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essential university physics

Questions and Answers of Essential University Physics

Photovoltaic (PV) cells convert sunlight energy directly into electricity, with no moving parts (recall Fig. 37.21). In a PV cell, photons incident on a semiconductor PN junction promote electrons to
Substitute the wave function ψ2 of Equation 36.7 into Equation 36.4 to verify that the equation is satisfied and that the energy is given by Equation 36.6 with n = 2.
Figure 35.19 shows an infinite square well with a step-like potential at the bottom. Sketch qualitatively what you think a wave function might look like for a particle whose energy is (a) less than
Particle physicists use the energy–time uncertainty relation to estimate the lifetimes of unstable particles produced in high-energy particle accelerators (Chapter 39). Some particles have
Particle physicists use the energy–time uncertainty relation to estimate the lifetimes of unstable particles produced in high-energy particle accelerators (Chapter 39). Some particles have
Particle physicists use the energy–time uncertainty relation to estimate the lifetimes of unstable particles produced in high-energy particle accelerators (Chapter 39). Some particles have
Particle physicists use the energy–time uncertainty relation to estimate the lifetimes of unstable particles produced in high-energy particle accelerators (Chapter 39). Some particles have
Use the momentum conservation equations given in Problem 77 and Equation 34.8 for the Compton shift to show that the electron’s recoil angle in Fig. 34.9b is given by tanϕ = sinθ/[(1 +
A source emitting light with frequency f moves toward you at speed u. By considering both time dilation and the effect of wave fronts “piling up” as shown in Fig. 14.33, show that you measure a
A Cassegrain telescope like that shown in Fig. 31.34b has 1.0-m focal length, and the convex secondary mirror is located 0.85m from the primary. What should be the focal length of the secondary in
For common materials like glass, the wavelength dependence of the refractive index at visual wavelengths is given approximately by n(λ) = b + c/ λ2 , where b and c are constants. The table below
Repeat Problem 38 for the case n = 1.75, α = 40°, and θ1 = 25°.
The table below shows the intensity of the radio signal received at Earth from a spacecraft on its way to the outer solar system, as a function of its distance from Earth. Distances are in
Differentiate Equation 29.12 with respect to x and Equation 29.13 with respect to t. Then, using the fact that mixed derivatives are equal (e.g., ), combine the resulting equations and show that
A long, flat conducting bar of width w carries a total current I distributed uniformly, as shown in Fig. 26.48. Use approximations to write expressions for the magnetic field strength (a) near the
The coaxial cable shown in Fig. 26.47 consists of a solid inner conductor of radius a and a hollow outer conductor of inner radius b and thickness c. The two carry equal but opposite currents I,
Write the node and loop equations for the circuit in Fig. 25.23a (Example 25.6), and find the time constant.
An electric heater is tested by immersing it in 0.500 kg of water and measuring the time ∆t it takes to raise the water temperature by 10.0°C. The experiment is repeated for different currents I
Engineers testing an ultracapacitor (see Application on page 420) measure the capacitor’s stored energy at different voltages. The table below gives the results. Determine a quantity that, when you
Using the dipole potential at points far from a dipole (given by Equation 22.6 in Example 22.5), show that the electric field at an arbitrary position can be written Where the x-axis coincides with
Show that the result of Example 22.8 approaches the field of a point charge for x >>a. (You’ll need to apply the binomial approximation from Appendix A to the expression .)
Problem 76 of Chapter 13 explored what happened to a person falling into a hole extending all the way through Earth’s center and out the other side, assuming that g(r) = g0(1r/RE) for points inside
A thin rod carries charge Q distributed uniformly over its length L and is situated on the x-axis between x ±L/2.(a) Find the electric field at an arbitrary point (x, y).(You’ll have to do
Figure 20.35 shows a thin, uniformly charged disk of radius R. Imagine the disk divided into rings of varying radii r, as suggested in the figure. (a) Show that the area of such a ring is very
Figure 20.34 shows a thin rod of length L carrying charge Qdistributed uniformly over its length.(a) What’s the line chargedensity on the rod? (b) Modify the calculation of Example 20.7to find an
You pick up an old astronomy book and read that the Hubble constant is 17 km/s/Mly. You know that today’s more accurate value is 20.8 km/s/Mly. Use the simplified reasoning of Example 39.2 to
A galaxy’s hydrogen-β spectral line, normally at 486.1 nm, appears at 495.4 nm.(a) Use the Doppler shift of Chapter 14 to find the galaxy’s recession speed, (b) infer the distance to the
Before the high-precision cosmological data from the Planck spacecraft became available in 2013, the best estimate for the Hubble constant was 22.7 km/s/Mly. Repeat Example 39.2 using this value for
Express the Hubble constant in SI units.
