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physics
physics scientists and engineers

Questions and Answers of Physics Scientists and Engineers

A pulse of light is created by the superposition of many waves that span the frequency range f0 - 1/2 Δf ≤ f ≤ f0 + 1/2 ≤f, where f0 = c/λ is called the center frequency of the pulse. Laser
The probability density for finding a particle at position x is and zero elsewhere.a. You will learn in Chapter 40 that the wave function must be a continuous function. Assuming that to be the case,
Consider the electron wave function a. Determine the normalization constant c. Your answer will be in terms of L.b. Draw a graph of ψ(x) over the interval -L ?? x ?? 2L.c. Draw a graph of |ψ(x)|2
Consider the electron wave functionwhere x is in cm.a. Determine the normalization constant c.b. Draw a graph of Ïˆ(x) over the interval -2 cm ‰¤ x ‰¤ 2 cm. Provide
An electron that is confined to x ?? 0 nm has the normalized wave function where x is in nm.What is the probability of finding the electron in a 0.010-nm-wide region at x = 1.0 nm? So (1.414 nm-V2
FIGURE P39.33 shows the probability density for finding a particle at position x. a. Determine the value of the constant a, as defined in the figure.b. At what value of x are you most likely to find
FIGURE P39.32 shows |ψ(x)|2for the electrons in an experiment. a. Is the electron wave function normalized? Explain.b. Draw a graph of ψ(x) over this same interval. Provide a numerical scale on
FIGURE P39.31 shows the wave function of a particle confined between x = 0 nm and x = 1.0 nm. The wave function is zero outside this region. a. Determine the value of the constant c, as defined in
An experiment finds electrons to be uniformly distributed over the interval 0 cm ≤ x ≤ 2 cm, with no electrons falling outside this interval.a. Draw a graph of |ψ(x)|2 for these electrons.b.
Consider a single-slit diffraction experiment using electrons. (Single-slit diffraction was described in Section 33.4.) Using Figure 39.5 as a model, drawa. A dot picture showing the arrival
FIGURE P39.28 shows a pulse train. The period of the pulse train is T = 2 Δt, where Δt is the duration of each pulse. What is the maximum pulse-transmission rate (pulses per second) through an
Ultrasound pulses with a frequency of 1.000 MHz are transmitted into water, where the speed of sound is 1500 m/s. The spatial length of each pulse is 12 mm.a. How many complete cycles are contained
A 1.0-mm-diameter sphere bounces back and forth between two walls at x = 0 mm and x = 100 mm. The collisions are perfectly elastic, and the sphere repeats this motion over and over with no loss of
What is the minimum uncertainty in position, in nm, of an electron whose velocity is known to be between 3.48 × 105 m/s and 3.58 ×105 m/s?
A proton is confined within an atomic nucleus of diameter 4.0 m. Use a one-dimensional model to estimate the smallest range of speeds you might find for a proton in the nucleus.
Andrea, whose mass is 50 kg, thinks she’s sitting at rest in her 5.0-m-long dorm room as she does her physics homework. Can Andrea be sure she’s at rest? If not, within what range is her velocity
A thin solid barrier in the xy-plane has a 10-μm-diameter circular hole. An electron traveling in the z-direction with vx = 0 m/s passes through the hole. Afterward, is it certain that vx is still
What minimum bandwidth is needed to transmit a pulse that consists of 100 cycles of a 1.00 MHz oscillation?
A radio-frequency amplifier is designed to amplify signals in the frequency range 80 MHz to 120 MHz. What is the shortest-duration radio-frequency pulse that can be amplified without distortion?
A 1.5-μm-wavelength laser pulse is transmitted through a 2.0-GHz-bandwidth optical fiber. How many oscillations are in the shortest-duration laser pulse that can travel through the fiber?
Sound waves of 498 Hz and 502 Hz are superimposed at a temperature where the speed of sound in air is 340 m/s. What is the length Δx of one wave packet?
