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physics
physics scientists and engineers

Questions and Answers of Physics Scientists and Engineers

A beam of electrons is incident upon a gas of hydrogen atoms.a. What minimum speed must the electrons have to cause the emission of 656 nm light from the 3 → 2 transition of hydrogen?b. Through
The electrons in a cathode-ray tube are accelerated through a 250 V potential difference and then shot through a 33-nm diameter circular aperture. What is the diameter of the bright spot on an
In the atom interferometer experiment ofFigure 38.13, lasercooling techniques were used to cool a dilute vapor of sodium atoms to a temperature of 0.0010 K = 1.0 mK. The ultracold atoms passed
Consider an electron undergoing cyclotron motion in a magnetic field. According to Bohr, the electron’s angular momentum must be quantized in units of ℏ.a. Show that allowed radii for the
What are the wavelengths of spectral lines in the Balmer series with n = 6, 8, and 10?
a. Summarize the experimental evidence prior to the research of Thomson by which you might conclude that cathode rays are some kind of particle.b. Summarize the experimental evidence prior to the
Figure 37.7 identified the wavelengths of four lines in the Balmer series of hydrogen.a. Determine the Balmer formula n and m values for these wavelengths.b. Predict the wavelength of the fifth
Thomson observed deflection of the cathode-ray particles due to magnetic and electric fields, but there was no observed deflection due to gravity. Why not?
The wavelengths in the hydrogen spectrum with m = 1 form a series of spectral lines called the Lyman series. Calculate the wavelengths of the first four members of the Lyman series.
What was the significance of Thomson’s experiment in which an off-center electrode was used to collect charge deflected by a magnetic field?
Two of the wavelengths emitted by a hydrogen atom are 102.6 nm and 1876 nm.a. What are the m and n values for each of these wavelengths?b. For each of these wavelengths, is the light infrared,
What is the evidence by which we know that an electron from an iron atom is identical to an electron from a copper atom?
A 2.0-cm-diameter metal sphere is glowing red, but a spectrum shows that its emission spectrum peaks at an infrared wavelength of 2.0 μm. How much power does the sphere radiate? Assume e = 1.
FIGURE Q37.6 shows a magnetic field between two parallel, charged electrodes. An electron with speed v0?passes between the plates, from left to right, with no deflection. If a proton is fired toward
What temperature, in °C, is a blackbody whose emission spectrum peaks at(a) 300 nm(b) 3.00 mm?
a. Describe the experimental evidence by which we know that the nucleus is made up not just of protons.b. The neutron is not easy to isolate or control because it has no charge that would allow
A ceramic cube 3.0 cm on each side radiates heat at 630 W. At what wavelength, in mm, does its emission spectrum peak? Assume e = 1.
Rutherford studied alpha particles using the crossed-field technique Thomson had invented to study cathode rays. Assuming that valpha ≈ vcathode ray (which turns out to be true), would the
The current in a Crookes tube is 10 nA. How many electrons strike the face of the glass tube each second?
Once Thomson showed that atoms consist of very light negative electrons and a much more massive positive charge, why didn’t physicists immediately consider a solar system model of electrons
Electrons pass through the parallel electrodes shown in FIGURE EX37.9 with a speed of 5.0 × 106m/s. What magnetic field strength and direction will allow the electrons to pass through without being
An electron in a cathode-ray beam passes between 2.5 cm-long parallel-plate electrodes that are 5.0 mm apart. A 2.0 mT, 2.5-cm-wide magnetic field is perpendicular to the electric field between the
An alpha particle (a bare helium nucleus with q = +2e) accelerates across a 100 V potential difference, starting from rest. What is the particle’s kinetic energy in eV when it reaches the negative
Identify the element, the isotope, and the charge state of each atom in FIGURE Q37.12. Give your answer in symbolic form, such as4He+or8Be-. a. b. n Pn n P. (P
A 0.80-μm-diameter oil droplet is observed between two parallel electrodes spaced 11 mm apart. The droplet hangs motionless if the upper electrode is 20 V more positive than the lower electrode. The
Suppose that in a hypothetical oil-drop experiment you measure the following values for the charges on the drops: 3.99 × 10-19 C, 6.65 × 10-19 C, 2.66 × 10-19 C, 10.64 × 10-19 C, and 9.31 ×
Determine:a. The speed of a 7.0 MeV neutron.b. The speed of a 15 MeV helium atom.c. The specific type of particle that has 1.14 keV of kinetic energy when moving with a speed of 2.0 × 107 m/s.
