A particle is confined to a one-dimensional box. While the

The quantized character of electromagnetic radiation is observed by (a) the Young double-slit experiment, (b) diffraction of light by a small aperture, (c) the photoelectric effect, (d) the J. J. Thomson cathode-ray experiment.

Two monochromatic light sources, A and B, emit the same number of photons per second. The wavelength of A is and the wavelength of B is The power radiated by source B (a) is equal to the power of source A, (b) is less than the power of source A, (c) is greater than the power of source A, (d) cannot be compared to the power from source A using the available data.

The work function of a surface is The threshold wavelength for emission of photoelectrons from the surface is equal to (a) hc>f, (b) f>hf, (c) hf>f, (d) none of the above. SSM

When light of wavelength is incident on a certain photoelectric cathode, no electrons are emitted, no matter how intense the incident light is. Yet, when light of wavelength is incident, electrons are emitted, even when the incident light has low intensity. Explain this observation.

True or false: (a) The wavelength of an electrons matter wave varies inversely with the momentum of the electron. (b) Electrons can undergo diffraction. (c) Neutrons can undergo diffraction.

If the wavelength of an electron is equal to the wavelength of a proton, then (a) the speed of the proton is greater than the speed of the electron, (b) the speeds of the proton and the electron are equal, (c) the speed of the proton is less than the speed of the electron, (d) the energy of the proton is greater than the energy of the electron, (e) both (a) and (d) are correct.

A proton and an electron have equal kinetic energies. It follows that the wavelength of the proton is (a) greater than the wavelength of the electron, (b) equal to the wavelength of the electron, (c) less than the wavelength of the electron.

The parameter represents the position of a particle. Can the expectation value of x ever have a value such that the probability density function P(x) is zero? Give a specific example.

It was once believed that if two identical experiments are done on identical systems under the same conditions, the results must be identical. Explain how this statement can be modified so that it is consistent with quantum physics.

A six-sided die has the numeral 1 painted on three sides and the numeral 2 painted on the other three sides. (a) What is the probability of a 1 coming up when the die is thrown? (b) What is the expectation value of the numeral that comes up when the die is thrown? (c) What is the expectation value of the cube of the numeral that comes up when the die is thrown?

During an advanced physics lab, students measure the Compton wavelength, \(\lambda_{\mathrm{C}}\). The students obtain the following wavelength shifts \(\lambda_{\mathrm{s}}-\lambda_{\mathrm{i}}\) as a function of scattering angle \(\theta\). \(\begin{array}{llllll} \boldsymbol{\theta} & 45^{\circ} & 75^{\circ} & 90^{\circ} & 135^{\circ} & 180^{\circ} \end{array}\) \(\begin{array}{llllll} \boldsymbol{\lambda}_{\mathrm{s}}-\boldsymbol{\lambda}_{\mathbf{i}} & 0.647 \mathrm{pm} & 1.67 \mathrm{pm} & 2.45 \mathrm{pm} & 3.98 \mathrm{pm} & 4.95 \mathrm{pm} \end{array}\) Use their data to estimate the value for the Compton wavelength. Compare this number with the accepted value.

SPREADSHEET Students in a physics lab are trying to determine the value of Plancks constant using a photoelectric apparatus similar to the one shown in Figure 34-2. The students are using a heliumneon laser that has a tunable wavelength as the light source. The data that the students obtain for the maximum electron kinetic energies are (a) Using a spreadsheet program or graphing calculator, plot versus light frequency. (b) Use the graph to estimate the value of Plancks constant. (Note: You may wish to use a feature of your spreadsheet program or graphing calculator to obtain the best straight-line fit to the data.) (c) Compare your result with the accepted value for Plancks constant.

SPREADSHEET The cathode that was used by the students in the experiment described in Problem 12 is constructed from one of the following metals: Metal Tungsten Silver Potassium Cesium Work function Determine which metal composes the cathode by using the same data given in Problem 12. (a) Using a spreadsheet program or graphing calculator, plot versus frequency. (b) Use the graph to estimate the value of the work function based on the students data. (Note: You may wish to use a feature of your spreadsheet program or graphing calculator to obtain the best straight-line fit to the data.) (c) Which metal was most likely used for the cathode in their experiment?

