| a. |
A
particle of mass m1 moving at speed u makes a perfectly elastic
head-on collision with a stationary particle of mass m2. After
the collision, the particles move off with speed v1 and v2
respectively. Show that
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Conservation of momentum and energy give |
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Define k = m1/m2. |
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From (1), |
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From (2), |
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Multiply (3) with (u + v1)
and compare with (4), we have |
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v2 = u
+ v1 .............(5) |
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Putting into (3), we have |
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| b. |
Using
the results in (a), explain how you would choose the atoms which make up
the moderators in a nuclear reactor. |
4
marks |
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If m1 is about the value
of m2, v1 would be close to zero. Thus,
in order to slow down m1, m2 should
be of similar mass to m1. |
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In a nuclear fission, the neutrons used to
carry out fission must be slow moving (moving at the same speed as room
temperature), otherwise, a new product U-238 is formed. |
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Moderator is used to slow down neutrons. |
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The atoms in the moderator are at rest and
the collision is perfectly elastic. Thus, they should have masses similar
to a neutron. In other words, they are light nuclei. |
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| c. |
In
the annihilation of a positron and an electron, the masses of the particles
are converted into two g-photons
which move in opposite directions. Write down an expression to illustrate
the conservation of energy in the annihilation process. Explain why the
photons move in opposite directions. |
4
marks |
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Mass is a form of energy according to Einstein's equation:
E = m c2. |
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Photon is a package of energy according to Planck's Equation:
E = h f. |
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Thus, the equation for the above annihilation is |
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The photons move in opposite directions in order to obey
the law of conservation of momentum. (Note: photons have momentum!) |
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| d. |
Explain
how you can work out the loss in mass in an a-decay
from the kinetic energy of the emitting a-particles.
Comment on the result of your method. |
4
marks |
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Let E be the kinetic energy of the a-particle.
The loss in mass in each decay is given by |
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The mass loss would be greater than given above
because, by conservation of momentum, the daugther nucleus would move in
opposite direction as the a-particle, with a
lower speed. |
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