Download Lecture 24. Nov. 30. 2016.

Lecture 24-1
Physics 219 Help Session
Date: Wed 12/07, 2016.
Time: 6:00-8:00 pm
Location: Physics 331
Lecture 24-2
Final Exam
Dec. 14. 2016.
1:00-3:00pm in Phys. 112
Bring your ID card, your calculator and a soft pencil with
you!
Exam Calculator: When taking a Physics 219 Exam, there
is only one type of calculator is accepted: CASIO fx-260
SLRSC FRACTION.
NO OTHER BRAND or TYPE WILL BE ALLOWED!
Lecture 24-3
The Hydrogen Atom
 According to the Uncertainty Principle, we cannot
know both the position and momentum of any particle
precisely at the same time.
The electron in a hydrogen atom cannot orbit the nucleus
in a circular orbit – or any other kind of orbit; otherwise,
both the position and momentum would be exactly known!
 Instead, the probability to find an electron is given
by a 3D standing wave.
Standing waves of different shapes for different
states (and different energy levels).
Ground state wave function
Lecture 24-4
Quantum Numbers
 The Bohr model quantum number which specifies the energy
level turns out to be only one of several such quantum numbers
that specifies the quantum state of the hydrogen atom:
13.6eV
En 
n2
n  1,2,3,...
principal quantum number
 There are other quantum numbers:
l for L
orbital angular momentum
ml for Lz
the “z-component” of L
s for s
spin angular momentum
ms for sz
the “z-component” of s
Lecture 24-5
Nuclear Structure
 A nucleus is at least O(103) times more massive than an
electron and is positively charged.
 A nucleus is actually NOT a point charge. It has a
size that is O(1) fm (1 femtometer = 10-15m).
 A nucleus is composed of protons
and electrically neutral neutrons
(i.e., nucleons).
 The number of protons, Z, is
called the atomic number. The
atomic number determines what
type of element the atom is.
A Z  N
Atomic mass number
(or nucleon number)
Number of
neutrons
Lecture 24-6
Nuclear Structure
 Each element has a fixed number Z of protons, but the
number of neutrons, N, can vary. These are called isotopes.
A Z  N
 Shorthand notation for isotopes: e.g., Oxygen 18 has 8
protons (because it is Oxygen), the atomic mass number
18, and the neutron number N=10 (because A=Z+N).
18
8
O
A
Element Symbol
Z

 Other examples:
16
8
O, 12 H , 13H , 126 C, 146 C
Some isotopes are stable, others are unstable and radioactive.
Lecture 24-7
Physics 219 – Question 1 – Dec. 05. 2016.
Isotopes of an element have the same number of ______
but different number of ______ . Fill the blanks with the
correct particle names.
A.
B.
C.
D.
E.
electrons, protons
neutrons, electrons
protons, electrons
neutrons, protons
protons, neutrons
Lecture 24-8
The Strong Force
 How are the protons (positive charge) and neutrons
(neutral) held together in the nucleus?
The answer is: by the strong force!
 The strong force is one of nature’s 4 fundamental forces:
Force
Relative Strength*
Range (m)
Strong
1
10-15
Electromagnetic
10-2

Weak
10-6
10-17
Gravitational
10-43

 The strong force holds a nucleus of multiple nucleons
together as well as the individual nucleons by themselves. It
competes with the electromagnetic repulsion among the protons.
(*for two u quarks separated by 0.03 fm)
Lecture 24-9
How large is a nucleus?
 Mass of Nuclei 1 atomic mass unit (u) = 1/12 of a neutral 12C atom
= 1.660539 x 10-27 kg
Mass of a nucleon is approximately 1 u. That of an
electron is approximately 0.00055 u.
1 mole of nucleons ≈ 6.02 x 1023 u ≈ 10-3 kg = 1 g
 Size of Nuclei
A  Mass M  volume V.
So the density ρ is roughly
independent of A.
 r  r0 A
1/ 3
where
4 3
M   r   A
3

