Transcript Orbitals and Quantum Numbers

Orbitals and Quantum
Numbers
Objective

Students will be able to describe the
quantum numbers n, l, and ml used to
define an orbital in an atom, and list the
limitations placed on the values each
may have.
What is an orbital?

An orbital is an allowed energy state of
an electron in the quantum-mechanical
model of the atom; the term orbital is
also used to describe the spatial
distribution of the electron.
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Defined by the values of 3 quantum
numbers: n, l, and ml
4 Quantum Numbers
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(reminder: quantum numbers specify
the properties of atomic orbitals and the
properties of electrons in orbitals)
1) The principle quantum number (n)
indicates the main energy level
occupied by the electron
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n can have integral values of 1, 2, 3, etc.
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2) the angular momentum (or
azimuthal) quantum number
(symbolized by l ) indicates the shape
of the orbital

l can take on integral values from 0 to n-1
for each value of n
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Value of l
0
1
2
3
letter used
s
p
d
f
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3) the magnetic quantum number (ml)
describes the orientation of the orbital
in space

It can take on values from l to –l
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4) Electron Spin Quantum Number (ms)
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This number indicates the two fundamental
spin states of an electron in an orbital
This quantum number can only have two
possible values, +1/2 or -1/2
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Pauli Exclusion Principle – states that no
two electrons in an atom can have the
same set of 4 quantum numbers n, l,
ml, and ms
Practice Problem

1) For n=4, what are the possible
values of l ?
Answer

l = 0,1,2,3
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(what do these values correspond to?)
Practice Problem #2
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For l =2, what are the possible values
of ml ?
Answer
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ml = 2,1,0,-1,-2
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(what do these values correspond to?)
Practice Problem #3
State whether the following is a
permissible set of quantum numbers for
an electron in a hydrogen atom:
n=2, l = 1, ml = 1
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Answer
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Yes, it’s permissible (2p)