Find the photon energy in electron volts for light of wavelength (a) (b) and (c)

Find the photon energy in electron volts for an electromagnetic wave of frequency (a) in the FM radio band and (b) in the AM radio band.

What are the frequencies of photons that have the following energies: (a) 1.00 eV, (b) 1.00 keV, and (c) 1.00 MeV?

Find the photon energy in electron volts if the wavelength is (a) (about 1 atomic diameter) and (b)

The wavelength of red light emitted by a heliumneon laser is If the diameter of the laser beam is what is the density of photons in the beam? Assume that the intensity is uniformly distributed across the beam.

ENGINEERING APPLICATION Lasers used in a telecommunications network typically produce light that has a wavelength near How many photons per second are being transmitted if such a laser has an output power of

The work function for tungsten is (a) Find the threshold frequency and wavelength for the photoelectric effect to occur when monochromatic electromagnetic radiation is incident on the surface of a sample of tungsten. Find the maximum kinetic energy of the electrons if the wavelength of the incident light is (b) and (c)

When monochromatic ultraviolet light that has a wavelength equal to is incident on a sample of potassium, the emitted electrons have maximum kinetic energy of (a) What is the energy of an incident photon? (b) What is the work function for potassium? (c) What would be the maximum kinetic energy of the electrons if the incident electromagnetic radiation had a wavelength of 430 nm? (d) What is the maximum wavelength of incident electromagnetic radiation that will result in the photoelectric emission of electrons by a sample of potassium?

The maximum wavelength of electromagnetic radiation that will result in the photoelectric emission of electrons from a sample of silver is (a) Find the work function for silver. (b) Find the maximum kinetic energy of the electrons if the incident radiation has a wavelength of

The work function for cesium is (a) Find the minimum frequency and maximum wavelength of electromagnetic radiation that will result in the photoelectric emission of electrons from a sample of cesium. Find the maximum kinetic energy of the electrons if the wavelength of the incident radiation is (b) and (c)

When a surface is illuminated with electromagnetic radiation of wavelength the maximum kinetic energy of the emitted electrons is What is the maximum kinetic energy if the surface is illuminated using radiation of wavelength

Find the shift in wavelength of photons scattered by free stationary electrons at (Assume that the electrons are initially moving with negligible speed and are virtually free of (unattached to) any atoms or molecules.)

When photons are scattered by electrons in a carbon sample, the shift in wavelength is Find the scattering angle. (Assume that the electrons are initially moving with negligible speed and are virtually free of (unattached to) any atoms or molecules.)

The photons in a monochromatic beam are scattered by electrons. The wavelength of the photons that are scattered at an angle of with the direction of the incident photon beam is 2.3 percent less than the wavelength of the incident photons. What is the wavelength of the incident photons?

Compton used photons of wavelength (a) What is the energy of one of those photons? (b) What is the wavelength of the photons scattered in the direction opposite to the direction of the incident photons? (c) What is the energy of the photon scattered in that direction?

For the photons used by Compton (see Problem 28), find x _ L, the momentum of the incident photon and the momentum of the photon scattered in the direction opposite to the direction of the incident photons. Use the conservation of momentum to find the momentum of the recoil electron in this case.

A beam of photons that have a wavelength equal to is scattered by electrons initially at rest. A photon in the beam is scattered in a direction perpendicular to the direction of the incident beam. (a) What is the change in wavelength of the photon? (b) What is the kinetic energy of the electron?

An electron is moving at Find the electrons wavelength.

An electron has a wavelength of Find (a) the magnitude of its momentum and (b) its kinetic energy.

An electron, a proton, and an alpha particle each have a kinetic energy of Find (a) the magnitudes of their momenta and (b) their de Broglie wavelengths.

A neutron in a reactor has a kinetic energy of approximately Calculate the wavelength of the neutron.

