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4) Calculate the Fermi energy of protons (in MeV) in 208Pb. 5) a) Derive the phase...
Problem 4. Low-dimensional materials play an important role in nanotechnology. Consider a two-dimensional Fermi gas of...
Problem 4. Low-dimensional materials play an important role in nanotechnology. Consider a two-dimensional Fermi gas of N non-interacting electrons confined to a plane of area A. Find the Fermi energy &r (in terms of A and N) and the average electron energy. Find (analytically) the chemical potential p as a function of er and T.
Question no 6.1, statistical physics by Reif Volume 5 Problems 6.1 Phase space of a classical harmonic oscillator The en...
Question no 6.1,
statistical physics by Reif Volume 5
Problems 6.1 Phase space of a classical harmonic oscillator The energy of a one-dimensional harmonic oscillator, whose position coordinate is x and whose momentum is p, is given by where the first term on the right is its kinetic and the second term its potential energy. Here m denotes the mass of the osellating particle and a the spring constant of the restoring force acting on the particle. Consider an ensemble...
3. (10 pts) High energy particle accelerators convert part of the energy of colliding particles into...
3. (10 pts) High energy particle accelerators convert part of the energy of colliding particles into the masses of particles produced in the collisions. Consider a collision of two protons that produces two charged kaons. The mass of the proton is mp- 938.3 MeV/c2, and the mass of each kaon is mK 493.7 MeV/c2. The reaction is a) The total energy (kinetic energy and rest energy) and total momentum is conserved. Suppose one of the protons is at rest in...
fer pourice 5. Calculate the ground state expectation values for position, <x>, and momentum <p> for...
fer pourice 5. Calculate the ground state expectation values for position, <x>, and momentum <p> for a particle confined by an infinite potential (in a box). Do your answers make sense? ψ( ( ) 1,2,3 Ψ( | 1 x)- Asin Jor n= ,
Question 21 5 pts Calculate the kinetic energy (in MeV) of an alpha particle whose DeBroglie...
Question 21 5 pts Calculate the kinetic energy (in MeV) of an alpha particle whose DeBroglie wavelength is equal to 1 femtometer (1E-15 m), which is about the size of a nucleus. The mass of the alpha particle is 6.65E-27 kg. 3.3E-11 MeV 5.3E-30 MeV 49.8 MeV 103 MeV 206 MeV Question 22 5 pts The electronic configuration for boron is 1s 2s22p1, and the electronic configuration for aluminum is 1s22s22p6 352 3p1. It requires 8.298 eV to remove the...
Please help me 1. In degenerate p-type silicon, a. The Fermi energy is above the valence...
Please help me
1. In degenerate p-type silicon, a. The Fermi energy is above the valence energy and below the intrinsic Fermi energy b. The Fermi energy is below the valence energy c. The Fermi energy is above the conduction energy d. The Fermi energy is below the conduction energy and above the intrinsic Fermi energy 2. A semiconductor has No 5X 1010 cm3 and N-2X 1018 cm2. It is a. b. C. d. N-type and electrons are the majority...
4. A (one dimensional) particle in a box of length 2a (i.e., zero potential energy) is...
4. A (one dimensional) particle in a box of length 2a (i.e., zero potential energy) is represented by the wavefunction v(x) 0, otherwise a. Sketch the wavefunction. Write down the (time independent) Schrodinger equation. Show whether or not the wavefunction is a solution to the equation. b. What does it mean physically if the wavefunction of the particle is NOT a solution to the Schrodinger equation? Explain. c. Determine the normalization constant A. 5. Same system. Find the average or...
A “wavicel” (wave-particle-duality thingy) is confined to be in a very small but finite region of...
A “wavicel” (wave-particle-duality thingy) is confined to be in a very small but finite region of one dimensional space. (Interpret the confinement as the existence of walls that this thingy is never able to penetrate or overcome, while it is able to move in its allotted region of space freely.) (a) Calculated the expectation value of position (x) and its spread (Δx) for the first exited state of that thingy. Calculate now the expectation value for the momentum (p) and...
Question # 1: Find the unit of energy in the energy expression of a free particle...
