Question: The diffraction pattern of a small circular

> What is the orbital radius of the electron in the n = 3 state of hydrogen?

> A hydroelectric power plant is situated at the base of a dam. Water exits the power plant 120 m below the top of the reservoir at a speed of about 4 m/s (at atmospheric pressure). The volume flow rate of water through the power plant is 1000 m3/s. The pl

> By directly substituting the values of the fundamental constants, show that the ground state energy for hydrogen in the Bohr model E1 = −mek2e4/(2ℏ2) has the numerical value −13.6 eV.

> Consider an induction stove utilizing a primary heating coil located just beneath the stove top. The circuit elements in the stove supply the coil with a peak ac voltage of 340 V at a frequency of 50 kHz. The coil has 18 turns; its inductance is 80 µH an

> By directly substituting the values of the fundamental constants, show that the Bohr radius a0 = ℏ2/(meke2) has the numerical value 5.29 × 10−11 m.

> Suppose a power plant produces 800 kW of power and is to send that power for many miles over a copper wire with a total resistance of 12 Ω. (a) If the power is sent across the copper wires at 48 kV rms, how much current flows through the wires? (b) Wha

> A fluorescent solid absorbs a photon of ultraviolet light of wavelength 320 nm. If the solid dissipates 0.500 eV of the energy and emits the rest in a single photon, what is the wavelength of the emitted light?

> Oliver has a mass of 76.2 kg. He is riding in an elevator that has a downward acceleration of 1.37 m/s2. With what magnitude force does the elevator floor push upward on Oliver?

> A parallel plate capacitor has two plates, each of area 3.0 × 10−4 m2, separated by 3.5 × 10−4 m. The space between the plates is filled with a dielectric. When the capacitor is connected to a source of 120 V rms at 8.0 kHz, an rms current of 1.5 × 10−4

> The Paschen series in the hydrogen emission spectrum is formed by electron transitions from ni > 3 to nf = 3. (a) What is the longest wavelength in the Paschen series? (b) What is the wavelength of the series limit (the lower bound of the wavelengths i

> An RLC series circuit is connected to a 240 V rms power supply at a frequency of 2.50 kHz. The elements in the circuit have the following values: R = 12.0 Ω, C = 0.26 µF, and L = 15.2 mH. (a) What is the impedance of the circuit? (b) What is the rms cu

> If an atom had only four distinct energy levels between which electrons could make transitions, how many spectral lines of different wavelengths could the atom emit?

> (a) What is the reactance of a 5.00 µF capacitor at the frequencies f = 12.0 Hz and 1.50 kHz? (b) What is the impedance of a series combination of the 5.00 µF capacitor and a 2.00 kΩ resistor at the same two frequencies? (c) What is the maximum current

> A hydrogen atom has an electron in the n = 5 level. (a) If the electron returns to the ground state by emitting radiation, what is the minimum number of photons that can be emitted? (b)What is the maximum number that might be emitted?

> In an RLC circuit, these three elements are connected in series: a resistor of 20.0 Ω, a 35.0 mH inductor, and a 50.0 µF capacitor. The ac source of the circuit has an rms voltage of 100.0 V and an angular frequency of 1.0 × 103 rad/s. (a) Find the rms

> The hydrogen atom emits a photon when making a transition between energy levels ni → nf. Rank the transitions according to the wavelength of the emitted photon, largest to smallest. (a) 4 → 2; (b) 3 → 1; (c) 2 → 1; (d) 3 → 2; (e) 4 → 3; (f) 5 → 4.

> A 40.0 mH inductor, with internal resistance of 30.0 Ω, is connected to an ac source (a) What is the impedance of the inductor in the circuit? (b) What are the peak and rms voltages across the inductor (including the internal resistance)? (

> Starting with the energy-momentum relation and the definition of total energy, show that (pc)2 = K2 + 2KE0 [Eq. (26-23)].

> A student, looking toward his fourth-floor dormitory window, sees a flowerpot with nasturtiums (originally on a window sill above) pass his 1.0 m high window in 0.051 s. The distance between floors in the dormitory is 4.0 m. From a window on which floor

> A certain circuit has a 25 Ω resistor and one other component in series with a 12 V (rms) sinusoidal ac source. The rms current in the circuit is 0.317 A when the frequency is 150 Hz and increases by 25.0% when the frequency increases to 250 Hz. (a) Wha

> Derive the energy-momentum relation Start by squaring the definition of total energy (E = K + E0) and then use the relativistic expressions for momentum and kinetic energy [Eqs. (26-15) and (26-18)].