FIGURE EX39.17 shows the wave function of an electron. a. What is the value of c?b. Draw a graph of |ψ(x)|2.c. What is the probability that the electron is located between x = -1.0 nm and x = 1.0
FIGURE EX39.16 shows the wave function of a neutron.a. What is the value of c?b. Draw a graph of |Ïˆ(x)|2.c. What is the probability that the neutron is located between x = -1.0 mm and x =
FIGURE EX39.15 is a graph of |ψ(x)|2for a neutron. a. What is the value of a?b. Draw a graph of the wave function ψ(x). (There is more than one acceptable answer.)c. What is the probability that
FIGURE EX39.14 is a graph of |ψ(x)|2for an electron. a. What is the value of a?b. Draw a graph of the wave function ψ(x). (There is more than one acceptable answer.)c. What is the probability that
FIGURE EX39.13 shows the probability density for an electron that has passed through an experimental apparatus. What is the probability that the electron will land in a 0.010-mm-wide strip at (a) X =
In an interference experiment with electrons, you find the most intense fringe is at x = 7.0 cm. There are slightly weaker fringes at x = 6.0 and 8.0 cm, still weaker fringes at x = 4.0 and 10.0 cm,
What are the units of ψ? Explain.
When 5 × 1012 photons pass through an experimental apparatus, 2.0 × 109 land in a 0.10-mm-wide strip. What is the probability density at this point?
1.0 × 1010 photons pass through an experimental apparatus. How many of them land in a 0.10-mm-wide strip where the probability density is 20 m-1?
In one experiment, 2000 photons are detected in a 0.10-mm-wide strip where the amplitude of the electromagnetic wave is 10 V/m. How many photons are detected in a nearby 0.10-mm-wide strip where the
FIGURE Q39.6 shows wave packets for particles 1, 2, and 3. Which particle can have its velocity known most precisely? Explain. (x) (x) Particle 1 Particle 2 Particle 3 FIGURE Q39.6
In one experiment, 6000 photons are detected in a 0.10 mm-wide strip where the amplitude of the electromagnetic wave is 200 V/m. What is the wave amplitude at a nearby 0.20 mm-wide strip where 3000
What is the value of the constant a in FIGURE Q39.5? P(x) =|4(x)* %3D x (mm) 3 0+ FIGURE Q39.5 0 1 2
Make a table in which you list all possible outcomes of rolling two dice. Call the dice A and B. What is the probability of rolling(a) A 7,(b) Any double,(c) A 6 or an 8?You can give the
FIGURE Q39.4 shows the dot pattern of electrons landing on a screen. a. At what value or values of x is the electron probability density at maximum? Explain.b. Can you tell at what value or values
Suppose you draw a card from a regular deck of 52 cards.a. What is the probability that you draw an ace?b. What is the probability that you draw a spade?
For the electron wave function shown in FIGURE Q39.3, at what position or positions is the electron most likely to be found? Least likely to be found? Explain. b(x) -x (nm) 4 2 FIGURE Q39.3
You are dealt 1 card each from 1000 decks of cards. What is the expected number of picture cards (jacks, queens, and kings)?
What is the difference between the probability and the probability density?
Suppose you toss three coins into the air and let them fall on the floor. Each coin shows either a head or a tail.a. Make a table in which you list all the possible outcomes of this experiment. Call
An experiment has four possible outcomes, labeled A to D. The probability of A is PA = 40, and of B is PB = 30,. Outcome C is twice as probable as outcome D. What are the probabilities PC and PD?
FIGURE Q39.1 shows the probability density for photons to be detected on the x-axis. a. Is a photon more likely to be detected at x = 0 m or at x = 1 m? Explain.b. One million photons are detected.
A brass plate at room temperature radiates 10 W of blackbody radiation. If the plate is cooled to –30°C, does the peak of maximum radiated intensity shift toward shorter wavelengths, shift toward
Explain why the observation of alpha particles scattered at very large angles led Rutherford to reject Thomson’s model of the atom and to propose a nuclear model.
a. A 238U nucleus has a radius of 7.4 fm. What is the density, in kg/m3, of the nucleus?b. A neutron star consists almost entirely of neutrons, created when electrons and protons are squeezed
The fission process n + 235U → 236U → 144Ba + 89Kr + 3n converts 0.185 u of mass into the kinetic energy of the fission products. What is the total kinetic energy in MeV?
