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Summary
Lecture 38
Electrons with the same n are in the same “shell”.
Electrons with the same n and l are in the same “subshell”: l = 0 s- subshell,
l = 1 p- subshell, l = 2 d- subshell.
The exclusion principle limits the maximum number of electrons in each
subshell to 2(2l + 1).
Nucleus
Radioactivity
α-, β-, and γ- Decay
Electron configurations are written by giving the value for n, the letter code
for l, and the number of electrons in the subshell as a superscript.
In some matter, atoms may have ionic or covalent bonding; potential-energy
diagram shows how potential energy depends on the distance between atoms.
Bond theory of matter divides all materials into conductors, semiconductors,
and insulators.
Conductors have high concentration of free electrons, insulators do not contain
free electrons, and semiconductors have low concentration of free electrons.
Semiconductors can be doped with some elements creating controlled free
electrons or holes.
Physics 112, Spring 2010, Apr 23, Lecture 38
Physics 112, Spring 2010, Apr 23, Lecture 38
Ionic Bonding
Covalent Bonding
Covalent bonding is caused by
Ionic bonding is caused by
1) the transfer of electrons between atoms
2) the sharing of electrons between atoms
3) unequal charge distributions around neutral molecules
4) atoms bonding to hydrogen molecules
1) the transfer of electrons between atoms
2) the sharing of electrons between atoms
3) unequal charge distributions around neutral molecules
4) atoms bonding to hydrogen molecules
A p-type Semiconductor
An n-type Semiconductor
A p-type semiconductor is produced by
An n-type semiconductor is produced by
1) doping the host crystal with donor impurities
2) doping the host crystal with accepter impurities
3) pure crystals of germanium or silicone
4) none of the given answers
1) doping the host crystal with donor impurities
2) doping the host crystal with accepter impurities
3) pure crystals of germanium or silicone
4) none of the given answers
Physics 112, Spring 2010, Apr 23, Lecture 38
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Physics 112, Spring 2010, Apr 23, Lecture 38
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Matter, Atom, Nucleus
Structure of Nucleus
Schematic representation of the structure of matter:
Nucleus is made of nucleons:
Electron
+
and
Positive
charge:
q = 1.6 × 10 −19 C
Matter
+
neutral
+ +
mn = 1.67493×10−27 kg
mp = 1.67262×10−27 kg
+
Atom
Molecules
or atoms
Ratio (proton mass)/(electron mass):
Each chemical element
shown in the Periodic
Table of Elements is build
of electrons and nucleus
with certain parameters.
Carbon14
6 protons
8 neutrons
(1.67262 × 10 −27 kg ) /(9.1× 10 −31 kg ) = 1838
+ + +
+
+
+
Nucleus
Nuclear matter is very dense:
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Physics 112, Spring 2010, Apr 23, Lecture 38
Isotopes
A
Z
Atomic number Z: the number of protons in a nucleus.
Neutron number N: the number of neutrons in a nucleus.
Nuclei of some atoms (e.g. carbon) contains the same number of protons but
different number of neutrons (e.g. in carbon: 6 protons but 5,6,7, 8, or 10 neutrons).
X
Such nuclei are called isotopes.
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C, 126C, 136C , 146C,
Atomic mass number A = Z+N : the sum of protons and neutrons in nucleus.
Atomic mass number “A”
Atomic number “Z”
235
92
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Physics 112, Spring 2010, Apr 23, Lecture 38
Nuclear Numerology and Symbols
Nuclei are labeled by several numbers.
ρ ≈ 1017 kg / m3
15
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and 166C
A
Z
X
A=Z +N
A is atomic mass number, Z atomic number (# of protons), N is the neutron number
U
Chemical symbol (name)
98.9% of naturally occurring carbon on Earth is the isotope
1.1% is the isotope
12
6
C
13
6
C
These percentages are referred to as the natural abundances.
Proton:
1
1
p
Neutron:
1
0
n
Electron:
0
−1
Some isotopes can be produced artificially.
e
The radius of nuclei:
The protons carry
positive charge:
+
The neutrons have no
electrical charge:
Physics 112, Spring 2010, Apr 23, Lecture 38
r ≈ (1.2 × 10
7
−15
The volume of nuclei:
V∝A
4 3⎞
⎛
⎜V = π r ⎟
3
⎝
⎠
Physics 112, Spring 2010, Apr 23, Lecture 38
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1/ 3
m)( A )
2
Comparison of Particles in Atom
Binding Energy and Nuclear Forces (#1)
Masses of atoms are measured with reference to the carbon-12 atom (6p+6n+6e),
which is assigned a mass of exactly 12u.
Binding energy:
The total mass of a stable nucleus is always less
than the sum of the masses of its separate protons
and neutrons.
1 u = 1.6605 × 10 −27 kg
“Unified atomic mass unit”
(mass of 12C carbon is 12.000000 u).
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E = mc2 =
+
Electron has a much smaller
mass than a nucleon.
Atomic mass unit can be specified using the electron-volt energy unit and eq.
−27
+ +
+
E = mc2
(1.67262×10 kg )(3 ×10 m / s)
= 931.5 MeV
1.6 ×10−19 J / eV
8
2
+
+
Where has the missing mass gone?
