AP Physics
Conceptual Questions
1. Why are atoms less massive than all of the pieces that had to be assembled to make them?
Atoms are less massive than the total mass of the pieces they are composed from because the components lose energy as they come together. The amount of energy they lose is called the binding energy and is equal to the amount of energy it would take to separate all of the pieces back into the separate components of the atom. Because of Einstein’s equation E=mc
2
, as the pieces lose energy while they are assembled, they are also losing mass, hence the assembled atom is less massive than the total mass of all of the pieces that make it up.
2. Decide which of the following nuclides are likely to be stable and which are likely to be unstable.
Give your reasons. a) Cl-36 b) Ag-107
Unstable Stable c) Ca-34
Unstable d) Pu-244
Unstable
Odd Protons (Z=17) Even Neutrons (60) N/Z = 0.7
Odd Neutrons (N=19) N/Z = 1.28 okay (too few neutrons) e) Au-197
Stable
Even Neutrons (N=118) f) O-16 g) Cs-114
No stable elements over Z=82 h) Fe-57
Stable Unstable Stable
Even Protons (Z=8) Odd (Z=55) (N=59) Even Protons (Z=26)
N/Z=1.5 okay Even Neutrons (N=8)
N/Z = 1 okay
N/Z = 1.07
(too few neutrons)
N/Z = 1.19 okay
3. What is the difference between fission and fusion?
Fission is the process whereby one massive nuclide splits into two smaller nuclides while fusion is the process whereby two small nuclides combine to form one more massive nuclide.
4. Why don’t heavy elements spontaneously undergo fusion? Why don’t light elements spontaneously fission?
Spontaneous processes are ones that carry the participants (in this case the nucleons) to lower energy levels.
Heavy elements do not spontaneously undergo fusion, because the nucleons in a heavy element would have to gain energy to form a more massive nuclide. This is because elements more massive than iron have progressively less binding energy per nucleon, meaning that each nucleon is at a higher energy level.
Similarly, light elements do not undergo fission because elements less massive than iron have progressively less binding energy per nucleon, meaning that the nucleons would have to gain energy if they fissioned into less massive nuclides.
5. According to the Standard Model of elementary particles what are the actual, fundamental elementary particles and what are their characteristics?
The Standard model has essentially 16 elementary particles: six leptons (electron, muon, tauon and their associated neutrinos)
The electron, muon and tauon vary in mass but all have –1 charge and 1/2 spin
The neutrinos have no charge and 1/2 spin six quarks (down, up, strange, charm, bottom, top)
The down, strange, bottom quarks vary in mass but all have –1/3 charge and 1/2 spin
The up, charm, top quarks vary in mass but all have +2/3 charge and 1/2 spin four mediator particles associated with forces, all of which have spin 1 photons – which mediate the electromagnetic force weak gauge bosons (W
+
, W
-
, Z
0
) – which mediate the weak nuclear force gluons – which mediate the strong nuclear force

