Nuclear Physics and Nuclear Energy
The Nuclear Force.
Rohlf Ch. 11. p296
Homework: Ch. 11: 4,5,11,12,42
Due Nov. 10
Additional homework:
Due Nov. 13
Assume a 238U ssions exactly into two equal nuclei.
1. What nuclei are the ssion products.
2. What is the
Schroedingers Equation
( r ,t)
2
( r ,t) + V ( r )( r ,t) = i
2m
t
2
( r ,t) = ( r )T (t)
Time equation:
T iE
+ T =0
t
T=
E
i t
Ae
= Aei t
Space equation:
2m
+ 2 V (r ) = 0
2
(
)
Particle in a box
2 ( x ) 2m
+ 2 E ( x) = 0
2
x
V ( x) = 0,
(x,t) = (k)T
Exam 1.-Tues. Oct. 6
1 problem on math. Preliminaries
- vector calculus.
3 problems on special relativity.
One page of double sided handwritten notes.
Schroedingers Equation -1925
Rohlf, Chapter 7, p. 191-218
Schroedinger Equation
( r ,t)
2 2
( r ,t) +
Physics 2961
Intro. to Modern Physics!
Textbook: Rohlf, Modern Physics, Wiley!
Imaginary Numbers and Complex Notation!
Representation on a 2-dimensional complex plane.!
z = x + iy = r(cos ! + i sin ! )
i!
e +e
cos ! =
2
"i!
i!
e "e
; sin ! =
2i
y=
Im(z)
"
Bohr Model of the Hydrogen Atom.!
Rohlf, p85-87"
(This was covered in Honors Physics II.)"
This is a semi-classical model which assumes the electron has well dened orbits "
(particle properties) and interference phenomena (wave properties) "
F(r)r = mar
e
V " 2m %
Number of states up to E : N =
$
'
6! 2 # ! 2 &
3/2
E 3/2 .
dN
Vm 3/2 1/2
Density of states:!
=
E
2 3
dE
2! !
2/3
(3 / ! ) h 2 2/3
Fermi energy: !EF =
ne
8m
Total zero point electron energy:
Total energy = N e E
x =
Ef
Ne E = Ne
!
dN
E
dE
dE
0
Ef
Spherical Coordinates
Review
Schroedinger's equation:
2 2
( r ,t)
( r ,t) + V ( r )( r ,t) = i
2m
t
Space
Time
2M
+ 2 E V (r ) = 0
2
(
)
T=
E
i t
Ae
Assume spherical symmetry:
1 2
1
1
2
2
2
r r + r 2 sin sin + r 2 sin 2 2 + k (r) = 0
r r
Schroedingers equation
in 3-dimensions
Rohlf 7.6 P213-216
Schroedingers Equation
( r ,t)
2
( r ,t) + V ( r )( r ,t) = i
2m
t
2
Separation of variables:
Time equation:
Space equation:
( r ,t) = ( r )T (t)
T i
+ T =0
t
2m
+ 2 V (r ) = 0
2
(
)
Solution to
Nuclear Physics and Nuclear Energy
The Nuclear Force.
Rohlf Ch. 11. p296
Homework: Ch. 11: 4,5,11,12,42
Due Nov. 10
Additional homework:
Due Nov. 13
Assume a 238U ssions exactly into two equal nuclei.
1. What nuclei are the ssion products.
2. What is the
Review
Balance electron kinetic energy and gravitational energy
Ee =
5/3
CN e
2
BN N
EG =
R
R2
C = 1.36 10 38 B = 1.12 10 64
E = Ee + EG =
dE
= 0
dR
5/3
CN e
R=
R2
2
BN N
R
5/3
2CN e
2
BN N
= 7.2 10 3 km
Massive star: need relativistic treatment.
Electro
Density of states and Fermi energy.
Rohlf Ch. 12 Sec.12.6
V 2m
Number of states up to E : N =
6 2 2
3/2
E 3/2 .
dN
Vm 3/2 1/2
Density of states:
=
E
2 3
dE
2
2/3
(3 / ) h 2 2/3
Fermi energy: EF =
ne
8m
Application of zero point energy
to astrophysics.
Special Relativity
Read P98 to 105
The principle of special relativity: The laws of nature look exactly the same for all observers in
inertial reference frames, regardless of their state of relative velocity.
(Note: accelerated reference frames are not in
Review of Quantum Physics!
(Rohlf Chapter 3.)
Homework 7!
Cavity radiation, etc: Ch. 3, problems 3, 8, 19, 21!
Due, Fri. Oct. 2.
Cavity Radiation!
Rohlf P63-66
Classical Rayleigh-Jeans law.
Number of oscillators per unit volume per :
Average energy per os