It has become energy, e.g. radiation or kinetic
energy, released during the formation of the
nucleus.
Smaller
total mass
Binding energy of the nucleus = [mass of constituents - mass of the nucleus]c2
The strong nuclear, weak nuclear, electromagnetic and gravitational forces are the
four known forces in nature.
Strong nuclear force binds nucleons together.
Weak nuclear force is responsible for radioactivity.
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Physics 112, Spring 2010, Apr 23, Lecture 38
Binding Energy and Nuclear Forces (#2)
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Physics 112, Spring 2010, Apr 23, Lecture 38
Radioactivity
One feature of the nucleus is that number of neutrons ≈ number of protons.
Radioactivity: Towards the end of the 19th century, minerals were found that
would darken a photographic plate even in the absence of light.
We can see this effect for stable nuclei with less than 20 protons.
This phenomenon is now called radioactivity.
There are 3 types of radioactive rays:
Number of neutrons (N)
Very large nuclei: no amount of extra
neutrons can overcome the increasing
Coulomb repulsion.
Alpha rays (helium nuclei = 2 protons + 2
neutrons).
Can barely penetrate a piece of paper.
No stable nuclides for Z > 82.
Bigger nuclei require extra neutrons (which
only feel the strong force) to overcome the
Coulomb repulsion of the extra protons.
Beta rays (electrons (β-) or positrons (β+)).
Can penetrate 3 mm of aluminum
Gamma rays (high energy photons).
Can penetrate several cm of lead
Number of protons (Z)
Physics 112, Spring 2010, Apr 23, Lecture 38
Unaffected
by B field
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Physics 112, Spring 2010, Apr 23, Lecture 38
α, β− are bent in
opposite directions
by B field.
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Alpha Decay
Beta Decay (#1)
Alpha decay occurs in large nuclei when the Coulomb repulsion becomes so
large that the strong nuclear force can no longer hold the nuclei together.
Transmission of elements can occur when a nucleus decays beta decay:
the emission of an electron or β- particle:
Three types of decay: β-, β+, Electron capture (EC)
For example, radium-226 will alpha-decay to radon-222:
226
88
4
222
Ra → 24 He + 222
86 X = 2 He + 86 Rn
Here, the following reactions occur inside the nucleus.
In general, alpha decay can
be written:
A
Z
+
Alpha
particle
Unstable
parent
nucleus
X→
A -4
Z-2
X + He
'
4
2
Total number of nucleons
is unchanged)
Daughter
nucleus
β-
n → p + e− + υ
β+
p → n + e+ + υ
EC
p + e → n +υ
-
Occurs when nucleus contains too
many neutrons.
Occurs when nucleus contains
too many protons.
υ
is antineutrino.
These reactions are governed by the weak nuclear force.
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Physics 112, Spring 2010, Apr 23, Lecture 38
Physics 112, Spring 2010, Apr 23, Lecture 38
Beta Decay (#1)
Beta Decay (#2)
2. Beta+ decay:
Anti-neutrino
1. Beta- decay:
p → n + e+ + υ
−
n → p + e + neutrino
n → p + e− + υ
Electron
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Electron is created within the nucleus itself.
Occurs when one of the neutrons in the nucleus changes into a proton. An
electron and “antineutrino”υ are also ejected.
Same number of nucleons,
one more proton and one less neutron.
A
Z
X
A=Z +N
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neutrino
electron
p + e- → n + υ
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A is atomic mass number, Z atomic number (# of protons), N is the neutron number
Physics 112, Spring 2010, Apr 23, Lecture 38
Ne → 199 F + e − + υ
3. Electron capture:
Finally, a nucleus can capture one of its
inner orbiting electrons.
beta- decay of carbon-14:
C → 147 N + e − + υ
positron
Occurs when one of the protons in the
nucleus transforms into a neutron. A
positron and neutrino are emitted.
“Neutrino” means “little neutral one”; the symbol is nu (υ).
14
6
14
Be + e - → 73 Li + υ
The electron is captured, a proton becomes
a neutron and a neutrino is emitted.
neutrino
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Gamma Decay
Three Types of Radioactive Decay
Gamma rays are very high-energy photons.
They are emitted when a nucleus decays from an excited state to a lower
state, just as photons are emitted by electrons returning to a lower state.
Law of conservation of nucleon
number:
γ
The total number of nucleons (A)
remains constant in any process,
although one type can change into
the other type (protons into
neutrons of vice versa).
A
Z
X → ZA X + γ
Physics 112, Spring 2010, Apr 23, Lecture 38
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Physics 112, Spring 2010, Apr 23, Lecture 38
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Mass of an Atom
The mass of an atom is
1) approximately equally divided between neutrons, protons, and electrons
2) evenly divided between the nucleus and the surrounding electron cloud
3) concentrated in the cloud of electrons surrounding the nucleus
4) concentrated in the nucleus
Atomic Number
An atom's atomic number is determined by the number of
1) neutrons in its nucleus
2) nucleons in its nucleus
3) protons in its nucleus
4) alpha particles in its nucleus
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