Determine:a. The speed of a 300 eV electron.b. The speed of a 3.5 MeV H+ ion.c. The specific type of particle that has 2.09 MeV of kinetic energy when moving with a speed of 1.0 × 107 m/s.
Express in eV (or keV or MeV if more appropriate):a. The kinetic energy of a Li++ ion that has accelerated from rest through a potential difference of 5000 V.b. The potential energy of two protons 10
Express in eV (or keV or MeV if more appropriate):a. The kinetic energy of an electron moving with a speed of 5.0 × 106 m/s.b. The potential energy of an electron and a proton 0.10 nm apart.c. The
A parallel-plate capacitor with a 1.0 mm plate separation is charged to 75 V. With what kinetic energy, in eV, must a proton be launched from the negative plate if it is just barely able to reach the
How many electrons, protons, and neutrons are contained in the following atoms or ions:(a) 10B,(b) 13N+,(c) 17O+++?
Identify the isotope that is 11 times as heavy as 12C and has 18 times as many protons as 6Li. Give your answer in the form AS, where S is the symbol for the element.
Write the symbol for an atom or ion with:a. five electrons, five protons, and six neutrons.b. five electrons, six protons, and eight neutrons.
Consider the gold isotope 197Au.a. How many electrons, protons, and neutrons are in a neutral 197Au atom?b. The gold nucleus has a diameter of 14.0 fm. What is the density of matter in a gold
Consider the lead isotope 207Pb.a. How many electrons, protons, and neutrons are in a neutral 207Pb atom?b. The lead nucleus has a diameter of 14.2 fm. What is the electric field strength at the
What is the total energy, in MeV, ofa. A proton traveling at 99% of the speed of light?b. An electron traveling at 99% of the speed of light?
What is the velocity, as a fraction of c, ofa. A proton with 500 GeV total energy?b. An electron with 2.0 GeV total energy?
The Large Hadron Collider accelerates two beams of protons, which travel around the collider in opposite directions, to a total energy of 6.5 TeV per proton. (1 TeV = 1 teraelectron volt = 1012 eV.)
The Large Hadron Collider accelerates protons to a total energy of 6.5 TeV per proton. (1 TeV = 1 teraelectron volt = 1012 eV.) What is the speed of a proton that has this energy? Give your answer as
You learned in Chapter 36 that mass has an equivalent amount of energy. What are the energy equivalents in MeV of the rest masses of an electron and a proton?
The factor g appears in many relativistic expressions. A value γ = 1.01 implies that relativity changes the Newtonian values by approximately 1% and that relativistic effects can no longer be
An electron in a cathode-ray beam passes between 2.5-cm-long parallel-plate electrodes that are 5.0 mm apart. A 1.0 mT, 2.5-cm-wide magnetic field is perpendicular to the electric field between the
The two 5.0-cm-long parallel electrodes in FIGURE P37.34 are spaced 1.0 cm apart. A proton enters the plates from one end, an equal distance from both electrodes. A potential difference ΔV = 500 V
An unknown charged particle passes without deflection through crossed electric and magnetic fields of strengths 187,500 V/m and 0.1250 T, respectively. The particle passes out of the electric field,
In one of Thomson’s experiments he placed a thin metal foil in the electron beam and measured its temperature rise. Consider a cathode-ray tube in which electrons are accelerated through a 2000 V
A neutral lithium atom has three electrons. As you will discover in Chapter 41, two of these electrons form an “inner core,” but the third—the valence electron—orbits at much larger radius.
A hydrogen atom 1H with 200 eV of kinetic energy has a headon, perfectly elastic collision with a 12C atom at rest. Afterward, what is the kinetic energy, in eV, of each atom?
The diameter of an atom is 1.2 × 10-10 m and the diameter of its nucleus is 1.0 × 10-14 m. What percent of the atom’s volume is occupied by mass and what percent is empty space?
