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physics
modern physics

College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions

Figure 27.21 shows a graph of stopping potential versus frequency for a photoelectric material. Determine(a) Planck€™s constant and(b) The work function of the material from the data contained in the graph.
The photoelectric effect threshold wavelength for a certain metal is 400 nm. Calculate the maximum speed of photoelectrons if we use light having a wavelength of (a) 300 nm, (b) 400 nm, and (c) 500 nm.
When light of wavelength of 250 nm is incident on a metal surface, the maximum speed of the photoelectrons is 4.0 x 105 m/s. What is the work function of the metal in eV?
The work function of a material is 3.5 eV. If the material is illuminated with monochromatic light (λ = 300m), what are (a) The stopping potential and (b) The cutoff frequency?
Blue light with a wavelength of 420 nm is incident on a certain material and causes the emission of photoelectrons with a maximum kinetic energy of 1.00 x 10-19 J. (a) What is the stopping voltage? (b) What is the material’s work function? (c) What is the stopping voltage if red light (λ =
When the surface of a particular material is illuminated with monochromatic light of various frequencies, the stopping potentials for the photoelectrons are determined to be the following:Plot these data, and from the graph determine Planck€™s constant and the metal€™s work
When a certain photoelectric material is illuminated with red light (λ = 700 nm) and then blue light (λ = 400 nm), it is found that the maximum kinetic energy of the photoelectrons resulting from the blue light is twice that from red light. What is the work function of the material?
What is half the maximum wavelength shift for Compton scattering from a free electron?
When the wavelength shift for Compton scattering from a free electron is a maximum, what is the scattering angle?
What are the wavelength and frequency of the most intense radiation component from a blackbody with a temperature of 0oC?
What is the change in wavelength when monochromatic X-rays are scattered by electrons ons through an angle of 30°?
A monochromatic beam of X-rays with a wavelength of 0.280 nm is scattered by a metal foil. If the scattered beam has a wavelength of 0.281 nm, what is the observed scattering angle?
X-rays with a wavelength of 0.0045 nm are used in a Compton scattering experiment. If the X-rays are scattered through an angle of 45o, what is the wavelength of the scattered radiation?
A photon with an energy of 5.0 keV is scattered by a free electron. (a) The recoiling electron could have an energy of (1) zero, (2) less than 5.0 keV, but not zero, (3) 5.0 keV. Why? (b) If the wavelength of the scattered photon is 0.25 nm, what is the recoiling electron’s kinetic energy?
X-rays of wavelength 0.01520 nm are scattered from a carbon atom. The wavelength shift is measured to be 0.000326 nm. (a) What is the scattering angle? (b) How much energy, in eV, does each photon impart to each electron?
X-rays of frequency 1.210 x 1018 Hz are scattered from electrons in an aluminum foil. The frequency of the scattered X-rays is 1.203 z 1018 Hz. (a) What is the scattering angle? (b) What is the recoiling speed of the electrons?
The Compton effect can occur for scattering from any particle— for example, from a proton. (a) Compared with the Compton wavelength for an electron, the Compton wavelength for a proton is (1) longer, (2) the same, (3) shorter. Why? (b) What is the value of the Compton wavelength for a proton?
Find the energy of a hydrogen atom whose electron is in the (a) n = 2 state and (b) n = 3 state.
Find the radius of the electron orbit in a hydrogen atom for states with the following principal quantum numbers: (a) n = 2, (b) n = 4, (c) n = 5.
Scientists are now beginning to study “large” atoms, that is, atoms with orbits that are almost large enough to be measured in our everyday units of measurement. For what excited state (give an approximate principal quantum number) of a hydrogen atom would the diameter of the orbit be in the
(a) If you have a fever, is the wavelength of the radiation component of maximum intensity emitted by your body (1) greater, (2) the same, or (3) smaller as compared with its value when your temperature is normal? Why? (b) Assume that human skin has a temperature of 34oC. What is the wavelength of
Find the binding energy of the hydrogen electron for states with the following principal quantum numbers: (a) n = 3, (b) n = 5, (c) n = 7.
Find the energy required to excite a hydrogen electron from (a) The ground state to the first excited state and (b) The first excited state to the second excited state. (c) Classify the type of light needed to create each of the transitions.
What is the frequency of light that would excite the electron of a hydrogen atom (a) From a state with a principal quantum number of n = 2 to that with a principal quantum number of n = 5? (b) What about from n = q to n = ∞?
