equation requires 3 quantum numbers (although there are a total of 4 quantum numbers) Quantum Numbers

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1.Principal Quantum Number, n. This number is related to the size and energy of the orbital. Quantum Numbers

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1.Principal Quantum Number, n, cont. This is the same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus. An increase in n also means higher energy. Quantum Numbers

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2.Azimuthal or Angular Momentum Quantum Number, l. This number is related to the shape of the atomic orbitals. Quantum Numbers

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2.Azimuthal or Angular Momentum Quantum Number, l, cont. This quantum number depends on the value of n. The values of l begin at 0 and increase to (n - 1). Quantum Numbers

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2. Azimuthal Quantum Number, l, cont. Usually we refer to the s, p, d and f orbitals. orbital l = l = s0 p1 d2 f3 Quantum Numbers

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3.Magnetic Quantum Number, m l. This quantum number is related to the orientation of the orbital in space relative to other orbitals in the atom. Quantum Numbers

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3.Magnetic Quantum Number, m l. This quantum number depends on l. The magnetic quantum number has integral values between - l and + l. Quantum Numbers

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3. Magnetic Quantum Number, m l, cont. orbital ml = ml = s0 p1, 0, -1 d2, 1, 0, -1, -2 f3, 2, 1, 0, -1, -2, -3 Quantum Numbers

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4.Spin Quantum Number, m s. This quantum number relates to the spin of an electron and can take on two possible values: m s = + ½ or m s = - ½. Quantum Numbers

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Note electrons don’t actually spin, but the magnetic properties of electrons are just what we would see if the electron were a spinning charged particle, and it is useful to picture the electron as spinning. Quantum Numbers

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Orbitals and Quantum Numbers Quantum Numbers

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Application of Quantum Numbers Write a set of quantum numbers for the electron in a 4s orbital. Quantum Numbers This is the energy level number (n) For the s orbital, l = 0

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Application of Quantum Numbers Write a set of quantum numbers for the electron in a 4s orbital. Quantum Numbers If the 2 nd quantum number is 0, the 3 rd quantum number must also be zero.

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Application of Quantum Numbers Write a set of quantum numbers for the electron in a 4s orbital. Quantum Numbers The spin can either be + ½ or -½.

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Application of Quantum Numbers Write a set of quantum numbers for the electron in a 4s orbital. Quantum Numbers ANSWER POSSIBILITIES: (4, 0, 0, + ½) or (4, 0, 0, -½)

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Application of Quantum Numbers Write a set of quantum numbers for the electron in a 3p orbital. Quantum Numbers This is the energy level number (n) For the p orbital, l = 1

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Application of Quantum Numbers Write a set of quantum numbers for the electron in a 3p orbital. Quantum Numbers If the 2 nd quantum number is 1, the 3 rd quantum number may be either 1, 0 or -1.

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Application of Quantum Numbers Write a set of quantum numbers for the electron in a 3p orbital. Quantum Numbers The spin can either be + ½ or -½.

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Application of Quantum Numbers Write a set of quantum numbers for the electron in a 3p orbital. Quantum Numbers ANSWER POSSIBILITIES: (3, 1, 1, + ½), (3, 1, 1, -½), (3, 1, 0, +½), (3, 1, 0, -½), (3, 1, -1, +½), (3, 1, -1, -½),

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