15
r0  1.2  10 m  1.2 fm
fermi
Lecture 24-10

Binding Energy
 The mass of a nucleus is less than the sum of the masses
of its parts!
 The mass defect, m, is the difference between the sum of the
masses of the protons and neutrons, and the mass of the nucleus.
m  m(Z protons  N neutrons)  m(nucleus)
 The binding energy of the nucleus
EB  m  c
2
represents the energy required to separate the nucleus into
individual nucleons.
Generally, a binding energy is the energy required to
separate a composite object into its constituent parts.
Lecture 24-11
How to find the binding energy
2
2

m
c

m
(
Z
protons

N
neu
t
rons
)

m
(
nucl
e
us
)
c
 


 Mass of neutral atoms can be found in a table (e.g., NIST
table posted on the course home page under Lectures).
(Relative Atomic Weight in that table gives the atomic mass in u.)
 To find the mass of the nucleus, you must subtract the
mass of the electrons contained within the neutral atom.
(But what about the binding due to electromagnetic forces?)
Example:
14N
nuclear binding energy?
Lecture 24-12
Example:
14N
nuclear binding energy?
Neutral 14N atom = 14.003074 u
Mass of 7 electrons = 7 x me = 7 x 0.0005486 u = 0.003840 u
So 14N nuclear mass = 13.999234 u
Mass of 7 individual protons and 7 neutrons
= 7 x mp + 7 x mn = 7 x 1.0072765 u + 7 x 1.0086649 u
= 14.111589 u
So the mass defect
m = (14.111589 u) – (13.999234 u) = 0.112355 u
EB   m  c 2  0.112355u  931.494 MeV / u
 104.659 MeV
c2
Lecture 24-13
Nuclear Energy Levels
 The nucleus has energy levels just like the electrons in an atom.
 Protons and neutrons have separate energy levels.
 They obey the exclusion principle and two of them can occupy
each level (one with spin up, one with spin down), like the electron.
The energy is lowest
with 6 protons and
6 neutrons, if
A=Z+N=12.
Lecture 24-14
Physics 219 – Question 2 – Dec. 05. 2016.
Which description of the isotope
A.
B.
C.
D.
E.
14
6
? is correct?
O (oxygen) with 8 protons and 6 neutrons
C (carbon) with 6 protons and 8 neutrons
Si (silicon) with 14 protons and 6 neutrons
Ca (calcium) with 6 protons and 20 neutrons
C (carbon) with 6 protons and 14 neutrons
Atomic numbers of the above elements are:
carbon 6, oxygen 8, silicon 14, calcium 20.
Lecture 24-15
Composition of Nuclei
 For smaller nuclides,
N=Z is most stable.
 For bigger nuclides, the
Coulomb repulsion of
protons favor more
neutrons than protons to be
in the nucleus.
 Some nuclides are
unusually stable: e.g.,
4
2
40
48
He, 168 O, 20
Ca, 20
Ca, 208
82 Pb
Binding Energy Per Nucleon Curve
tighter
Lecture 24-16
For smaller nuclides, binding gets tighter as
the mass number increases (as the nucleons
gain more neighbors to bind with). For
larger nuclides, the Coulomb repulsion
among the protons begins to make them less
tightly bound. The maximum binding occurs
around A=60.
Lecture 24-17
Radioactive Decay
 There are stable nuclides and unstable ones. An unstable
nuclide decays by emitting particles and/or radiation.
radioactive decay
Most (~80%) of nuclides are radioactive,
including all those with Z > 83.
 There are 3 types of decays: alpha, beta, and gamma decays
 Radioactive decays occur with a probability which depends
on the isotope and the type of decay.
Decays are random events, i.e., they don’t occur at predicted times.
Lecture 24-18
Conservation Laws in Radioactive Decay
1. The number of nucleons must remain the same
(though the types may change).
2. The total electric charge must remain the same.
3. The total energy must remain the same.
Energy here includes both the rest mass energy
2
and the kinetic energy.
E  mc
0
The sum of the masses of the decay products must
be less than the mass of the original nucleus in order
for a spontaneous decay from the nucleus at rest to
be possible.
Disintegration energy is the name for that part of rest mass
energy of the original nucleus that is converted into other
forms of energy (such as kinetic energy or EM radiation).