A hydrogen atom has an ionization energy of 13.6eV. When it absorbs a photon with an energy greater than this energy, the electron will be emitted with some kinetic energy. (a) If the energy of such a photon is doubled, the kinetic energy of the emitted electron will (1) more than double, (2)
A hydrogen atom in its ground state is excited to the n = 5 level. It then makes a transition directly to the n = 2 level before returning to the ground state. (a) What are the wavelengths of the emitted photons? (b) Would any of the emitted light be in the visible region?
(a) For which of the following transitions in a hydrogen atom is the photon of longest wavelength emitted: (1) n = 5 to n = 3, (2) n = 6 to n = 5, or (3) n = 2 to n = 1? (b) Justify your answer mathematically.
The hydrogen spectrum has a series of lines called the Lyman series, which results from transitions to the ground state. What is the longest wavelength in this series, and in what region of the EM spectrum does it lie?
A hydrogen atom absorbs light of wavelength 486 nm. (a) How much energy did the atom absorb? (b) What are the values of the principal quantum numbers of the initial and final states of this transition?
If the electron in a hydrogen atom is to make a transition from the first excited state to the fourth excited state, what frequency of photon is needed? What type of light is this?
(a) How many transitions in a hydrogen atom result in the absorption of red light: (1) one, (2) two, (3) three, or (4) four? (b) What are the principal quantum numbers of the initial and final states for this process? (c) What are the energy of the required photon and the wavelength of the light
A “red-hot” object is measured to have a frequency of 1.0 x 1014 Hz. What is the Celsius temperature of the object?
What is the binding energy for an electron in the ground state in the following hydrogen-like ions: (a) He + (Z = 2) and (b) Li2+(Z = 3)?
Show that the orbital speeds of an electron in the Bohr orbits are given (to two significant figures) by vn = (2.2 x 106 m/s/n).
For an electron in the ground state of a hydrogen atom, calculate its (a) Potential energy, (b) Kinetic energy, and (c) Total energy.
Suppose a hypothetical atom had two metastable excited states, one 2.0 eV above the ground state and one 4.0 eV above the ground state. If used in a laser with transitions only to the ground state, (a) What is the wavelength for each excited state? (b) Which transition is in the visible range?
In order to achieve population inversion between two states that are separated by an energy difference of 3.5 eV, what wavelength of pumping light should be used?
Light of wavelength 340 nm is incident on a metal surface and ejects electrons that have a maximum speed of 3.5 x 105 m/s. (a) What is the work function of the metal? (b) What is its stopping voltage? (c) What is its threshold wavelength?
A 10.0-keV X-ray photon is successively scattered by two free electrons initially at rest. In the first case, it is scattered through an angle of 41o; the second scattering is through an angle of 72o. (a) What is the final photon energy? (b) How much kinetic energy does each electron receive?
Under the right circumstances, if a photon’s energy is above a minimum energy level, that energy can be completely converted into creating an electron–positron pair (a positron is identical to an electron except that it has a positive charge). Recall that the energy equivalent of the electron
Consider an electron in its first excited state in a hydrogen atom. Determine its (a) Orbital speed, (b) Angular speed, (c) Linear momentum, and (d) Angular momentum.
A gamma-ray photon scatters off a free proton (initially at rest) at an angle of 45o. The wavelength of the scattered light is measured to be 6.20 x 10-13m. (a) What was the energy of the incoming photon? (b) How much kinetic energy did the proton receive? (You may need to carry an extra figure
What is the minimum energy of a thermal oscillator in a blackbody producing radiation at λmax at a temperature of 212oF?
In the nuclear version of the photoelectric effect (called the photonuclear effect), a high-energy photon is absorbed by an atomic nucleus and a proton is freed from that nucleus. If the minimum energy needed to free a proton from a particular nucleus is 5.00 MeV, (a) Determine the maximum
A photon of wavelength 320 nm is absorbed by a hydro-gen atom when the electron is in the second excited state. What is the speed of the ionized electron?
If the minimum energy of a thermal oscillator in a blackbody’s most intense radiation is 3.5 x 10-19J, what is the Celsius temperature of the blackbody?
The temperature of a blackbody increases from 200oC to 400oC. (a) Will the frequency of the most intense spectral component emitted by this blackbody (1) increase, but not double; (2) double; (3) be reduced in half; or (4) decrease, but not by half? Why? (b) What is the change in the frequency of
The temperature of a blackbody is 500oC. If the intensity of the emitted radiation, 2.0 W/m2, were due entirely to the most intense frequency component, how many quanta of radiation would be emitted per second per square meter?
A bowling ball has well- defined position and speed, whereas an electron does not. Why?