Repeat Exercise 32 for the 1015 GeV energy of grand unification. Section 39.5 The Evolving UniverseData from Problem 32Estimate the temperature in a gas of particles such that the thermal energy kT
What data provide the most robust confirmation of cosmological theory as well as the most precise values for cosmological parameters?
If the hypothetical graviton is ever discovered, what should its mass be? Use Yukawa’s argument and the fact that the gravitational force falls as 1/r2.
The radiation that we observe as the cosmic microwave background started out largely as infrared. Why is it now the microwave background?
What medical diagnostic procedure makes use of the fact that every particle has an antiparticle? What particle/antiparticle pair is involved?
Explain how particle accelerators can help us understand the early universe.
Describe the origin of the cosmic microwave background.
Is it possible for a charged particle to be its own antiparticle?
How can Hubble’s law hold without the universe having a center?
Why do we need higher-energy particle accelerators to explore fully the standard model?
What forces would be unified by GUTs?
What forces are unified in the electroweak theory?
Name the fundamental force involved in(a) binding of a proton and a neutron to make a deuterium nucleus;(b) decay of a neutron to a proton, an electron, and a neutrino;(c) binding of an electron and
Classify(a) mesons(b) baryons as fermions or bosons, and relate your classification to the particles’ quark compositions.
What’s the role of gluons?
Describe the relation between the strong force and the nuclear force.
Why are we unlikely to observe an isolated quark?
What coordinates are changed under the inversion processes P and T?
How are baryons fundamentally different from leptons?
How can we follow the tracks of individual particles?
Why did Yukawa conclude that the particle mediating the strong force should have nonzero mass?
How much 235U would be needed to fuel the reactor of Exercise 37 for 1 year?
Rework Example 38.2, now using the international guideline of 100 Bq/kg for milk.
Why would it have been easier to make bombs fueled with uranium-235 a few billion years ago?
Squeezing a particular solid in all directions reduces the interatomic spacing to 76.6% of its equilibrium value; the result is that the solid’s total potential energy becomes zero. Find the value
You’re troubled that Example 37.1 neglects the mass of the hydrogen, and you wonder how much error this introduces. So you consider a diatomic molecule consisting of different atoms with masses m1
The density of rubidium iodide (RbI) is 3.55 g/cm3 , and its ionic cohesive energy is -145 kcal/mol. Determine(a) the equilibrium separation(b) the exponent n in Equation 37.4 for RbI.
Use the result of Problem 47 to determine the Fermi energy for calcium, which has 4.6x1028 conduction electrons per cubic meter.
The Fermi energy in aluminum is 11.6 eV. Use the result of Problem 47 to find the density of conduction electrons in aluminum.
For the HCl molecule of Example 37.2, determine (a) the energy of the vibrational ground state and (b) the energies of photons emitted in transitions among adjacent vibrational states, for the cases
Use the answer in the back of the book for Problem 59 to find the bond length in carbon monoxide (CO), given that excitation of the first rotational state requires photons of wavelength 2.59 mm.
Find the energies of the first four rotational states of the HCl molecule described in Example 37.1.
Repeat Exercise 25 for the case where you know only that the principal quantum number is 3; that is, l might have any of its possible values.
Adapt part (b) of Example 36.1 to find the probability that an electron in the hydrogen ground state will be found beyond two Bohr radii.
Solve the final equation of Problem 59 to find all possible values of ∈ for (a) μ = 2, (b) μ = 20, and (c) μ = 50. You’ll need to use a numerical root-finding routine on a calculator or
A photon undergoes a 90° Compton scattering off a stationary electron, and the electron emerges with total energy γmec2 , where g is the relativistic factor introduced in Chapter 33. Find an
Find the maximum work function, in eV, for a surface to emit electrons when illuminated with 945-nm infrared light. Section 34.4 Atomic Spectra and the Bohr Atom
Could there be observers who would judge the two events in Problem 40 to be simultaneous? If so, how fast and in what direction must these observers be moving?Data From Problem 39You’re writing a
For the soap film described in Conceptual Example 32.1’s “Making the Connection,” what portion of the film will appear dark when it’s illuminated with white light?