Find the wavelength of a proton that has a kinetic energy of

What is the kinetic energy of a proton whose wavelength is (a) and (b)

The kinetic energy of the electrons in the electron beam in a run of Davisson and Germers experiment was Calculate the wavelength of the electrons in the beam.

The distance between and ions in a LiCl crystal is Find the energy of electrons that have a wavelength equal to that spacing.

An electron microscope uses electrons that have energies equal to Find the wavelength of the electrons.

What is the wavelength of a neutron that has a speed of

(a) Find the energy of the ground state and the first two excited states of a neutron in a one-dimensional box of length (about the diameter of an atomic nucleus). Make an energy-level diagram for the system. Calculate the wavelength of electromagnetic radiation emitted when the neutron makes a transition from (b) to (c) to and (d) to

(a) Find the energy of the ground state and the first two excited states of a neutron in a one-dimensional box of length (about the diameter of a molecule). Calculate the wavelength of electromagnetic radiation emitted when the neutron makes a transition from (b) to (c) to and (d) to

A particle is in the ground state of a one-dimensional box that has length (The box has one end at the origin and the other end on the positive axis.) Determine the probability of finding the particle in the interval of length x _ 0.002L and centered at (a) (b) and (c) (Because is very small you need not do any integration.)

A particle is in the second excited state ( ) of a onedimensional box that has length (The box has one end at the origin and the other end on the positive axis.) Determine the probability of finding the particle in the interval of length and centered at (a) (b) and (c) (Because is very small you need not do any integration.)

A particle is in the first excited ( ) state of a onedimensional box that has length (The box has one end at the origin and the other end on the positive axis.) Find (a) and (b)

A particle in a one-dimensional box that has length is in the first excited state ( ). (The box has one end at the origin and the other end on the positive axis.) (a) Sketch versus for this state. (b) What is the expectation value for this state? (c) What is the probability of finding the particle in some small region centered at (d) Are your answers for Part (b) and Part (c) contradictory? If not, explain why your answers are not contradictory.

A particle of mass m has a wave function given by \(\psi(x)=A e^{-|x| / a}\) where A and a are positive constants. (a) Find the normalization constant A. (b) Calculate the probability of finding the particle in the region \(-a \leq x \leq a\).

A one-dimensional box is on the axis in the region of A particle in this box is in its ground state. Calculate the probability that the particle will be found in the region (a) (b) and (c)

A one-dimensional box is on the axis in the region of Aparticle in this box is in its first excited state. Calculate the probability that the particle will be found in the region (a) (b) and (c)

The classical probability distribution function for a particle in a one-dimensional box on the axis in the region of is given by Use this expression to show that and for a classical particle in the box.

A one-dimensional box is on the axis in the region of (a) The wave functions for a particle in the box are given by For a particle in the state, show that and (b) Compare these expressions for and for with the expressions for and for the classical distribution of Problem 50.

SPREADSHEET (a) Use a spreadsheet program or graphing calculator to plot as a function of the quantum number for the particle in the box described in Problem 48 and for values of from 1 to 100. Assume for your graph. Refer to Problem 51. (b) Comment on the significance of any asymptotic limits that your graph shows.

The wave functions for a particle of mass in a onedimensional box of length centered at the origin (so that the ends are at ) are given by and Calculate and for the ground state

Calculate and for the first excited state of the box described in Problem 53.

Photons in a uniform light beam have wavelengths equal to and the beam has an intensity of (a) What is the energy of each photon in the beam? (b) How much energy strikes an area of perpendicular to the beam in (c) How many photons strike this area in

A particle is moving with a speed of approximately in a one-dimensional box that has a length equal to Calculate the approximate value of the quantum number of the state occupied by the particle.

(a) For the particle and box of Problem 56, find and assuming that these uncertainties are given by percent and percent. (b) What is

In 1987, a laser at Los Alamos National Laboratory produced a flash that lasted and had a power of Estimate the number of emitted photons, assuming they all had wavelengths equal to

ENGINEERING APPLICATION You cannot “see” anything smaller than the wavelength of the wave used to make the observation. What is the minimum energy of an electron needed in an electron microscope to “see” an atom that has a diameter of about 0.1 nm?

