HW 1  Solutions
Due: January 30
th
1.
(Problem 2.4 from Callister 7
th
Ed):
In this question, you are asked to list some of the difference between the Bohr’s
treatment of the atomic structure vs. the modern quantum mechanical view:
a.
Cite two important quantum mechanical concepts associated with the Bohr model
of the atom.
•
Bohr’s Model:
o
This model assumes electrons behave like particles, orbiting around
the nucleus (wrong!)
o
The orbits, however, are quantized (good!)
o
The position of any particular electron is well defined in a particular
orbit (completely wrong!!!)
b.
Cite two important additional refinements that resulted from the wavemechanical
atomic model
•
Quantum View:
o
Electrons exhibit waveparticle characteristics
o
‘Discreteness’ of orbits results from wavemechanical nature of
electron states (only integer wave numbers ‘fit’ in determined orbitals)
o
At best, you can only say that there is a certain probability of
observing an electron around the nucleus
o
There are four quantum numbers necessary to describe the state of an
electron in an atom
2.
(Problem 2.7 Callister) Give the electron configurations for the following ions:
P
5+
, P
3
, Sn
4+
, Se
2
, I

and Ni+
2
•
P [15]: 1s
2
2s
2
2p
6
3s
2
3p
3
= [Ne] 3s
2
3p
3
o
P
5+
= [Ne]
o
P
3
= 1s
2
2s
2
2p
6
3s
2
3p
6
= [Ne] 3s
2
3p
6
=[Ar]
•
Sn [50]: 1s
2
2s
2
2p
6
3s
2
3p
6
4s
2
3d
10
4p
6
5s
2
4d
10
5p
2
=[Kr]5s
2
4d
10
5p
2
o
Sn
+4
= [Kr]5s
0
4d
10
5p
0
(d shells like to be half full or completely full)
•
Se [34] : 1s
2
2s
2
2p
6
3s
2
3p
6
3d
10
4s
2
4p
4
= [Ar]3d
10
4s
2
4p
4
o
Se
2
= [Ar] 3d
10
4s
2
4p
6
•
I [53] : 1s
2
2s
2
2p
6
3s
2
3p
6
4s
2
3d
10
4p
6
5s
2
4d
10
5p
6
=[Kr]4d
10
5s
2
5p
5
o
I

= [Kr] 4d
10
5s
2
5p
6
•
Ni[28]: 1s
2
2s
2
2p
6
3s
2
3p
6
4s
2
3d
8
= [Ar]3d
8
4s
2
o
Ni
+2
= [Ar]3d
8
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3.
The net potential energy between two adjacent ions, E
N
, may be represented by
the following equation:
N
n
A
B
E
r
r
= −
+
(1.1)
a.
Find an expression for the interatomic force as a function of separation
The interatomic force is just the rate of change of the potential energy with
respect to separation:
( )
( )
2
1
n
E r
A
Bn
F r
r
r
r
+
∂
=
=
−
∂
b.
Determine the equilibrium separation, r
0
, in terms of A, B and n
The equilibrium separation corresponds to the separation where the
interatomic force banishes (first instance for this condition, since the force
also vanishes at infinite separation!!):
( )
( )
2
1
1/
1
1/1
0
0
n
n
n
E r
A
Bn
F r
r
r
r
nB
A
r
A
nB
+
−
−
∂
=
=
−
=
∂
⎛
⎞
⎛
⎞
=
=
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
c.
Determine the expression for bonding energy, E
0
The bonding energy corresponds to the Energy of the system at the
equilibrium separation:
0
1/(1
)
/(1
)
0
0
n
n
n
n
A
B
A
B
E
r
r
A
A
nB
nB
−
−
−
= −
+
=
+
⎛
⎞
⎛
⎞
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
4.
List four characteristics of each of the different kinds of primary bonds.
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 Spring '08
 Zhang
 Atom, equilibrium separation

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