Chemistry 344: Physical Chemistry II for Biochemists
Total: 10 pts
1. (1 pt) Normalize the following 3-dimensional complex vector:
v? = (2.3 + 1.60i, ?1.80 ? 1.00i, 3.20)
2. (1 pt) Are the following two vectors orthogonal? Show your work.
u ? = (21/2 21/2) and v? = (?21/2 21/2)
3. (2 pts) A 10.0 kg kettle bell is lifted 3.00 m above the ground and dropped to a nal height
of 0.0m. What is the potential energy (V, in J), kinetic energy (K, in J), total energy (E, in J)
and velocity (in m/s) when the kettle bell is at a height of 3.00 m, 2.00 m, 1.00 m and 0.0
m? (Hint: V = mgh with g = 9.81 m s-2)
4. (2 pts) A wavefunction exists in a 1-dimensional box from x = 0m to x = 1m. What is the
value of the normalization constant R?
? = A cos(2m ?1x)
5. (2 pts) What is the kinetic energy of the following wavefunction of an electron over the
interval x = 0m and x = 1m?
? = A cos(2m ?1x)
6. (2 pts) A system has two eigenvectors, ?1 and ?2, and an angular momentum operator Lz.
What are the eigenvalues for each eigenvector and the operator Lz? Show your work.
?
0
1
0
2
?1 =
, ?2 =
, L? z =
?
(0)
(1)
0 ?2
e
ae + bf
a b
=
,
(c d) ( f ) (ec + d f )
e.g.
17
5
1 2
=
(3 4) (6) (39)
fi
Hint:

Purchase answer to see full
attachment