The diameter of an aluminum atom of mass 27 u is approximately 1.2 × 10-10 m. The diameter of the nucleus of an aluminum atom is approximately 8 × 10-15 m. The density of solid aluminum is 2700
A 222Rn atom (radon) in a 0.75 T magnetic field undergoes radioactive decay, emitting an alpha particle in a direction perpendicular to B. The alpha particle begins cyclotron motion with a radius of
The polonium isotope 211Po is radioactive and undergoes alpha decay. In the decay process, a 211Po nucleus at rest explodes into an alpha particle (a 4He nucleus) and a 207Pb lead nucleus. The lead
In a head-on collision, the closest approach of a 6.24 MeV alpha particle to the center of a nucleus is 6.00 fm. The nucleus is in an atom of what element? Assume the nucleus remains at rest.
Through what potential difference would you need to accelerate an alpha particle, starting from rest, so that it will just reach the surface of a 15-fm-diameter 238U nucleus?
The oxygen nucleus 16O has a radius of 3.0 fm.a. With what speed must a proton be fired toward an oxygen nucleus to have a turning point 1.0 fm from the surface? Assume the nucleus remains at rest.b.
a. A negatively charged electroscope can be discharged by shining an ultraviolet light on it. How does this happen?b. You might think that an ultraviolet light shining on an initially uncharged
To initiate a nuclear reaction, an experimental nuclear physicist wants to shoot a proton into a 5.50-fm-diameter 12C nucleus. The proton must impact the nucleus with a kinetic energy of 3.00 MeV.
An alpha particle approaches a197Au nucleus with a speed of 1.50 × 107m/s. As FIGURE CP37.47 shows, the alpha particle is scattered at a 49? angle at the slower speed of 1.49 × 107m/s. In what
Physicists first attempted to understand the hydrogen atom by applying the laws of classical physics. Consider an electron of mass m and charge -e in a circular orbit of radius r around a proton of
Consider an oil droplet of mass m and charge q. We want to determine the charge on the droplet in a Millikan-type experiment. We will do this in several steps. Assume, for simplicity, that the charge
A classical atom orbiting at frequency f would emit electromagnetic waves of frequency f because the electron’s orbit, seen edge-on, looks like an oscillating electric dipole.a. At what radius, in
Firecracker A is 300 m from you. Firecracker B is 600 m from you in the same direction. You see both explode at the same time. Define event 1 to be “firecracker A explodes” and event 2 to be
Bjorn is standing at x = 600 m. Firecracker 1 explodes at the origin and firecracker 2 explodes at x = 900 m. The flashes from both explosions reach Bjorn’s eye at t = 3.0 μs. At what time did
Jill claims that her new rocket is 100 m long. As she flies past your house, you measure the rocket’s length and find that it is only 80 m. What is Jill’s speed, as a fraction of c?
A very fast pole vaulter lives in the country. One day, while practicing, he notices a 10.0-m-long barn with the doors open at both ends. He decides to run through the barn at 0.866c while carrying
A ball of mass m traveling at a speed of 0.80c has a perfectly inelastic collision with an identical ball at rest. If Newtonian physics were correct for these speeds, momentum conservation would tell
Some particle accelerators allow protons (p+) and antiprotons (p-) to circulate at equal speeds in opposite directions in a device called a storage ring. The particle beams cross each other at
Two rockets are each 1000 m long in their rest frame. Rocket Orion, traveling at 0.80c relative to the earth, is overtaking rocket Sirius, which is poking along at a mere 0.60c. According to the crew
An electron moving to the right at 0.90c collides with a positron moving to the left at 0.90c. The two particles annihilate and produce two gamma-ray photons. What is the wavelength of the photons?
Consider the inelastic collision e- + e- → e- + e- + e- + e+ in which an electron-positron pair is produced in a head-on collision between two electrons moving in opposite directions at the
The nuclear reaction that powers the sun is the fusion of four protons into a helium nucleus. The process involves several steps, but the net reaction is simply 4p → 4He + energy. The mass of a
The radioactive element radium (Ra) decays by a process known as alpha decay, in which the nucleus emits a helium nucleus. (These high-speed helium nuclei were named alpha particles when
The sun radiates energy at the rate 3.8 × 1026 W. The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is 2.0 × 1030 kg.a. How much
Many science fiction spaceships are powered by antimatter reactors. Suppose a 20-m-long spaceship, with a mass of 15,000 kg when empty, carries 2000 kg of fuel: 1000 kg each of matter and antimatter.
