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

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Chapter7: Atoms And Spectra
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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
Transcribed Image Text: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
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