A 14-kg mass, attached to a massless spring whose force constant is 3,100 N/m, has an amplitude of 5 cm. Assuming the energy is quantized, find the quantum number of the system, {image} , if {image} . 1. {image} 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Find the kinetic energy (in terms of Planck's constant) of a tennis ball (m = 50 g) confined to a one-dimensional box that is 50 cm wide if the tennis ball can be treated as a wave in the ground state. 1. {image} 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Calculate the ground state energy (in eV) for an electron in a box (an infinite well) having a width of 0.052 nm. 95 200 24 70 140 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A particle is in the ground state of a one-dimensional box of length 1 m. What is the minimum value of its momentum (in {image} )? 1. {image} cannot be solved unless mass of particle is known 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A particle is in the first excited state of a one-dimensional box of length 3 m. What is the minimum value of its momentum (in {image} )? 1. {image} 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A particle is in the second excited state of a one-dimensional box of length 3 m. What is its momentum (in {image} )? 1. {image} cannot be solved unless mass of particle is known 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

What is the quantum number {image} of a particle of mass {image} confined to a one-dimensional box of length {image} when its momentum is {image} ? 8 32 16 64 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

What is the quantum number {image} of a particle of mass {image} confined to a one-dimensional box of length {image} when its energy is {image} ? 8 15 16 32 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

The wave function for a particle confined to a one-dimensional box located between {image} and {image} is given by {image} . What are the constants {image} and {image} determined to be? 1. {image} , {image} {image} , 0 0, {image} 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Classically, the concept of "tunneling" is impossible. Why? The kinetic energy of the particle would be negative. The total energy for the particle would be negative. The kinetic energy must be equal to the potential energy. The total energy of a particle is equal to the kinetic and potential energies. The velocity of the particle would be negative. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

exponentially decreasing exponentially increasing none of the above A particle has a total energy that is less than that of a potential barrier. When the particle penetrates the barrier, what is its wave function? a positive constant oscillatory exponentially decreasing exponentially increasing none of the above 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

What is the ground state energy of a harmonic oscillator? 1. {image} 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Particles in degenerate energy levels all have the same _____. wave function energy momentum all of the above velocity 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

The wave function for a particle in a one-dimensional box is {image} The wave function for a particle in a one-dimensional box is {image} . Which statement is true? 1. 2. This wave function gives the probability of finding the particle at {image} . {image} gives the probability of finding the particle between {image} and {image} . {image} gives the probability of finding the particle at {image} . 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

We can only calculate probabilities for values of physical quantities in quantum measurements. What does this mean? the average values of a large number of measurements correspond to the calculated probabilities the probabilities cannot be calculated from mathematical relationships the average of the values calculated in a large number of different theories corresponds to the results of a measurement the results of physical measurements bear no relationship to theory radiation and matter are not described by mathematical relations between measurements 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

When the potential energy of a system is independent of time, the wave function of the system _____. 1. is directly proportional to the time depends only on the center of mass, {image} , of the system cannot be normalized is a constant depends on the vector positions, {image} , of each particle in the system 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A physically reasonable wave function, {image} , for a one-dimensional system must _____. be continuous at all points in space be defined at all points in space be single-valued obey all the constraints listed above obey only the second and the third constraints above. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

The average position, or expectation value, of a particle whose wave function {image} depends only on the value of {image} , is given by {image} _____. 1. {image} 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

The expectations value of a function {image} of {image} when the wave function depends only on {image} is given by {image} _____. 2. 1. {image} 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

If the interaction of a particle with its environment restricts the particle to a finite region of space, the result is the quantization of _____ of the particle. the momentum the energy the velocity all of the above properties only the first and the second properties 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A particle in a finite potential well has energy {image} , as shown below. {applet} 1. 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A particle in a finite potential well has energy {image} , as shown below. {applet} 1. 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A particle in a finite potential well has energy {image} , as shown below. {applet} 1. 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Quantum tunneling occurs in _____. the scanning tunneling microscope nuclear fusion radioactive decay by emission of alpha particles all of the above only the first and third above. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Consider the wave function for the free particle, {image} At what value of x is the particle most likely to be found at a given time? at x = 0 at small nonzero values of x at large values of x anywhere along the x axis 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A particle is in a box of length L A particle is in a box of length L. Suddenly, the length of the box is increased to 2L. What happens to the energy levels shown in the figure below? {image} Nothing-they are unaffected. They move farther apart. They move closer together. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Which of the following will exhibit quantized energy levels? an atom in a crystal an electron and a proton in a hydrogen atom a proton in the nucleus of a heavy atom all of the above none of the above 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

The zero-point energy is the same in all three cases. Consider an electron, a proton, and an alpha particle (a helium nucleus), each trapped separately in identical infinite square wells. Which particle corresponds to the highest zero-point energy? the electron the proton the alpha particle The zero-point energy is the same in all three cases. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

All three particles have the same wavelength. Consider the three particles: the electron, the proton, the alpha particle. Which particle has the longest wavelength when the system is in the ground state? the electron the proton the alpha particle All three particles have the same wavelength. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

The wavelengths of the wave functions in the first figure are longer than those in the second figure because the wave function spreads out into the classically forbidden region. For an infinite and a finite square well of the same length L, the quantized energies of the particle in a finite well are _____. {image} {image} the same as those for a particle in an infinite well higher than those for a particle in an infinite well lower than those for a particle in an infinite well impossible to determine 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Which of the following changes would increase the probability of transmission of a particle through a potential barrier? (You may choose more than one answer.) decreasing the width of the barrier increasing the width of the barrier decreasing the height of the barrier increasing the height of the barrier decreasing the kinetic energy of the incident particle increasing the kinetic energy of the incident particle 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

For a particle undergoing simple harmonic motion in the n = 0 state, the most probable value of x for the particle according to quantum mechanics is _____. 1. x = 0 {image} All values of x are equally likely. 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50