A common flea that has a mass of can jump vertically as high as Estimate the wavelength for the flea immediately after takeoff.

BIOLOGICAL APPLICATION A source radiates light of wavelength uniformly in all directions. An eye that has been adapted to the dark has a pupil and can detect the light if at least 20 photons per second enter the pupil. How far from the source can the light be detected under these rather extreme conditions?

BIOLOGICAL APPLICATION The diameter of the pupil of an eye under room-light conditions is approximately Find the intensity of light that has a wavelength equal to so that 1 photon per second passes through the pupil.

A incandescent lightbulb radiates of visible light uniformly in all directions. (a) Find the intensity of the light from the bulb at a distance of (b) If the average wavelength of the visible light is and counting only those photons in the visible spectrum, find the number of photons per second that strike a surface that has an area equal to is oriented so that the line to the bulb is perpendicular to the surface, and is a distance of from the bulb.

When light of wavelength is incident on the cathode of a photoelectric tube, the maximum kinetic energy of the emitted electrons is If the wavelength is reduced to the maximum kinetic energy of the emitted electrons is Find the work function of the cathode material.

An incident photon of energy \(E_{\mathrm{i}}\) undergoes Compton scattering at an angle of \(\theta\). Show that the energy of the scattered photon is given by \(E_{\mathrm{s}}=\frac{E_{\mathrm{i}}}{1+\left(E_{\mathrm{i}} / m_{\mathrm{e}} c^{2}\right)(1-\cos \theta)}\)

A particle is confined to a one-dimensional box. While the particle makes a transition from the state to the state radiation of is emitted. While the particle makes the transition from the state to the state radiation of wavelength is emitted. The ground-state energy of the particle is Determine

The Pauli exclusion principle states that no more than one electron may occupy a particular quantum state at a time. Electrons intrinsically occupy two spin states. Therefore, if we wish to model an atom as a collection of electrons trapped in a onedimensional box, no more than two electrons in the box can have the same value of the quantum number Calculate the energy that the most energetic electron(s) would have for the uranium atom that has an atomic number 92. Assume the box has a length of and the electrons are in the lowest possible energy states. How does this energy compare to the rest energy of the electron?

A beam of electrons that each have the same kinetic energy illuminates a pair of slits separated by a distance The beam forms bright and dark fringes on a screen located a distance beyond the two slits. The arrangement is otherwise identical to that used in the optical two-slit interference experiment described in Chapter 33 and in Figure 33-7 and the fringes have the appearance shown in Figure 34-8d. The bright fringes are found to be separated by a distance of What is the kinetic energy of the electrons in the beam?

When a surface is illuminated by light of wavelength the maximum kinetic energy of the emitted electrons is If the wavelength is used, the maximum kinetic energy increases to For wavelength the maximum kinetic energy of the emitted electrons is Determine the work function of the surface and the wavelength

A simple pendulum has a length equal to and has a bob that has a mass equal to The energy of this oscillator is quantized, and the allowed values of the energy are given by where is an integer and is the frequency of the pendulum. (a) Find if the angular amplitude is (b) Find such that exceeds by 0.010 percent.

(a) Show that for large the fractional difference in energy between state and state for a particle in a one-dimensional box is given approximately by (b) What is the approximate percentage energy difference between the states and (c) Comment on how this result is related to Bohrs correspondence principle.

A mode-locked, titaniumsapphire laser has a wavelength of and produces pulses of light each second. Each pulse has a duration of and consists of photons. What is the average power produced by the laser?

This problem estimates the time lag in the photoelectric effect that is expected classically but not observed. Let the intensity of the incident radiation falling on an atom be (a) If the area presented by an atom is find the energy per second falling on an atom. (b) If the work function is how long would it take for this much energy to fall on the atom if the radiation energy was distributed uniformly rather than in compact packets (photons)?