Find the second-order angular separation of the two wavelengths in Example 32.2.
Consider the inverse of Example 31.4: You’re inside a 70.0-cmdiameter hollow tube containing air, and the tip of your nose is 15.0cm from the tube’s wall. The tube is immersed in water, and a
Rework Example 31.4 for a fish 15.0 cm from the far wall of the tank.
LCD projectors commonly used for computer and video projection create an image on a small LCD display (see Application on page 369). The display is mounted before a lens and illuminated from behind.
Reconsider Example 30.4, now in a glass with n700 = 1.482 and n400 = 1.615. Determine what happens to the red and violet light with these respective wavelengths, and speculate on what happens to the
Suppose the red and blue beams of Exercise 26 are now propagating in the same direction inside the glass. For what range of incidence angles on the glass–air interface will one beam be totally
Find the refractive index of a material for which the polarizing angle in air is 62°. Section 30.3 Total Internal Reflection
Use appropriate data from Appendix E to calculate the radiation pressure on a light-absorbing object at the Sun’s surface.
Although the maximum current flows in the speaker circuit of Example 28.4 at the 1-kHz resonant frequency, the peak voltage across the capacitor is a maximum at a somewhat lower frequency. Find that
Find a second frequency where the current in the speaker of Example 28.4 has half its maximum value.
Electroencephalography (EEG) elucidates brain function by analyzing brain waves, AC voltages resulting from electrical activity in the brain. Alpha waves are brain waves with frequencies from 7.5Hz
Use the node and loop laws to determine the current in R2 as a function of time after the switch is closed in Conceptual Example 27.1.
How long does it take to dissipate 90% of the magnetic energy in Example 27.9?
In a series RL circuit like Fig. 27.23a, ε0 = 45 V, R = 3.3 Ω, and L = 2.1 H. If the current is 9.5 A, how long has the switch been closed?
In Example 27.2 take a = 1.0 cm, w = 3.5 cm, and l = 6.0 cm. Suppose the rectangular loop is a conductor with resistance 50 mΩ, and the current I in the long wire is increasing at 25 A/s. Find the
Find an expression for the electric-field strength inside the solenoid of Example 27.10, a distance r from the axis. Problems
Suppose the current sheet in Example 26.9 is actually a slab with non-negligible thickness d and that the current is distributed uniformly throughout its volume. Find an expression for the magnetic
In standard household wiring, parallel wires about 1 cm apart carry currents of about 15 A. What’s the force per unit length between these wires? Section 26.6 Magnetic Dipoles
For the circuit of Example 25.6, take ε = 100 V, R1 = 4.0 kΩ, and R2 = 6.0 kΩ, and assume the capacitor is initially uncharged. Find the capacitor voltage and the currents in both resistors(a)
Find an expression for the voltage across the capacitor in Example 25.6 when it’s fully charged.
Find I2 in Example 25.4 for the case ε2= 2.0 V.
You’re heading out for spring break, but your car won’t start. Your friend says you might have corrosion at the battery terminals a frequent cause of hard starting because of increased
Each pulse produced by the Taser described in the Application on page 449 typically delivers 100 μC of charge to the victim. Use this value, along with other quantities given in the Application, to
A typical lightning flash transfers 30 C across a potential difference of 30 MV. Assuming such flashes occur every 5 s in the thunderstorm of Example 23.4, roughly how long would the storm last if
(a) How much charge must be transferred between the initially uncharged plates of the capacitor in Exercise 19 in order to store 15 mJ of energy? (b) What will be the resulting potential difference
Find an equation describing the V = 0 equipotential in the x-y plane for the situation of Conceptual Example 22.1. That is, find a relation between x and y that holds on this equipotential.
Use the result of Example 22.6 to determine the on-axis field of a charged ring, and verify that your answer agrees with the result of Example 20.6.
Dielectric breakdown of air occurs at fields of 3 MV/m. Find(a) the maximum potential (measured from infinity) for the sphere of Example 22.3 before dielectric breakdown occurs at the sphere’s

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