Download Ch.43- Nuclear spin example. Examples of radioactive decay

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The ECAFE evaluation system is now open.
Please take a few minutes to review the course.
Today: Nuclear Spin example, radioactivity,
radioactive decay law and half-life.
Quiz 32 will be given by Professor Lam. Today will
have some clicker questions.
Not required but inspiring and interesting.
(29min BBC documentary on the birth of quantum mechanics.
The part about the Solvay conference is especially good)
https://www.youtube.com/watch?v=LLvihoOeNpI
Copyright © 2012 Pearson Education Inc.
Intuition: Some interesting nuclear physics simulations
PHET simulation of NMR (Hint: Larmor frequency 42.58 MHz/T)
https://phet.colorado.edu/en/simulation/legacy/mri
PHET simulation of alpha radioactive decay:
https://phet.colorado.edu/en/simulation/legacy/alpha-decay
PHET simulation of a beta decay
https://phet.colorado.edu/en/simulation/legacy/beta-decay
PHET simulation of nuclear fission
https://phet.colorado.edu/en/simulation/legacy/nuclear-fission
Copyright © 2012 Pearson Education Inc.
Nuclear spin example
Protons are placed in a 2.30 T field that
points in the z-direction.
a) What is the energy difference between
the states with the spin parallel or antiparallel to the B field ?
b) A proton can make a transition
between these states, what is the
wavelength of the photon emitted ?
Copyright © 2012 Pearson Education Inc.
Nuclear spin example
Protons are placed in a 2.30 T field that points in the zdirection.
a) What is the energy difference between the states with
the spin parallel or anti-parallel to the B field ?
U = - | mz | B = -(2.7928)(3.152 ´10 -8 eV / T )(2.30T )
Þ U = -2.025 ´10 -7 eV
Remember the proton has a magnetic moment that is 2.7928 μn
This is just the energy when aligned. The energy when
anti-parallel is U=+2.025 x 107eV. Do you see why ?
Copyright © 2012 Pearson Education Inc.
Nuclear spin example
Protons are placed in a 2.30 T field that points in the zdirection.
A proton can make a transition between these states, what
is the wavelength of the photon emitted ?
-7
-7
DE = 2(2.025 ´10 eV ) = 4.05 ´10 eV
DE
4.05 ´10 -7 eV
7
f=
=
=
9.79
´10
Hz = 97.9MHz
-15
h
4.136 ´10 eV - s
c
3´10 m / s
l= =
= 3.06m
7 -1
f 9.79 ´10 s
8
Question: Is the transition photon an x-ray, a gamma ray,
in the visible, infrared, or radio range ?
Copyright © 2012 Pearson Education Inc.
Nuclear spin example
Protons are placed in a 2.30 T field that points in the zdirection.
A proton can make a transition between these states, what
is the wavelength of the photon emitted ?
c
3´10 8 m / s
l= =
= 3.06m
7 -1
f 9.79 ´10 s
Question: Is this the same as the 21 cm hyperfine
transition that we discussed earlier ? (Yes or no, explain)
Ans: No, the 21 cm line arises from the interaction of
electron spin magnetic moment and nuclear spin moment
but also corresponds to a spin flip. It does not involve an
external B field.
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Experimentalist’s viewpoint (α, β, γ)
Penetration (explain)
How they bend in a magnetic field (explain)
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Beta and gamma decay
• There are three types of β decay: β- beta-minus, β+
beta-plus, and electron capture.
• A beta-minus β– particle is an electron. (example
Co60)
• A γ ray is a photon (note the A or Z do not change
in this type of decay, go from excited state to a
lower energy state).
+
p
®
n
+
b
+ ne
n ® p + b + ne
p + b - ® n + ne
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Question: What happens to
Z and A in beta decay
processes ?
Clicker question on alpha decay
Which kinds of unstable nuclei typically decay by
emitting an α particle?
A. those with too many neutrons
B. those with too many protons
C. those with too many neutrons and too many
protons
D. Misleading question—the numbers of neutrons
and protons in a nucleus are unrelated to whether
or not it emits an alpha particle.
Copyright © 2012 Pearson Education Inc.
Q43.3
Which kinds of unstable nuclei typically decay by emitting
an alpha particle?
A. those with too many neutrons
B. those with too many protons
C. those with too many neutrons and too many
protons
D. Misleading question—the numbers of neutrons
and protons in a nucleus are unrelated to whether
or not it emits an alpha particle.
Copyright © 2012 Pearson Education Inc.