What is the aperture diameter of a 12-mm-focal-length lens set to f/4.0?
To focus parallel light rays to the smallest possible spot, should you use a lens with a small f-number or a large f-number? Explain.
What is the f-number of a lens with a 35 mm focal length and a 7.0-mm-diameter aperture?
A friend lends you the eyepiece of his microscope to use on your own microscope. He claims the spatial resolution of your microscope will be halved, since his eyepiece has the same diameter as yours
A diffraction-limited lens can focus light to a 10-μm-diameter spot on a screen. Do the following actions make the spot diameter larger, make it smaller, or leave it unchanged?a. Decreasing the
A red card is illuminated by red light. What color will the card appear? What if it’s illuminated by blue light?
How would the graph ofFigure 38.2 look if classical physics provided the correct description of the photoelectric effect? Draw the graph and explain your reasoning. Assume that the light
How would the graphs ofFigure 38.3 look if classical physics provided the correct description of the photoelectric effect? Draw the graph and explain your reasoning. Include curves for both weak
Imagine that the horizontal box ofFigure 38.14 is instead oriented vertically. Also imagine the box to be on a neutron star where the gravitational field is so strong that the particle in the
The diameter of the nucleus is about 10 fm. What is the kinetic energy, in MeV, of a proton with a de Broglie wavelength of 10 fm?
The diameter of the nucleus is about 10 fm. A simple model of the nucleus is that protons and neutrons are confined within a one-dimensional box of length 10 fm. What are the first three energy
Find the radius of the electron’s orbit, the electron’s speed, and the energy of the atom for the first three stationary states of He+.
Calculate all the wavelengths of visible light in the emission spectrum of the hydrogen atom.
A proton confined in a one-dimensional box emits a 2.0 MeV gamma-ray photon in a quantum jump from n = 2 to n = 1. What is the length of the box?
Very large, hot stars—much hotter than our sun—can be identified by the way in which He+ ions in their atmosphere absorb light. What are the three longest wavelengths, in nm, in the Balmer series
What are the wavelengths of the transitions 3 → 2, 4 → 2, and 5 → 2 in the hydrogen-like ion O+7? In what spectral range do these lie?
Ultraviolet light with a wavelength of 70.0 nm shines on a gas of hydrogen atoms in their ground states. Some of the atoms are ionized by the light. What is the kinetic energy of the electrons that
Which metals in Table 38.1 exhibit the photoelectric effect forElement.................E0 (eV)Potassium ..............2.30Sodium ...................2.75Aluminum ...............4.28Tungsten
How many photoelectrons are ejected per second in the experiment represented by the graph of FIGURE EX38.2? I (µA) 10- ΔV (V) 3 FIGURE EX38.2 -3 -2 -1 0 1 1 2
a. Explain why the graphs ofFigure 38.3 are mostly horizontal for Î”V > 0.b. Explain why photo-electrons are ejected from the cathode with a range of kinetic energies, rather than
Electrons in a photoelectric-effect experiment emerge from an aluminum surface with a maximum kinetic energy of 1.30 eV. What is the wavelength of the light?
Photoelectrons are observed when a metal is illuminated by light with a wavelength less than 388 nm. What is the metal’s work function?
FIGURE Q38.5 is the current-versus-potential-difference graph for a photoelectric-effect experiment with an unknown metal. If classical physics provided the correct description of the photoelectric
A photoelectric-effect experiment finds a stopping potential of 1.56 V when light of 200 nm is used to illuminate the cathode.a. From what metal is the cathode made?b. What is the stopping potential
Metal 1 has a larger work function than metal 2. Both are illuminated with the same short-wavelength ultraviolet light. Do photoelectrons from metal 1 have a higher speed, a lower speed, or the same
What is the wavelength, in nm, of a photon with energy(a) 0.30 eV,(b) 3.0 eV,(c) 30 eV?For each, is this wavelength visible, ultraviolet, or infrared light?