A typical nuclear power plant generates electricity at the rate of 1000 MW. The efficiency of transforming thermal energy into electrical energy is 1/3 and the plant runs at full capacity for 80% of
At what speed, as a fraction of c, is the kinetic energy of a particle twice its Newtonian value?
a. What are the momentum and total energy of a proton with speed 0.99c?b. What is the proton’s momentum in a different reference frame in which E' = 5.0 × 10-10 J?
Let’s examine whether or not the law of conservation of momentum is true in all reference frames if we use the Newtonian definition of momentum: px = mux. Consider an object A of mass 3m at rest in
A rocket is fired from the earth to the moon at a speed of 0.990c. Let two events be “rocket leaves earth” and “rocket hits moon.”a. In the earth’s reference frame, calculate Δx, Δt, and
a. Derive a velocity transformation equation for uy and u'y. Assume that the reference frames are in the standard orientation with motion parallel to the x- and x'-axes.b. A rocket passes the earth
Derive the Lorentz transformations for t and t'.
This chapter has assumed that lengths perpendicular to the direction of motion are not affected by the motion. That is, motion in the x-direction does not cause length contraction along the y- or
The half-life of a muon at rest is 1.5 μs. Muons that have been accelerated to a very high speed and are then held in a circular storage ring have a half-life of 7.5 μs.a. What is the speed, as a
What is the speed, in m/s, of a proton after being accelerated from rest through a 50 × 106 V potential difference?
Through what potential difference must an electron be accelerated, starting from rest, to acquire a speed of 0.99c?
A rocket fires a projectile at a speed of 0.95c while traveling past the earth. An earthbound scientist measures the projectile’s speed to be 0.90c. What was the rocket’s speed as a fraction of c?
Two rockets, A and B, approach the earth from opposite directions at speed 0.80c. The length of each rocket measured in its rest frame is 100 m. What is the length of rocket A as measured by the crew
Two rockets approach each other. Each is traveling at 0.75c in the earth’s reference frame. What is the speed, as a fraction of c, of one rocket relative to the other?
The star Delta goes supernova. One year later and 2.0 ly away, as measured by astronomers in the galaxy, star Epsilon explodes. Let the explosion of Delta be at xD = 0 and tD = 0. The explosions are
A rocket traveling at 0.50c sets out for the nearest star, Alpha Centauri, which is 4.3 ly away from earth. It will return to earth immediately after reaching Alpha Centauri. What distance will the
The quantity dE/dv, the rate of increase of energy with speed, is the amount of additional energy a moving object needs per 1 m/s increase in speed.a. A 25,000 kg truck is traveling at 30 m/s. How
In an attempt to reduce the extraordinarily long travel times for voyaging to distant stars, some people have suggested traveling at close to the speed of light. Suppose you wish to visit the red
On a futuristic highway, a 15-m-long rocket travels so fast that a red stoplight, with a wavelength of 700 nm, appears to the pilot to be a green light with a wavelength of 520 nm. What is the length
The Stanford Linear Accelerator (SLAC) accelerates electrons to v = 0.99999997c in a 3.2-km-long tube. If they travel the length of the tube at full speed (they don’t, because they are
A starship voyages to a distant planet 10 ly away. The explorers stay 1 year, return at the same speed, and arrive back on earth 26 years, as measured on earth, after they left. Assume that the time
Two events in reference frame S occur 10 μs apart at the same point in space. The distance between the two events is 2400 m in reference frame S'.a. What is the time interval between the events in
The star Alpha goes supernova. Ten years later and 100 ly away, as measured by astronomers in the galaxy, star Beta explodes.a. Is it possible that the explosion of Alpha is in any way responsible
A 30-m-long rocket train car is traveling from Los Angeles to New York at 0.50c when a light at the center of the car flashes. When the light reaches the front of the car, it immediately rings a
The diameter of the solar system is 10 light hours. A spaceship crosses the solar system in 15 hours, as measured on earth. How long, in hours, does the passage take according to passengers on the
One of the important ways in which the Higgs boson was detected at the Large Hadron Collider was by observing a type of decay in which the Higgs—which decays too quickly to be observed

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