A laser requires a metastable state that is a relatively long- lived excited atomic state. What is the uncertainly in the energy of the metastable state compared to non-metastable excited states?
Why is the energy threshold for electron–positron pair production actually higher than the sum of their two masses (1.022 MeV in energy terms)?
Explain why there are always two photons created in pair annihilation. Why cannot the process create just one photon?
How would the radius for the maximum probability in Fig. 28.3a change if the charge on the proton in the hydrogen atom were suddenly decreased? Explain your reasoning.
What is the de Broglie wavelength associated with a 1000-kg car moving at 25 m/s?
A scientist wants to use an electron microscope to observe details on the order of 0.25 nm. Through what potential difference must the electrons be accelerated from rest so that they have a de Broglie wavelength of this magnitude?
What is the energy of a beam of electrons that exhibits a first-order maximum at an angle of when diffracted by a crystal grating with a lattice plane spacing of 0.215 nm?
According to the Bohr theory of the hydrogen atom, the speed of the electron in the first Bohr orbit is 2.19 x 106 m/s. (a) What is the wavelength of the matter wave associated with the electron? (b) How does this wavelength compare with the circumference of the first Bohr orbit?
(a) What is the de Broglie wavelength of the Earth in its orbit about the Sun? (b) Treating the Earth as a de Broglie wave in a large “gravitational” atom, what would be the principal quantum number, n, of its orbit? (c) If the principal quantum number increased by 1, how would the radius of
If you are twice as likely to find an electron at a distance of 0.0400 nm than 0.0500 nm from the nucleus, what is the ratio of the absolute value of the wave function at 0.0400 nm to that at 0.0500 nm?
A particle in box is constrained to move in one dimension, like a bead on a wire, as illustrated in Fig. 28.16. Assume that no forces act on the particle in the interval 0Using this relationship, show that the €œallowed€ kinetic energies Kn of the particle are given by Kn =
Let’s model a nucleus as a particle trapped in the one-dimensional box. Assume the particle is a proton and it is in a one-dimensional nucleus of length of 7.11 fm (the approximate diameter of a Pb-208 nucleus). (a) Using the results of Exercise 16, determine the energies of the proton in the
(a) How many possible sets of quantum numbers are there for the n = 1 and n = 2 shells? (b) Write the explicit values of all the quantum numbers (n, ℓ, mℓ, ms) for these levels.
How many possible sets of quantum numbers are there for the subshells with (a) ℓ = 2 and (b) ℓ = 3?
If the de Broglie wavelength associated with an electron is 7.50 x 10-7, what is the electron’s speed?
(a) Which has more possible sets of quantum numbers associated with it, n = 2 or ℓ = 2? (b) Prove your answer to part (a).
An electron in an atom is in an orbit that has a magnetic quantum number of mℓ = 2. What are the minimum values that (a) ℓ and (b) n could be for that orbit?
Draw the ground state energy-level diagrams like those in Fig. 28.8 for (a) Nitrogen (N) and (b) Potassium (K).
Draw schematic diagrams for the electrons in the subshells of (a) Sodium (Na) and (b) Argon (Ar) atoms in the ground state.
Identify the atoms of each of the following ground state electron configurations: (a) 1s2 2s2; (b) 1s2 2s2 2p3; (c) 1s2 2s2 2p6; (d) 1s2 2s2 2p6 3s2 3p4.
Write the ground state electron configurations for each of the following atoms: (a) Boron (b), (b) Calcium (Ca), (c) Zinc (Zn), and (d) tin (Sn).
(a) If there were no electron spin, the 1s state would contain a maximum of (1) zero, (2) one, (3) two electrons. Why? (b) What would be the first two inert or noble gases if there were no electron spin?
A 1.0-kg ball has a position uncertainty of 0.20 m. What is its minimum momentum uncertainty?
An electron and a proton each have a momentum of 3.28470 x 10-30 kg ∙ m/s ± 10-30 kg ∙ m/s. (a) The minimum uncertainty in the position of the electron compared with that of the proton will be (1) larger, (2) the same, (3) smaller. Why? (b) Calculate the minimum uncertainty in the position
An electron and a proton are moving with the same speed. (a) Compared with the proton, will the electron have (1) a shorter, (2) an equal, or (3) a longer de Broglie wave-length? Why? (b) If the speed of the electron and proton is 100 m/s, what are their de Broglie wavelengths?
If an excited state of an atom has a lifetime of 2.0 x 10-7 s, what is the minimum error associated with the measurement of the energy of this state?