> Transformers are often rated in terms of kilovoltamps. A pole on a residential street has a transformer rated at 35 kVA to serve four homes on the street. (a) If each home has a fuse that limits the incoming current to 60 A rms at 220 V rms, find the ma

> In a beam of electrons used in a diffraction experiment, each electron is accelerated to a kinetic energy of 150 keV. (a) Are the electrons relativistic? Explain. (b) How fast are the electrons moving?

> (a) Calculate the rms current drawn by the load in the figure with Problem 88 if / kV and the average power supplied by the generator is 12 MW. (b) Suppose that the average power supplied by the generator is still 12 MW, but the load is not purely resi

> For a nonrelativistic particle of mass m, show that K = p2/(2m). [Hint: Start with the nonrelativistic expressions for kinetic energy K and momentum p.]

> A generator supplies an average power of 12 MW through a transmission line that has a resistance of 10.0 Ω. What is the power loss in the transmission line if the rms line voltage / is (a) 15 kV and (b) 110 kV? What percentage of the tota

> An experimental form of cancer therapy involves the use of a beam of highly ionized carbon atoms with a charge of +6e (all six electrons have been removed). The mass of the ions is 11.172 GeV/c2. If the accelerator is 7.50 m long and the ions are acceler

> A variable inductor is connected to a voltage source whose frequency can vary. The rms current is Ii. If the inductance is increased by a factor of 3.0 and the frequency is reduced by a factor of 2.0, what will be the new rms current in the circuit? The

> In a medical treatment known as fast-neutron therapy, neutrons of kinetic energy 25 MeV are directed toward a patient's tumor. Neutrons are known to decay, when at rest, with an average lifetime of 886 s. What is the lifetime, as measured in the laborato

> A person stands on a bathroom scale in an elevator. Rank the scale readings from highest to lowest based on the given information about the speed v or the magnitude of the acceleration a. (a) ascending with increasing speed (a = 1.0 m/s2); (b) descendi

> An antibaryon with charge +e composed of up and/or strange quarks and/or antiquarks.

> An RLC circuit has a resistance of 255 Ω, an inductance of 146 mH, and a capacitance of 877 nF. (a) What is the resonant frequency of this circuit? (b) If this circuit is connected to a sinusoidal generator with a frequency 0.50 times the resonant frequ

> PET scans involve the use of positron-emitting isotopes like carbon-11 and fluorine-18. These isotopes can be produced at hospital-based accelerators that first accelerate deuterons (hydrogen-2 nuclei) and then direct the deuterons onto a solid or gaseou

> (a) When the resistance of an RLC series circuit that is at resonance is doubled, what happens to the power dissipated? (b) Now consider an RLC series circuit that is not at resonance. For this circuit, the initial resistance and impedance are related b

> A typical hospital accelerator built for proton beam therapy accelerates protons from rest by passing them through an electric potential difference of magnitude 75 MV. Find the speed of these protons.

> An ac series circuit containing a capacitor, inductor, and resistance is found to have a current of amplitude 0.50 A for a source voltage of amplitude 10.0 V at an angular frequency of 200.0 rad/s. The total resistance in the circuit is 15.0 Ω. (a) What

> An electron accelerator used in a hospital for cancer treatment produces a beam of electrons with kinetic energy 25 MeV. (a) What is the speed of the electrons produced by this accelerator? (b) If the end of the electron accelerator is placed 15 cm fro

> A large coil used as an electromagnet has a resistance of R = 450 Ω and an inductance of L = 2.47 H. The coil is connected to an ac source with a voltage amplitude of 2.0 kV and a frequency of 9.55 Hz. (a) What is the power factor? (b) What is the impe

> An electron has a total energy of 6.5 MeV. What is its momentum (in MeV/c)?

> A variable capacitor is connected in series to an inductor with negligible internal resistance and of inductance 2.4 × 10−4 H. The combination is used as a tuner for a radio. If the lowest frequency to be tuned in is 0.52 MHz, what is the maximum capacit

> When an electron travels at 0.60c, what is its total energy in mega- electron-volts?

> A 15 kg crate starts at rest at the top of a 60.0° incline. The coefficients of friction are μs = 0.40 and μk = 0.30. The crate is connected to a hanging 8.0 kg box by an ideal rope and pulley. (a) As the crate slides down the incline, what is the tensi

> What is the rms current flowing in a 4.50 kW motor connected to a 220 V rms line when (a) the power factor is 1.00 and (b) when it is 0.80?