Nuclear stability and radioactivity
• Figure 43.4 (right) is a Segrè
chart showing N versus Z for
stable nuclides.
• In α decay, Z decreases by 2
and A decreases by 4, moving
the nuclei closer to the line of
stability.
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Uranium decay chart
Note the α
decay and β
decays in the
chain
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Clicker question on β emission
Which kinds of unstable nuclei typically decay by emitting
an electron?
A. those with too many neutrons
B. those with too many protons
C. those with too many neutrons and too many
protons
D. Misleading question—the numbers of neutrons
and protons in a nucleus are unrelated to whether
or not it emits an electron.
Copyright © 2012 Pearson Education Inc.
Q43.4
Which kinds of unstable nuclei typically decay by emitting
an electron?
A. those with too many neutrons
B. those with too many protons
C. those with too many neutrons and too many
protons
D. Misleading question—the numbers of neutrons
and protons in a nucleus are unrelated to whether
or not it emits an electron.
Copyright © 2012 Pearson Education Inc.
Q43.5
Which kinds of unstable nuclei typically decay by
emitting a γ ray ?
A. those with too many neutrons
B. those with too many protons
C. those with too many neutrons and too many
protons
D. Misleading question—the numbers of neutrons
and protons in a nucleus are unrelated to whether
or not it emits gamma rays.
Copyright © 2012 Pearson Education Inc.
Q43.5
Which kinds of unstable nuclei typically decay by emitting
a gamma-ray photon?
A. those with too many neutrons
B. those with too many protons
C. those with too many neutrons and too many
protons
D. Misleading question—the numbers of neutrons
and protons in a nucleus are unrelated to whether
or not it emits gamma rays.
Copyright © 2012 Pearson Education Inc.
Radioactive decay law
dN(t)
= l N(t)
dt
Here N(t) is the number of radioactive nuclei present. The
quantity λ is the “decay constant” and determines the
probability per unit time that a nuclei will decay.
dN(t)
= l dt
N(t)
- ln(N(t)) = lt + C
Copyright © 2012 Pearson Education Inc.
Question: How do we
integrate this ?
Question: What is the solution ?
N(t) = N 0 e
- lt
Radioactive decay law
N(t) = N 0 e
- lt
What is the half-life ? This corresponds to N(t)/N0=1/2
1
= e- lT1/2
2
Tmean
T1/2
T1/2
= =
=
l ln 2 0.693
1
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T1/2 =
ln 2
l
=
0.693
l
Summary: Activities and half-lives
• The half-life is the time for the
number of radioactive nuclei to
decrease to one-half of their
original number.
N(t) = N 0 e
- lt
• The number of remaining nuclei
decreases exponentially with
decay constant λ (see Figure on
the right).
Activity is measured in either Curies (US) or Becquerel (Europe
or Japan)
1 Ci= 3.7 x 1010Bq =3.7 x 1010decays/sec
Copyright © 2012 Pearson Education Inc.
Clicker question on radioactive decay law
As a sample of radioactive material decays, the decay
rate
A. is directly proportional to the half-life and directly
proportional to the number of radioactive nuclei
remaining.
B. is directly proportional to the half-life and inversely
proportional to the number of radioactive nuclei
remaining.
C. is inversely proportional to the half-life and directly
proportional to the number of radioactive nuclei
remaining.
D. is inversely proportional to the half-life and
inversely proportional to the number of radioactive
nuclei remaining.
Copyright © 2012 Pearson Education Inc.
Clicker question on radioactive decay law
As a sample of radioactive material decays, the decay
rate
A. is directly proportional to the half-life and directly
proportional to the number of radioactive nuclei
remaining.
B. is directly proportional to the half-life and inversely
proportional to the number of radioactive nuclei
remaining.
C. is inversely proportional to the half-life and directly
proportional to the number of radioactive nuclei
remaining.
D. is inversely proportional to the half-life and
inversely proportional to the number of radioactive
nuclei remaining.
Copyright © 2012 Pearson Education Inc.
Q43.7
Why does nuclear fusion of hydrogen require high
temperatures?
A. Positive charges repel each other.
B. The nuclear force only acts at short range.
C. both A. and B.
D. neither A. nor B.
Copyright © 2012 Pearson Education Inc.
Q43.7
Why does nuclear fusion of hydrogen require high
temperatures?
A. Positive charges repel each other.
B. The nuclear force only acts at short range.
C. both A. and B.
D. neither A. nor B.
Copyright © 2012 Pearson Education Inc.