6. What is the primary difference between the particles that mediate forces and the particles that compose the building blocks of matter? (Note: you do need the force particles to hold the “matter” particles together to form matter, but ignore that point for right now)
The most obvious difference is that “matter” particles have spin 1/2 and “force” particles have spin 1.
7. What is the difference between a particle and an anti-particle?
A particle and its antiparticle are exactly identical in every way (same mass, same spin, same amount of charge) except that the antiparticle has the opposite sign charge from the particle. So an electron has a –1 charge and its antiparticle, the positron, has a +1 charge.
8. What are the differences between hadrons and leptons according to the Standard Model of particle physics?
Hadrons are particles that experience the strong nuclear force, which means they are made from quarks. Leptons are fundamental particles in their own right and are not made up of any other particles.
9. Explain how quark theory can create the properties of protons and neutrons from combinations of three quarks.
A proton has to be built up to have a charge of +1, this can be accomplished by adding two up quarks with +2/3 charge to one down quark with –1/3 charge. Other combinations could give you the same charge, but they would be made of more massive quarks and would not be stable.
A neutron has to built up to have no charge. This requires that the positive and negative charges cancel each other out. The way to do this is with 1 up quark (+2/3) and 2 down quarks (–1/3 each). Similar, to the proton the up and down quark are the lowest mass option for getting the right charge.
10. What is meant by a virtual particle? How can a virtual particle exist?
A virtual particle is a particle that is impossible to observe because its combination of energy and duration fall under the limits of measurement established by the Heisenberg Uncertainty
Principle.
Review Questions
1. Use a periodic table to identify the components of the nucleus for the most common isotope of each of these atoms: a) Copper (Cu)
Z = 29
N = 35 (rounded) b) Phosphorus (P)
Z = 15
N = 16 c) Potassium (K)
Z = 19
N = 20 d) Osmium (Os)
Z = 76
N = 114
2. For each of the following decays, write out a nuclear equation predicting the products of the decay: a) Electron capture by Nb-83
83
,
41
Nb +
0
,
-1 e →
83
,
40
Zr c) Alpha decay of Hf-157
157
,
72
Hf →
153
,
70
Yb +
4
,
2
He b) Beta (-) decay of Ta-186
186
,
73
Ta →
186
,
74
W +
0
,
-1 e d) Beta (+) decay of Ne-18
18
,
10
Ne →
18
,
9
F +
0
,
+1 e +
3. The half life of Radium-216 is 25.6
 s. A sample of pure radium 216 starts with 9,000,000,000 atoms.
How many are left after 1 s?

=
Ошибка!
=
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= 27076.06 s
-1
N = N
0
· e -
 t 
= 9 x 10
9 ·e -27076.06 s -1
·
1s = 0

4. A sample of 1.00 x 10
24
tritium (hydrogen-3) atoms is left on a shelf for 1 year. When it is examined, there are only 9.45 x 10
23
N = N
0
· e -
 t 
tritium atoms remaining. What is the half-life of tritium? so
Ошибка!
= e
-
 t
so ln
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= -
 t
With numbers originally in problem:

=
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=
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= 53.01 y
-1
= 0.1451 d
-1
With Correct Numbers (as shown above):

=
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=
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= 0.05657 y
-1 t
½
=
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=
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= 4.78 days t
½
=
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=
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= 12.25 y
5. A 20.0 g sample of animal bone found at a 12,000 year old human encampment, has a radioactive activity of 75 counts per minute from the decay of Carbon-14 in it. Carbon-14 has a half-life of
5730 yrs. What was the bone’s activity when it was fresh?

=
Ошибка!
=
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= 1.209 x 10
-4
y
-1
Because activity is proportional to the number of particles present Ошибка!
, it decreases exponentially as well:
Ошибка!
= Ошибка!Ошибка!
· e -
 t
Ошибка!
= 320 c/m
 so Ошибка!Ошибка!
= Ошибка!
=
6. a) An atom of Bromine-79 has a mass of 78.9183376 u. What is the total binding energy? What is the binding energy per nucleon?
35
1
,
1
H 35(1.0078250) = 35.2738750 u
+ 44
1
,
0 n 44(1.0086649) = 44.3812556 u neutrons
Bromine-79 is made from:
35 H-1 atoms and 44
Total Mass
–Mass Atom
79.6551306 u
–78.9183376 u
Mass Defect
Binding Energy
0.7367930 u
E b
= 0.7367930 u x
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= 686.32 MeV
Binding Energy Per Nucleon
Ошибка!
=
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= 8.6876 MeV/nucleon b) An atom of Antimony-123 has a mass of 122.9042157 u. What is the total binding energy? What is the binding energy per nucleon?
51
1
,
1
H 51(1.0078250) = 51.3990750 u Antimony-123 is made from:
+ 72
1
,
0 n 72(1.0086649) = 72.6238728 u 51 H-1 atoms and 72 neutrons
Total Mass
–Mass Atom
124.0229478 u
–122.9042157 u
Mass Defect
Binding Energy
1.1187321 u
E b
= 1.1187321 u x
Ошибка!
= 1042.10 MeV
Binding Energy Per Nucleon
Ошибка!
=
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= 8.4723 MeV/nucleon
7. Niobium-83 has a mass of 82.936703 u and Zirconium-83 has a mass of 82.9286521 u. a) How much energy is given off in the decay from question 2a?
Find mass lost in decay:
83
,
41
Nb +
0
,
-1 e → 83
,
40
Zr
83
,
41
Nb
+
0
,
-1 e
82.936703 u
+0.000549 u
Total Mass 82.937252 u
–
83
,
40
Zr –82.9286521 u

