Exam 14: Wave Particle Duality and Quantum Physics

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An electron that is not localized in space is described by the wave function Ψ\Psi = A sin (kx - ω \omega t). The kinetic energy of the electron is 10 keV. The value of ω \omega is approximately

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  A classical point particle moves back and forth with constant speed between two walls at x = 0 and x = 2 cm. Which graph best represents its probability density Function P(x)? A classical point particle moves back and forth with constant speed between two walls at x = 0 and x = 2 cm. Which graph best represents its probability density Function P(x)?

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Calculate the wavelength of light of energy 1 keV divided by the de Broglie wavelength of a proton of kinetic energy 1 meV.

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You want to make simultaneous measurements of the position and velocity of an electron that is moving in the positive-x direction. If the velocity is measured to an accuracy of 10-7 m/s, the limit of accuracy with which you can locate the electron is approximately

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Use the following figure to answer the next questions.  Use the following figure to answer the next questions.   -The graphs show  \Psi <sup>2</sup> as a function of x for a particle in a one-dimensional box of length L. The graph that represents the second excited state is -The graphs show Ψ\Psi 2 as a function of x for a particle in a one-dimensional box of length L. The graph that represents the second excited state is

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What is the shift in wavelength of a photon scattered off an electron at 160º?

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An electron has a kinetic energy of 1.5 eV. If its momentum is uncertain by ± 2.5%, the minimum uncertainty in its position is approximately

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A gamma-ray photon of energy 1.00 MeV scatters off an electron at an angle perpendicular to its original direction. Calculate the kinetic energy of the recoiling electron.

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Use the following equation statement to answer the next four questions. The normalized wave functions for the infinite square-well potential are Ψ\Psi n = (2/L)1/2 sin(n π\pi x/L) You may find it useful to use  Use the following equation statement to answer the next four questions. The normalized wave functions for the infinite square-well potential are  \Psi <sub>n</sub> = (2/L)<sup>1/2</sup> sin(n  \pi x/L) You may find it useful to use    \theta sin<sup>2</sup> \theta d \theta =  \theta <sup>2</sup>/4 - ( \theta  sin 2 \theta /4 - (cos 2 \theta /8 + C -The expectation value <x> for a particle in its first excited (n = 2) state in a box of length L is θ\theta sin2 θ\theta d θ\theta = θ\theta 2/4 - ( θ\theta sin 2 θ\theta /4 - (cos 2 θ\theta /8 + C -The expectation value <x> for a particle in its first excited (n = 2) state in a box of length L is

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Suppose that the world could be changed so that the de Broglie wavelength of a 40-kg runner who goes 100 m in 10.0 s was 5 m. Assuming that all other constants remain the same, the value of Planck's constant would have to be

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Use the following figure for the next two problems.  Use the following figure for the next two problems.   -The electrons coming out of the electron gun in an electron microscope are being accelerated by a potential of 100 kV. The electrons then pass through a region of magnetic field of distance y = 8 cm which points perpendicularly to the direction of travel of the electron. What is the strength of the magnetic field needed to deflect the electron by an angle of  \theta  = 25 \degree ? (Ignore any relativistic effect. 1 Gauss = 10<sup>-4</sup> T) -The electrons coming out of the electron gun in an electron microscope are being accelerated by a potential of 100 kV. The electrons then pass through a region of magnetic field of distance y = 8 cm which points perpendicularly to the direction of travel of the electron. What is the strength of the magnetic field needed to deflect the electron by an angle of θ\theta = 25 °\degree ? (Ignore any relativistic effect. 1 Gauss = 10-4 T)

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Use the following figure to answer the next questions.  Use the following figure to answer the next questions.   -The graphs show  \Psi <sup>2</sup> as a function of x for a particle in a one-dimensional box of length L. The graph that represents the third excited state is -The graphs show Ψ\Psi 2 as a function of x for a particle in a one-dimensional box of length L. The graph that represents the third excited state is

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The wave function for a particle between x = -4 cm and 4 cm is given by The wave function for a particle between x = -4 cm and 4 cm is given by   where L = 8 cm. Outside this range, the wave function is equal to zero. The value of A is where L = 8 cm. Outside this range, the wave function is equal to zero. The value of A is

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An electron (me = 9.11* 10-31 kg) traveling with a velocity of 1.1 *106 m/s has a De Broglie wavelength of approximately

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In a photoelectric experiment, the threshold frequency for a material is 3.2 * 1014 Hz. An electron ejected from this surface by a photon of frequency 9.4 * 1014 Hz can be stopped by a stopping potential of

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In the photoelectric effect, the work function depends on the

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The maximum wavelength for the photoemission of electrons from a metal surface depends on

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Use the following equation statement to answer the next four questions. The normalized wave functions for the infinite square-well potential are Ψ\Psi n = (2/L)1/2 sin(n π\pi x/L) You may find it useful to use  Use the following equation statement to answer the next four questions. The normalized wave functions for the infinite square-well potential are  \Psi <sub>n</sub> = (2/L)<sup>1/2</sup> sin(n  \pi x/L) You may find it useful to use    \theta sin<sup>2</sup> \theta d \theta =  \theta <sup>2</sup>/4 - ( \theta  sin 2 \theta /4 - (cos 2 \theta /8 + C -The expectation value <x> for a particle in its second excited (n = 3) state in a box of length L is θ\theta sin2 θ\theta d θ\theta = θ\theta 2/4 - ( θ\theta sin 2 θ\theta /4 - (cos 2 θ\theta /8 + C -The expectation value <x> for a particle in its second excited (n = 3) state in a box of length L is

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A classical wave

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Magnetic Resonance Imaging (MRI) is a much used noninvasive diagnostic technique in medicine. The radio frequency photons used have energies of about 10-7 eV. What wavelength does this correspond to?

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