Lecture3 - Chem 1A Lecture 3: Quantum numbers Understanding...

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Quantum numbers Chem 1A Lecture 3:
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Understanding Hydrogen n =1 n =2 n =3 n =4 n =5 n = ʿ E " n , l , m l " n , l , m l is the wavefunction. It describes the shape of the orbital. Each orbital is labeled with 3 quantum numbers : n, l, m l transition " E = # R H Z 2 n f 2 # Z 2 n i 2 $ % ( )
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Quantum numbers Each orbital is characterized by a set of quantum numbers. Principal quantum number (n): integral values (1,2,3). Related to the size and energy of the orbital. Angular momentum quantum number ( l ): integral values from 0 to (n-1) for each value of n. Magnetic quantum number (m l ): integral values from - l to l for each value of n.
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Quantum numbers A subshell is a set of orbitals with the same value of l . They have a number for n and a letter indicating the value of l . l = 0 (s) l = 1 (p) l = 2 (d) l = 3 (f) l = 4 (g)
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Quantum numbers Quantum numbers for the first four levels in the hydrogen atom.
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Quantum numbers How many orbitals are there for each principal quantum number n = 2 and n = 3? For each n, there are n different l -levels and (2 l +1) different m l levels for each l . n=2: n = 2 different l -levels (2 l +1) = 2 x 0 + 1 = 1 m l -levels for l = 0 l = 0, 1 (2 l +1) = 2 x 1 + 1 = 3 m l -levels for l = 1 Total: 1 + 3 = 4 levels for n = 2
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Quantum numbers How many orbitals are there for each principal quantum number n = 2 and n = 3? For each n, there are n different l -levels and (2 l +1) different m l levels for each l . n=3: n = 3 different l -levels (2 l +1) = 2 x 0 + 1 = 1 m l -levels for l = 0 l = 0, 1,2 (2 l +1) = 2 x 1 + 1 = 3 m l -levels for l = 1 Total: 1 + 3 + 5 = 9 levels for n = 3 (2 l +1) = 2 x 2 + 1 = 5 m l -levels for l = 2 The total number of levels for each n is n 2
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Wavefunction and probability " n , l , m l ‘function’ " n , l , m l r " n , l , m l 2 ‘probability’
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The orbital is defined as the surface that contains 90% or the total electron probability.
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Lecture3 - Chem 1A Lecture 3: Quantum numbers Understanding...

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