Question

1.A neutron in an atomic nucleus is bound to other neutrons and protons in the nucleus by the strong nuclear force when it comes within about 1 fm of another particle . What is the approximate kinetic energy in MeV of a neutron that is localised to within such a region? Take delta(x)*delta(p) = h/(4pi) and rest energy of neutron to be 939 MeV. Give your result to 2 significant figures.

2. What would be the corresponding kinetic energy in MeV of an electron localised to within such a region as in the following question for the neutron? Take the rest mass of the electron to be 0.511 MeV. Give your answer to 3 significant figures.

Answer #1

Neutrons and protons in atomic nuclei are confined within a
region whose diameter is about d=1.1 fm. Let's imagine a proton
trapped inside such a region and being in its lowest energy state,
i.e. in its ground state. You can treat it as a particle in a box
problem and use m=938 MeV/c^2.
a) Use the de Broglie relation to find the momentum p of a
proton inside the nucleus.
b) Calculate the pc/(mc^2) ratio and justify the neccessity of...

The nuclear potential energy that
binds protons and neutrons in a nucleus is often approximated by a
square well. Imagine a proton confined in an infinitely high square
well of length 10.3 fm, a typical nuclear diameter. Assuming the
proton makes a transition from the n = 3 state to the
ground state, calculate the following. (a) the energy of the
emitted photon (b) the wavelength of the emitted photon (c)
Identify the region of the electromagnetic spectrum to which...

The diameter of the nucleus is about 11 fm . A simple model of
the nucleus is that protons and neutrons are confined within a
one-dimensional box of length 11 fm .
Part A
What is the first energy level, in MeV, for a proton in such a
box?
Express your answer using three significant figures.
Part B
What is the second energy level, in MeV, for a proton in such a
box?
Express your answer using three significant figures....

QUESTION 1
Calculate the k-factor, to 2 decimal places, for a reactor in
which:
3% of the neutrons are fast neutrons which produce a fission
in the fuel,
5% of the fast neutrons escape from the reactor,
3% of the slow neutrons escape from the reactor,
29.8% of the neutrons are absorbed in the moderator before
becoming thermal,
31.8% of the thermal neutrons get absorbed into the moderator
and other material,
Each original thermal neutron produces, on average, 2.08
fissions...

Carbon-12 contains 6 protons and 6 neutrons. The radius of the
nucleus is approximately 2.7 fm (femtometers) and the radius of the
atom is approximately 70 pm (picometers).
Part A Calculate the volume of the nucleus and the volume of the
atom. (Assume two significant figures.) Express your answers using
two significant figures separated by a comma.
Part B What percentage of the carbon atom's volume is occupied
by the nucleus? (Assume two significant figures.) Express your
answer using two...

A helium nucleus (called an alpha particle) contains 2 neutrons
and 2 protons with no electrons. If any electrons are added, there
is a negligible amount of mass added but obviously one negative
charge per electron is added. Three particles are injected into a
constant B-field of 2T at a velocity of
3×106ms. The first
particle is only the alpha particle
(He++), the second particle is a nucleus
with 1 electron (He+), and the third
particle is a nucleus with...

A bare helium nucleus consists of two protons and two neutrons
and has a mass of 6.64 × 10–27 kg
Calculate its kinetic energy in joules at 2.00% of the speed of
light. Use the non-relativistic formula.
What is this in electron volts?
What voltage would be needed to obtain this energy?

An atomic nucleus can be crudely modeled as a gas of nucleons
with a number density of 0.18 fm-3 (where 1 fm = 10-15 m). Because
nucleons come in two different types (protons and neutrons), each
with spin 1/2, each spatial wavefunction can hold four nucleons.
(a) [10 pts] Calculate the Fermi energy εF of this system, in MeV.
Also calculate the Fermi temperature TF. Is it reasonable to treat
the nucleus as a degenerate Fermi gas at room temperature?...

An alpha particle (a He nucleus, containing two protons and two
neutrons and having a mass of 6.64×10−27 kg ) traveling
horizontally at 34.8 km/s enters a uniform, vertical, 1.08 T
magnetic field.
Part A
What is the diameter of the path followed by this alpha
particle?
Express your answer in millimeters to three significant
figures.
ANSWER:
d =
______
mm
Part C
What is the magnitude of the acceleration of the alpha particle
while it is in the magnetic...

An atom is made of positively charged protons and neutral
neutrons concentrated in a nucleus, while negatively charged
electrons orbit around them. If I want to make a Helium atom out of
two Hydrogen atoms, I am going to have to have to get 2 Hydrogen
atoms very close together so that they can form a new nucleus. This
is a process called nuclear fusion, and it takes a lot of energy.
a) If, in order for this to happen,...

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