The energy of the first excited state of a hydrogen atom is –0.34eV ± 0.0003 eV. What is the minimum average lifetime for this state?
What is the minimum uncertainty in the speed of an electron that is known to be somewhere between 0.050 nm and 0.10 nm from a proton?
What is the minimum uncertainty in the position of a 0.50-kg ball that is known to have a speed uncertainty of 3.0 x 10-28 m/s?
The energy of a 2.00-keV electron is known to within ± 3.00%. How accurately can its position be measured?
(a) If the lifetime of excited state A is longer than that of another excited state B, then the width of a spectral line due to natural broadening for a transition from state A to the ground state will be (1) smaller than, (2) the same as, (3) greater than that for a transition from state B to the
What is the threshold energy for the production of an electron–positron pair?
What is the energy of the photons produced in proton–antiproton pair annihilation, assuming that both particles are essentially at rest initially?
A muon, or μ meson, has the same charge as an electron, but is 207 times as massive. (a) Compared with electron–positron pair production, the pair production of a muon and an antimuon requires a photon of (1) more, (2) the same amount of, (3) less energy. Why? (b) What would be the minimum
(a) The minimum photon energy to create a proton–antiproton pair is (1) more than, (2) the same as, or (3) less than the minimum photon energy to create a neutron–antineutron pair. Explain. (b) Calculate minimum photon frequency to create the proton–antiproton pair and the
An electron is accelerated from rest through a potential difference of 100 V. What is the de Broglie wave-length of the electron?
An electron traveling at 3.00 x 104 m/s is further accelerated by a potential difference so as to reduce its de Broglie wavelength to one-third of its original value. How much voltage is required to accomplish this?
Abeam of electrons moving at 5.0 x 105 m/s is incident on a single slit that is wide. On a screen that is 1.0 m behind the slits, an electron diffraction pattern is observed. What is the width of the central maximum?
The average kinetic energy of a particle at a temperature of T is 3/2 kBT(Section 10.5). What is the wavelength of an electron at 20oC? How about a proton at the same temperature?
An electron microscope is an instrument that uses electrons instead of light for the imaging of objects. A mono-chromatic beam of electrons is accelerated through a potential difference of 50 V. What is the ratio of the minimum angle of resolution (Section 25.4) of this electron microscope compared
Suppose a starship had a mass of 1.25 x 109 kg and was initially at rest. If its “matter–antimatter engines” produced photons from electron–positron annihilation and focused them to travel backward out from the ship, how many photons would they have to emit to reach of the speed of light?
Using a typical nuclear diameter of 4.25 x 10-15 as its location uncertainty, compute the uncertainty in momentum and kinetic energy associated with an electron if it were part of the nucleus. For energies greater than a few MeV, particles such as electrons would escape the nucleus. What does this
The lifetime of the excited state involved in a He–Ne laser of wavelength 832.8 nm is about 10-4 s. What is the ratio of the frequency width of a spectral line due to natural broadening to the frequency of the laser?
An electron is accelerated from rest through a potential difference so that its de Broglie wavelength is 0.010 nm. What is the potential difference?
Electrons are accelerated from rest through an electric potential difference. (a) If this potential difference increases to four times the original value, the new de Broglie wavelength will be (1) four times, (2) twice, (3) one-fourth, (4) one-half that of the original. Why? (b) If the original
A proton traveling at a speed of 4.5 x 104 m/s is accelerated through a potential difference of 37 V. (a) Will its de Broglie wavelength (1) increase, (2) remain the same, or (3) decrease, due to the potential difference? Why? (b) By what percentage does the de Broglie wave-length of the proton
A proton and an electron are accelerated from rest through the same potential difference V. What is the ratio of the de Broglie wavelength of an electron to that of a proton (to two significant figures)?
A charged particle is accelerated through a potential difference V. If the voltage were doubled, what would be the ratio of the new de Broglie wavelength to the original value?
In the Rutherford scattering experiment, the minimum distance of approach for the alpha particle is given by Eq. 29.1. Explain why this distance does not necessarily represent the nuclear radius. Is it larger or smaller than the nuclear radius?
During a particular decay sequence in a decay chain, a nucleus first decays by alpha emission, followed by a emission, and lastly a gamma- ray emission. Compare the number of neutrons, protons, and nucleons in the final nucleus to that in the initial nucleus. How would your answer differ if the
Nuclide A has a decay constant that is half that of nuclide B. Samples of both types start with the same number of undecayed nuclei, N. In terms of N, after two of A’s half-lives have elapsed, (a) How many of type A have decayed? (b) How many of type B have decayed?

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