Electron 1 is accelerated from rest through a potential difference of 100 V. Electron 2 is accelerated from rest through a potential difference of 200 V. Afterward, which electron has the larger de
a. Determine the energy, in eV, of a photon with a 550 nm wavelength.b. Determine the wavelength of a 7.5 keV x-ray photon.
What is the energy, in eV, of(a) A 450 MHz radio-frequency photon,(b) A visible-light photon with a wavelength of 450 nm,(c) An x-ray photon with a wavelength of 0.045 nm?
FIGURE Q38.9 is a simulation of the electrons detected behind two closely spaced slits. Each bright dot represents one electron. How will this pattern change if a. The electron-beam intensity is
An FM radio station broadcasts with a power of 10 kW at a frequency of 101 MHz.a. How many photons does the antenna emit each second?b. Should the broadcast be treated as an electromagnetic wave or
A red laser with a wavelength of 650 nm and a blue laser with a wavelength of 450 nm emit laser beams with the same light power. How do their rates of photon emission compare? Answer this by
If an electron is in a stationary state of an atom, is the electron at rest? If not, what does the term mean?
For what wavelength of light does a 100 mW laser deliver 2.50 × 1017 photons per second?
FIGURE Q38.12 shows the energy-level diagram of Element X. a. What is the ionization energy of Element X?b. An atom in the ground state absorbs a photon, then emits a photon with a wavelength of
A 100 W incandescent lightbulb emits about 5 W of visible light. (The other 95 W are emitted as infrared radiation or lost as heat to the surroundings.) The average wavelength of the visible light is
What is the energy, in keV, of 75 keV x-ray photons that are backscattered (i.e., scattered directly back toward the source) by the electrons in a target?
55 keV x-ray photons are incident on a target. At what scattering angle do the scattered photons have an energy of 50 keV?
At what speed is an electron’s de Broglie wavelength(a) 1.0 pm,(b) 1.0 nm,(c) 1.0 μm,(d) 1.0 mm?
What is the de Broglie wavelength of a neutron that has fallen 1.0 m in a vacuum chamber, starting from rest?
Through what potential difference must an electron be accelerated from rest to have a de Broglie wavelength of 500 nm?
a. What is the de Broglie wavelength of a 200 g baseball with a speed of 30 m/s?b. What is the speed of a 200 g baseball with a de Broglie wavelength of 0.20 nm?
What is the quantum number of an electron confined in a 3.0-nm-long one-dimensional box if the electron’s de Broglie wavelength is 1.0 nm?
What is the length of a one-dimensional box in which an electron in the n = 1 state has the same energy as a photon with a wavelength of 600 nm?
FIGURE EX38.24 is an energy-level diagram for a simple atom. What wavelengths, in nm, appear in the atom??s (a) Emission spectrum (b) Absorption spectrum? n= 3 Ez = 4.00 eV n=2- E = 1.50 eV FIGURE
An electron with 2.00 eV of kinetic energy collides with the atom shown in FIGURE EX38.24. a. Is the electron able to excite the atom? Why or why not?b. If your answer to part a was yes, what is the
The allowed energies of a simple atom are 0.00 eV, 4.00 eV, and 6.00 eV. An electron traveling with a speed of 1.30 × 106 m/s collides with the atom. Can the electron excite the atom to the n = 2
The allowed energies of a simple atom are 0.00 eV, 4.00 eV, and 6.00 eV.a. Draw the atom’s energy-level diagram. Label each level with the energy and the quantum number.b. What wavelengths appear
What is the radius of a hydrogen atom whose electron is bound by 0.378 eV?
What is the radius of a hydrogen atom whose electron moves at 7.3 × 105 m/s?
a. Calculate the de Broglie wavelength of the electron in the n = 1, 2, and 3 states of the hydrogen atom. Use the information inTable 38.2.
a. What quantum number of the hydrogen atom comes closest to giving a 100-nm-diameter electron orbit?b. What are the electron’s speed and energy in this state?
How much energy does it take to ionize a hydrogen atom that is in its first excited state?

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