> A laboratory observer measures an electron's energy to be 1.02 × 10−13 J. What is the electron's speed?

> At what frequency does the maximum current flow through a series RLC circuit containing a resistance of 4.50 Ω, an inductance of 440 mH, and a capacitance of 520 pF?

> The energy to accelerate a starship comes from combining matter and antimatter. When this is done, the total rest energy of the matter and antimatter is converted to other forms of energy. Suppose a starship with a mass of 2.0 × 105 kg accelerates to 0.3

> An alternator supplies a peak current of 4.68 A to a coil. The voltage of the alternator is 420 V peak at 60.0 Hz. When a capacitor of 38.0 µF is placed in series with the coil, the power factor is found to be 1.00. Find (a) the inductive reactance of t

> A white dwarf is a star that has exhausted its nuclear fuel and lost its outer mass so that it consists only of its dense, hot inner core. It will cool unless it gains mass from some nearby star. It may form a binary system with such a star and gradually

> A capacitor to be used in a radio is to have a reactance of 6.20 Ω at a frequency of 520 Hz. What is the capacitance?

> A capacitor is rated at 0.025 µF. How much rms current flows when the capacitor is connected to a 110 V rms, 60.0 Hz line?

> An eagle can determine that two light brown shrews sitting 1.0 cm apart on a pathway 125 m below her are in fact two shrews rather than a small rat. Assuming that only diffraction limits her ability to resolve the two shrews, estimate the diameter of her

> A projectile is launched at t = 0 with initial speed vi at an angle θ above the horizontal. (a) What are vx and vy at the projectile's highest point? (b) Find the time t at which the projectile reaches its maximum height. (c) Show that th

> The field coils used in an ac motor are designed to have a resistance of 0.45 Ω and an impedance of 35.0 Ω. What inductance is required if the frequency of the ac source is (a) 60.0 Hz? (b) 0.20 kHz?

> The radio telescope at Arecibo, Puerto Rico, has a reflecting spherical bowl of 305 m (1000 ft) diameter. Radio signals can be received and emitted at various frequencies with appropriate antennae at the focal point of the reflecting bowl. At a frequency

> A coil with an internal resistance of 120 Ω and inductance of 12.0 H is connected to a 60.0 Hz, 110 V rms line. (a) What is the impedance of the coil? (b) Calculate the current in the coil.

> A beam of yellow laser light (590 nm) passes through a circular aperture of diameter 7.0 mm. What is the angular width of the central diffraction maximum formed on a screen?

> An x-ray machine uses 240 kV rms at 60.0 mA rms when it is operating. If the power source is a 420 V rms line, (a) what must be the turns ratio of the ideal transformer? (b) What is the rms current in the primary? (c) What is the average power used by

> The Hubble Space Telescope (HST) has excellent resolving power because there is no atmospheric distortion of the light. Its 2.4 m diameter primary mirror can collect light from distant galaxies that formed early in the history of the universe. How far ap

> A 22 kV power line that is 10.0 km long supplies the electric energy to a small town at an average rate of 6.0 MW. (a) If a pair of aluminum cables of diameter 9.2 cm are used, what is the average power dissipated in the transmission line? (b) Why is a

> One way to measure the width of a narrow object is to examine its diffraction pattern. When laser light is shone on a long, thin object, such as a straightened strand of human hair, the resulting diffraction pattern has minima at the same angles as for a

> What is the rms voltage of the oscilloscope trace of the figure, assuming that the signal is sinusoidal? The central horizontal line represents zero volts. The oscilloscope voltage knob has been clicked into its calibrated position.

> Light of wavelength 490 nm is incident on a narrow slit. The diffraction pattern is viewed on a screen 3.20 m from the slit. The distance on the screen between the central maximum and the third minimum is 2.5 cm. What is the width of the slit?

> You are designing a high-speed elevator for a new skyscraper. The elevator will have a mass limit of 2400 kg (including passengers). For passenger comfort, you choose the maximum ascent speed to be 18 m/s, the maximum descent speed to be 10 m/s, and the

> A portable heater is connected to a 60 Hz ac outlet. How many times per second is the instantaneous power a maximum?

