PHYSICS 13
HOUR EXAM 2
FALL 2003
NAME___________________________________________
Grades:
points/possible points
I
/50
II
/30
III
/50
IV
/50
V
/20
Total:
/200
This is a closed book, closed notes exam. You may use
calculators.
Make sure you show all your work! You will get partial credit.
Useful data and equations
:
1 dimensional Schrödinger equation:
−
h
´
2
2m
d
2
dx
2
ψ
(x)
+
V(x)
ψ
(x)
=
E
ψ
(x)
(
η
=h/2
π
)

ψ
(x)
2
is the Probability per unit length.
Kinetic Energy = 1/2 mv
2
= p
2
/2m (for a plane wave =
η
2
k
2
/2m)
de Broglie:
λ
=h/p ;
wave number k=2
π
/
λ
Photon energy
E = hf = h
ω/2π
Quantum mechanical angular momentum 
L
= [
λ
(
λ
+1)]
1/2
η
and
L
z
= m
l
η
Transition and photon selection rule:
λ
→
λ
±
1
Atomic electron spectroscopic notation: principal quantum number n = 0,1,2,...;
orbital angular momentum quantum
number symbol
λ
= 0,1,2,...,n1, with notation
λ
= 0>s, 1>p, 2>d, 3>f,...; magnetic quantum no. m
λ
= l, l+1, ... , l1, l
.
Spin m
s
= 1/2, +1/2
Electric dipole moment p
E1
= Q r (Q=charge)
Rydberg Constant = 13.6 eV = k
EM
2
e
4
m/2
η
2
= E
0
(=  E
1
ground state
energy of Hydrogen)
Atomic electron around nucleus of charge Z,
E
n
= Z
2
E
0
/n
2
Magnetic moment  orbital:
µ
L
= [
λ
(
λ
+1)]
1/2
µ
B
spin
:
µ
S
=
g
S
[s(s+1)]
1/2
µ
B
Magnetic moment along zaxis
µ
L
z
=  m
λ
µ
B
and
µ
Sz
= 
g
S
m
s
µ
B
with g
S
= 2 and
µ
B
= 5.79x10
5
eV/Tesla
Interaction Energy U = 
µ •
B
= 
µ
z
B
c = 3.00x 10
8
meter/sec
electron charge: e=1.60x10
19
Coul
h = 6.63 x 10
34
J sec= 4.14 x 10
15
eV sec
η
= 6.58 x 10
16
eV sec
k
EM
=
1
4
πε
0
= 8.99x10
9
Nm
2
/Coul
2
hc = 1.24 x 10
6
eV m
η
c = 1.97x10
7
eVm
Rest energy of electron = m
e
c
2
= 5.11x10
5
eV
Rest mass of electron = m
e
= 9.11x10
31
Kg
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