Question # 1: Find the unit of energy in the energy expression of a free particle in 1-D box: Question # 2: A proton in a box is in a state n = 5 falls to a state n = 4 and loose energy with a wavelength of 2000 nm, what is the length of the box? (answer: 4 x 10 m) Question # 3: a. Consider an electron confined to move in an atom in one dimension over a...
5. (a) Derive the following Maxwell relation for a fluid system: ()-), (b) Show that for...
5. (a) Derive the following Maxwell relation for a fluid system: ()-), (b) Show that for an ideal gas at a given temperature T, the chemical potential difference between an arbitrary pressure, P, and a reference pressure, Po, is given by u(P) – u(Po) = kbT In (P/Po). (c) For the case of an incompressible liquid, the volume per particle, v = V/N, is independent of the pressure; show that in this case, one has u(P) – ”(Po) = v...
Problem 4. Low-dimensional materials play an important role in nanotechnology. Consider a two-dimensional Fermi gas of N non-interacting electrons confined to a plane of area A. Find the Fermi energy &r (in terms of A and N) and the average electron energy. Find (analytically) the chemical potential p as a function of er and T.
Question no 6.1,
statistical physics by Reif Volume 5
Problems 6.1 Phase space of a classical harmonic oscillator The energy of a one-dimensional harmonic oscillator, whose position coordinate is x and whose momentum is p, is given by where the first term on the right is its kinetic and the second term its potential energy. Here m denotes the mass of the osellating particle and a the spring constant of the restoring force acting on the particle. Consider an ensemble...
3. (10 pts) High energy particle accelerators convert part of the energy of colliding particles into the masses of particles produced in the collisions. Consider a collision of two protons that produces two charged kaons. The mass of the proton is mp- 938.3 MeV/c2, and the mass of each kaon is mK 493.7 MeV/c2. The reaction is a) The total energy (kinetic energy and rest energy) and total momentum is conserved. Suppose one of the protons is at rest in...
fer pourice 5. Calculate the ground state expectation values for position, <x>, and momentum <p> for a particle confined by an infinite potential (in a box). Do your answers make sense? ψ( ( ) 1,2,3 Ψ( | 1 x)- Asin Jor n= ,
Question 21 5 pts Calculate the kinetic energy (in MeV) of an alpha particle whose DeBroglie wavelength is equal to 1 femtometer (1E-15 m), which is about the size of a nucleus. The mass of the alpha particle is 6.65E-27 kg. 3.3E-11 MeV 5.3E-30 MeV 49.8 MeV 103 MeV 206 MeV Question 22 5 pts The electronic configuration for boron is 1s 2s22p1, and the electronic configuration for aluminum is 1s22s22p6 352 3p1. It requires 8.298 eV to remove the...
Please help me
1. In degenerate p-type silicon, a. The Fermi energy is above the valence energy and below the intrinsic Fermi energy b. The Fermi energy is below the valence energy c. The Fermi energy is above the conduction energy d. The Fermi energy is below the conduction energy and above the intrinsic Fermi energy 2. A semiconductor has No 5X 1010 cm3 and N-2X 1018 cm2. It is a. b. C. d. N-type and electrons are the majority...
4. A (one dimensional) particle in a box of length 2a (i.e., zero potential energy) is represented by the wavefunction v(x) 0, otherwise a. Sketch the wavefunction. Write down the (time independent) Schrodinger equation. Show whether or not the wavefunction is a solution to the equation. b. What does it mean physically if the wavefunction of the particle is NOT a solution to the Schrodinger equation? Explain. c. Determine the normalization constant A. 5. Same system. Find the average or...
Question # 1: Find the unit of energy in the energy expression of a free particle in 1-D box: Question # 2: A proton in a box is in a state n = 5 falls to a state n = 4 and loose energy with a wavelength of 2000 nm, what is the length of the box? (answer: 4 x 10 m) Question # 3: a. Consider an electron confined to move in an atom in one dimension over a...
5. (a) Derive the following Maxwell relation for a fluid system: ()-), (b) Show that for an ideal gas at a given temperature T, the chemical potential difference between an arbitrary pressure, P, and a reference pressure, Po, is given by u(P) – u(Po) = kbT In (P/Po). (c) For the case of an incompressible liquid, the volume per particle, v = V/N, is independent of the pressure; show that in this case, one has u(P) – ”(Po) = v...
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