Download Beta Decay

Beta Decay
In this lesson you will use the Cloud Chamber applet to investigate the beta
decay process.
Prerequisites:
•
You should be familiar with the physics of charged particles moving in
magnetic fields and know how to use the hand-rules.
Learning Outcomes: When finished you should be familiar with both "beta-plus"
and "beta-minus" decay modes as well understanding why the beta decay
process leads to the prediction of the existence of the neutrino.
Open the Cloud Chamber applet in the toolbox on the right and use it as you
answer the following questions. In this applet the magnetic field is assumed to
point out of the screen. The strength of the magnetic field is shown on the info
panel on the right hand side of the applet.
The Beta Decay of Tritium
1. What is Tritium?
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2. The paths that you see in the applet are created by particles emitted by
Tritium atoms. Explain why one could speculate that these are charged
particles and determine whether they are positively or negatively charged.
3. When beta decay was first discovered, it was soon determined that beta
particles have a charge to mass ratio q/m = 1.759 x 1011 C/kg. What kind
of particle does this suggest?
4. In a previous unit you learned that a magnetic field of strength B exerts a
force on a moving particle of charge q. If the particle is moving at right
angles to the field, then the magnetic force is given by the expression
Fmagnetic = qvB⊥ . Explain why this creates a circular arc and use your
knowledge of circular motion to show that the momentum of the particle
can be written as p = B⊥ qr , where p is the magnitude of the momentum
and r is the radius of the path's arc.
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5. Show that the kinetic energy of a particle can be related to its momentum
by the equation Ek =
p2
and that the kinetic energy of a particle can be
2m
related to the radius of its arc by the expression Ek =
B2q2r 2
.
2m
6. Use the applet to create three different Tritium beta-decay events. Use the
measurement tool to determine the radius of the particle tracks and
complete the following table. Express the particle energy in both Joules
and electron volts:
Trial #
Radius (m)
Kinetic Energy (J)
Kinetic Energy (eV)
1
2
3
Summary
We now understand beta-minus decay to be the emission of electrons from some
nuclei when they undergo radioactive decay. Your data shows an interesting
problem: beta particles do not all have the same energy. Instead, a particular
element will emit beta particles with a considerable range in energies. We will
address this problem in a few moments.
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Different Kinds of Beta Decay
In the previous section, we learned that beta-minus decay is the emission of
electrons from some nuclei when they undergo radioactive decay. In this section
we will look at different nuclei and investigate the evidence for different types of
beta decay.
1. Select "Advanced Settings" from the Options menu and compare the
tracks produced by the decay of the following four nuclei. Make a simple
sketch of the track produced by one run with each of the nuclei and record
this in the following table:
Element
Sketch
Tritium
Sodium
Cobalt
Strontium
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2. Explain how your data provides evidence that there must be at least two
different kinds of beta decay process?
3. Without performing any calculations, rank the beta particle energies
emitted by the different element from least energetic to most energetic.
Explain how you determined this.
Summary
Your data reveals an important feature of beta decay: There are two distinct beta
decay processes:
Beta-minus (β−) decay emits an electron and increases the atomic number (Z) of
the emitting nucleus by 1 unit.
Beta-plus (β+) decay emits an anti-electron (positron) and decreases the atomic
number (Z) of the emitting nucleus by 1 unit.
Beta Decay and the Existence of the Neutrino
In the previous sections, we learned that a nuclei undergoing radioactive decay
could experience one of two types of beta decay: beta-minus, which is the
emission of an electron, and beta-plus, which is the emission of an anti-electron.
We also noticed that beta particles, whether they are beta-minus or beta-plus, do
not all have the same energy. In this section we will see why that is.
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1. Select one of the beta decay nuclei listed in the advanced options menu
and analyze 10 different particle tracks for that element. Record your data
in the following table:
Element Name: ______________________________
Trial #
Radius of
Path (m)
Kinetic Energy (MeV)
1
2
3
4
5
6
7
8
9
10
2. What is the range of values of energy that you measured for the beta
decay of the element that you chose?
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3. How could this be explained by the suggestion that one or more
undetected particles are also being emitted during the beta decay
process?
Summary
The discovery of the beta decay process is credited to Lord
Rutherford, who was the first to show that beta particles are
electrons (for the beta-minus process). As early as 1911,
Lise Meitner demonstrated that beta particles are emitted
with a continuous range of energies.
This seemed to violate the conservation of energy, since it
appeared that energy was sometimes lost during beta
decay. In 1930, Wolfgang Pauli conjectured that an
additional particle was being emitted during beta decay and
that it was carrying away the "missing energy". In 1934,
Enrico Fermi published the first detailed theory of beta
decay and named this "mystery particle" the neutrino.
Wolfgang Pauli
The two main beta decay process can be written symbolically as:
Beta-minus (β−):
A
Z
X→
Beta-plus (β+): ZA X →
Y + e− + υ
A
Z +1
Y + e+ + υ
A
Z −1
The neutrino is a very elusive particle. It can penetrate several
light-years of lead before being absorbed. For this reason, the
neutrino is extremely difficult to detect. The experimental
detection of neutrinos occurred in 1956 in a Nobel prize winning
experiment by Cowan and Reines.
Enrico Fermi
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Beta Decay and the Weak Interaction
We have now learned what beta decay is and why it has some of the properties it
does. It remains to explore how beta decay can
occur at all.
The Standard Model of Particle Physics describes
the beta decay process as a conversion of a down
quark into an up quark with a W- boson being
emitted and decaying into an electron and an antineutrino, as pictured to the right. The force that
governs this interaction is the Weak Nuclear Force.
Feynman diagram for the conversion of a down
quark into an up quark and the creation of a
beta particle and anti-neutrino.
1. Show, by using the fractional charges on the up and down quarks, that
this process will create a particle of charge +1.
Summary
After investigating beta decay, physicists concluded that a neutron can decay (by
the process described above) into a proton, electron, and antineutrino. For a
decay to occur, there must be some force acting on the neutron. This decay,
however, often occurs outside of the nucleus, and hence could not be explained
by any of the known fundamental forces (that is, gravitational, electromagnetic,
and strong nuclear force). This led to the eventual discovery of the weak nuclear
force, the only force which is known to act on neutrinos!
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