Mass Lost 0.0085999 u
Energy Lost 0.0085999 u x
Ошибка!
= 8.011 MeV b) If the energy were emitted as a photon, what wavelength would it be?
Photon Energy = 8.011 MeV x
Ошибка!
= 1.283 x 10
-12
J f =
Ошибка!
=
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= 1.937 x 10
21
Hz

=
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=
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= 1.549 x 10
-13
m Definitely in the gamma ray range of EM spectrum
8. An atom of Ne-18 has a mass 18.0056971 u, an atom of F-18 has a mass of 18.0009377 u and a positron has a mass of 0.000548 u. How much energy is given off in the decay from question 2d?
Find mass lost in decay:
18
,
10
Ne →
18
,
9
F +
0
,
+1 e +
18
,
10
Ne 18.0056971 u
– 18
,
9
F –18.0009377 u
–
0
,
-1 e
–0.000549 u
Mass Lost 0.0042104 u
Energy Lost 0.0042104 u x
Ошибка!
= 3.9219876 MeV
9. Plutonium-244 occasionally spontaneously fissions. If one of the daughter elements is Molybdenum-
105 and there are 5 neutrons released, what is the other daughter element?
244
,
94
Pu →
105
,
42
Mb + 5
1
,
0 n + ?
In order for the protons and neutrons to remain extant, ? must have 94 – 42 = 52 protons, so it is
Tellurium and it must have a mass number of 244 – 105 – 5(1) – 134. Therefore ? =
134
,
52
Te
10. Curium-248 (248.0723422 u) will undergo spontaneous fission. If its daughter elements are
Gadolinium-165 (164.9393800 u) and Germanium-80 (79.9254448 u), how much energy is released?
Find mass lost in decay:
248
,
96
Cm → 165
,
64
Gd +
80
,
32
Ge + 3
1
,
0 n
248
,
96
Cm
–
165
,
64
Gd
–
80
,
32
Ge
–3 1
,
0 n
248.0723422 u
–164.9393800 u
–79.9254448 u
–3.0259947 u
Mass Lost 0.1815227 u
Energy Lost 0.1815227 u x
Ошибка!
= 169.088 MeV
11. In the center of the sun, carbon nuclides fuse with helium nuclides to form oxygen. Take the fusion of Carbon-12 (12.0000000 u) and Helium-4 (4.0026032 u) to form Oxygen-16 (15.9949146 u).
How much energy is released in each such fusion event?
12
,
6
C +
4
,
2
He →
16
,
8
O
Find mass lost in decay:
12
,
6
C 12.0000000 u
+
4
,
2
He +4.0026032 u
Total Mass 16.0026032 u
–
16
,
8
O –15.9949146 u
Mass Lost 0.0076886 u
Energy Lost 0.0076886 u x
Ошибка!
= 7.162 MeV

12. Palladium-106 (105.9034831 u) can be formed by the fusion of Calcium-48 (47.9525335 u) and
Iron-58 (57.9332805 u). How much energy is released in such a fusion event?
Find mass lost in decay:
48
,
20
Ca +
58
,
26
Fe → 106
,
46
Pa
48
,
20
Ca
+
58
,
26
Fe
47.9525335 u
+57.9332805 u
Total Mass 105.885814 u
–
106
,
46
Pa –105.9034831 u
Mass Lost –0.0176691 u
Energy Lost –0.0176691 u x
Ошибка!
= –16.459 MeV
Negative energy released means that energy must be added in order for this fusion to occur.