Quantum Numbers
1) State the maximum number of electrons present in the following:
a) n = 4
2(4)2 = 32
b) 3d sublevel
10
c) valence shell of Sb
(s + p electrons) = 5
2) What is the maximum number of electrons in an atom that can have the following quantum
numbers?
a) n = 3
18
b) n = 4, l = 2
10 (4d)
c) n = 4, l = 3, ml = +2
2
3) For the principal quantum number n = 3, what values of l are allowed, what values of ml are
possible, and how many orbitals are there?
l
= 0, 1, or 2
for
l
= 0, ml = 0
for
l
= 1, ml = -1, 0, or +1
for
l
= 2, ml = -2, -1, 0, +1, or +2
Therefore, 9 orbitals.
4) Name the orbitals described by the following quantum numbers:
a) n = 3, l = 0 3s
b) n = 3, l = 1
3p
c) n = 3, l = 2 3d
d) n = 5, l = 0
5s
5) What are the n, l, and possible ml values for the following orbital types?
a) 2s
n = 2,
l
= 0, ml = 0
c) 5d
n = 5,
l
= 2, ml = -2, -1, 0, +1, or +2
d) 4f
n = 4,
l
= 3, ml = -3, -2, -1, 0, +1, +2, or +3
e) 1s
n = 1,
l
= 0, ml = 0
b) 3p n = 3,
l
= 1, ml = -1, 0, or +1
6) Place the following orbitals in order of increasing energy:
1s, 3s, 4s, 6s, 3d, 4f, 3p, 7s, 5d, 5p
1s, 3s, 3p, 4s, 3d, 5p, 6s, 4f, 5d, 5p
7) What orbital type can be described by the following sets of quantum numbers?
a) n = 2, l = 0, ml = 0
2s
b) n = 5, l = 3, ml = -2
5f
8) Label each of the following sets of quantum numbers as ALLOWED or NOT ALLOWED. Identify
the problem for each of the NOT ALLOWED sets.
a) n = 3, l = 2, ml = 0
allowed
b) n = 1, l = 1, ml = -1
not allowed; l=1 does not exist for n=1
c) n = 0, l = 0, ml = 0
not allowed; n=1 does not exist
d) n = 5, l = 1, ml = +3
not allowed; ml can only be -1, 0, and +1
9) Give the element whose last electron would have the following set of quantum numbers:
a) 2, 1, +1, +½
N
b) 3, 2, +1, -½
Cu
c) 5, 3, 0, -½
Es
d) 7, 0, 0, -½
Ra
10) List the four quantum numbers for each of the designated electrons:
a) the 9th electron of F
2, 1, 0, -½
b) the 19th electron of K
4, 0, 0, +½
c) the 28th electron of Ni
3, 2, 0, -½
d) the 50th electron of Sn
5, 1, 0, +½
11) How many possible orbitals are there for n = ?
a) 4
16
b) 10 100