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- Question : 1RQ - Give examples of physical systems to which the theories of classical mechanics apply.
- Question : 2RQ - On what was Planck's hypothesis based?
- Question : 3RQ - What was Bohr's contribution to the science of Wave Mechanics and what were the weaknesses of his postulates?
- Question : 4RQ - What prompted Bohr to quantize the energy of an electron?
- Question : 5RQ - Why was the hydrogen atom selected for consideration?
- Question : 6RQ - What is the significance of Heisenberg's principle?
- Question : 7RQ - What was de Broglie's contribution to Wave Mechanics?
- Question : 8RQ - Briefly state the significance of ? in Schrodinger's equation.
- Question : 9RQ - Interpret the solution of Schrodinger's equation to the deep potential well and how it relates to the science of Wave Mechanics.
- Question : 1E - a) Determine the binding energy for an electron in a hydrogen atom at a quantum number 3 level. Give the answer in eV and in joules. b) Repeat the above determination for an electron in a silicon coulombic potential, using the results of the hydrogen atom. The relative dielectric constant for silicon is 11.8 and the effective mass of a silicon electron is assumed to be 1.18 times that of the hydrogen electron. Ans: a) ? = -1.5eV b) ? = 0.02 X 10-1 9J
- Question : 2E - a) Use Planck's hypothesis to calculate the wavelength associated with a leV photon, b) Repeat (a) for an electron. Ans: b) ? = 1.22 X 10"9m
- Question : 3E - A tennis player serves a 75g ball at a speed of 200 km/h. If the uncertainty in the velocity of the ball is lOcm/s, determine the uncertainty in its position. Ans: ?? = 1.4 X 10"3 2m
- Question : 4E - Use Schrodinger's second postulate to determine the expression for A in the solution of Schrodinger's equation, in one dimension, for the infinitely deep potential well. Ans: A = Vl/a
- Question : 5E - Determine the energy in eV of an electron for ? = 1 in the infinitely deep well when a = 50A. Ans: ? = 14.92 ? ??"3 eV
- Question : 1P - Determine the density of GaAs given the lattice constant L = 5.65A, and the molecular weight is 144.63/mole. Avogadro's number is 6.02 ? 102 3 atoms/mole.
- Question : 2P - Use the Bohr model for the hydrogen atom to plot potential energy and total energy as the radius r from the proton increases. Clearly identify the magnitudes of the kinetic energy at two separate radii.
- Question : 3P - Determine the velocity of an electron in the ground state of the hydrogen atom.
- Question : 4P - The laws of classical physics apply to the motion of a particle provided the dimensions of the system are much larger than the deBroglie wavelength. For the following electrons, determine whether the laws of classical physics apply: a) An electron is accelerated in the beam of a cathode-ray tube that has an accelerating voltage of 30KV. b) An electron that is accelerated by a potential of 100V in a device whose dimensions are of the order of 2cm/s. c) An electron in a hydrogen atom.
- Question : 5P - Determine the energy of a photon having wavelengths ? = ??,???? and ? = 10A. Express the energy in eV and J.
- Question : 6P - The antenna of an AM radio station transmitter radiates 100KW of power at lOOOKHz. a) Calculate the energy of each radiated photon. b) Calculate the number of photons radiated per second.
- Question : 7P - An oscillator is operating at a frequency of 10MHz. a) Calculate the energy of the quantum of radiation of the oscillator. b) Calculate the number of quanta in 10 6J
- Question : 8P - a) Derive an expression for the wavelength of spectral lines emitted by the transitions from the excited states to the ground state using the Bohr relation for the electron energy in the hydrogen atom, b) Calculate the wavelength of the first four spectral lines.
- Question : 9P - The velocity of a certain free particle is 5 X 105m/sec. The mass of the particle is 10~30kg. Determine: a) the particle energy. b) the de Broglie wavelength.
- Question : 10P - In accordance with physics statistics, the average energy of an electron in a medium of free electrons at thermal equilibrium is 3kT/2, where k is Boltzmann's constant and ? is in degrees kelvin. Determine, for the electron, a) its velocity, b) its momentum, c) the de Broglie wavelength at ? = 300K.
- Question : 11P - An electron is moving with a velocity of 105m/s. Determine, for the electron: a) its momentum, b) its de Broglie wavelength in m and A, c) its energy in J and eV.
- Question : 12P - An electron has a de Broglie wavelength of 100A. Determine: a) electron momentum, b) electron velocity.
- Question : 13P - For an infrared radiation of 1 ???, determine: a) the frequency of the radiation, b) the energy of the photon in eV.
- Question : 14P - The uncertainty in the position of a particle having mass 10~30Kg is 10A. Determine the uncertainty in: a) the momentum of the particle, b) kinetic energy of the particle.
- Question : 15P - For the electron in Problem 1.11, determine the wave vector k.
- Question : 16P - For an infinitely deep potential well having a = 100A, determine for an electron the energy levels for
- Question : 17P - An electron is located in a one-dimensional potential energy well having width of 3A. Determine a) the kinetic energy of the electron in the ground state. b) the frequency of the spectral radiation of an electron that drops from the next higher state to the ground state.
- Question : 18P - For a particle that has a mass of 2 grams and energy 1.5kT, determine the de Broglie wavelength at ? = 300K.

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