Thermal neutrons are produced by a fission nuclear reactor. The temperature of the neutrons is about room temperature, T × 299 K. The kinetic energy of the neutron is E = kgT, where kB = 1.38 × 10–23 J/K is the Boltzmann constant. The mass of a neutron is mn = 1.67 × 10-27 kg. Part 1) Calculate the de Broglie wavelength of a thermal neutron. nm
Quantum mechanics and hydrogen atom
Consider an electron of mass m moves with the velocity v in a hydrogen atom. If an electron is at a distance r from the proton, then the potential energy function of the electron can be written as follows:
Isotopes of Hydrogen Atoms
To understand isotopes, it's easiest to learn the simplest system. Hydrogen, the most basic nucleus, has received a great deal of attention. Several of the results seen in more complex nuclei can be seen in hydrogen isotopes. An isotope is a nucleus of the same atomic number (Z) but a different atomic mass number (A). The number of neutrons present in the nucleus varies with respect to the isotope.
Mass of Hydrogen Atom
Hydrogen is one of the most fundamental elements on Earth which is colorless, odorless, and a flammable chemical substance. The representation of hydrogen in the periodic table is H. It is mostly found as a diatomic molecule as water H2O on earth. It is also known to be the lightest element and takes its place on Earth up to 0.14 %. There are three isotopes of hydrogen- protium, deuterium, and tritium. There is a huge abundance of Hydrogen molecules on the earth's surface. The hydrogen isotope tritium has its half-life equal to 12.32 years, through beta decay. In physics, the study of Hydrogen is fundamental.
![Thermal neutrons are produced by a fission nuclear reactor. The temperature of the neutrons is about room temperature, T 2 299 K.
The kinetic energy of the neutron is E = kgT, where kp = 1.38 x 10–23 J/K is the Boltzmann constant. The mass of a neutron is m, =
1.67 x 10-27
kg.
Part 1)
Calculate the de Broglie wavelength of a thermal neutron.
nm
Part 2)
The highest energy photons ever observed are y-rays with energies up to 311 trillion electron volts, Ey = 311 × 102 eV. The rays come from the Crab nebula, the remnant of a
supernova explosion.
Calculate the wavelength of these photons.
m
Part 3)
A position uncertainty of an electron in a hydrogen atom is about size of the atom, which is Aæ = 0.500 Å = 0.500 × 10–10 m.
Using the Heisenberg uncertainty relation, Ap Ax = , calculate the related kinetic energy (zero motion energy):
(Ap?
2m
E =
2m
The electron mass is m =
:0.910 x 10-30
kg.
E
eV](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96f456c6-6d78-4224-82d3-41d67da4c9bf%2Fd7881adf-827e-44e9-b5d4-1a447aa68ab3%2Fe2fhg2p_processed.png&w=3840&q=75)
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