> The diffraction pattern from a single slit is viewed on a distant screen. Using violet light, the width of the central maximum is 2.0 cm. (a) Would the central maximum be narrower or wider if red light is used instead? (b) If the violet light has wavel

> The phasor diagram for a particular RLC series circuit is shown in the figure. If the circuit has a resistance of 100 Ω and is driven at a frequency of 60 Hz, find (a) the current amplitude, (b) the capacitance, and (c) the inductance.

> Light from a red laser passes through a single slit to form a diffraction pattern on a distant screen. If the width of the slit is increased by a factor of two, what happens to the width of the central maximum on the screen?

> For a particular RLC series circuit, the capacitive reactance is 12.0 Ω, the inductive reactance is 23.0 Ω, and the maximum voltage across the 25.0 Ω resistor is 8.00 V. (a) What is the impedance of the circuit? (b) What is the maximum voltage across th

> Light of wavelength 630 nm is incident on a single slit with width 0.40 mm. The figure shows the pattern observed on a screen positioned 2.0 m from the slit. Determine the distance from the center of the central bright fringe to the second minimum on one

> A parallel plate capacitor is used in a series RLC circuit along with a 0.650 H inductor. When the space between the plates is filled with a dielectric with k = 5.50, the resonant frequency is 220 Hz. Now the dielectric is removed, leaving air between th

> The first two dark fringes on one side of the central maximum in a single-slit diffraction pattern are 1.0 mm apart. The wavelength of the light is 610 nm, and the screen is 1.0 m from the slit. What is the slit width?

> A square loop of wire of side 2.3 cm and electrical resistance 79 Ω is near a long straight wire that carries a current of 6.8 A in the direction indicated. The long wire and loop both lie in the plane of the page. The left side of the loop i

> The central bright fringe in a single-slit diffraction pattern from light of wavelength 476 nm is 2.0 cm wide on a screen that is 1.05 m from the slit. (a) How wide is the slit? (b) How wide are the first two bright fringes on either side of the centra

> What is the ground-state electron configuration of tellurium (Te, atomic number 52)?

> A circular conducting coil with radius 2.6 cm is placed in a vertical magnetic field of 0.33 T. The coil is made of copper wire with a diameter of 0.90 mm. The coil starts in a horizontal plane and is flipped over (rotated 180° about a horizontal axis) i

> A grating spectrometer is used to resolve wavelengths 660.0 nm and 661.4 nm in second order. (a) How many slits per centimeter must the grating have to produce both wavelengths in second order? (The answer is either a maximum or a minimum number of slit

> In the past, bicycles used small bottle-shaped dc generators to power the headlight. A small wheel (the top of the “bottle”) in contact with a tire caused the shaft of the generator to rotate. Suppose the generator has 150 turns of wire in a circular coi

> A grating 1.600 cm wide has exactly 12000 slits. The grating is used to resolve two nearly equal wavelengths in a light source: λa = 440.000 nm and λb = 440.936 nm. (a) How many orders of the lines can be seen with the grating? (b) What is the angular

> A square loop of wire is made up of 50 turns of wire, 45 cm on each side. The loop is immersed in a 1.4 T magnetic field perpendicular to the plane of the loop. The loop of wire has little resistance but it is connected to two resistors in parallel as sh

> White light containing wavelengths from 400 nm to 700 nm is shone through a grating. Assuming that at least part of the third-order spectrum is present, show that the second- and third-order spectra always overlap, regardless of the slit separation of th

> Compare the electric energy that can be stored in a capacitor to the magnetic energy that can be stored in an inductor of the same size (i.e., the same volume). For the capacitor, assume that air is between the plates; the maximum electric field is then

> A spectrometer is used to analyze a light source. The screen-to- grating distance is 50.0 cm, and the grating has 5000.0 slits/cm. Spectral lines are observed at the following angles: 12.98°, 19.0°, 26.7°, 40.6°, 42.4°, 63.9°, and 77.6°. (a) How many di

> A 15.0 g conducting rod of length 1.30 m is free to slide downward between two vertical rails without friction. The ends of the rod maintain electrical contact with the rails. The rails are connected to an 8.00 Ω resistor, and the entire appa

> A reflection grating spectrometer is used to view the spectrum of light from a helium discharge tube. The three brightest spectral lines seen are red, yellow, and blue in color. These lines appear at the positions labeled A, B, and C in the figure, thoug

> A suspension bridge is 60.0 m above the level base of a gorge. A stone is thrown or dropped from the bridge. Ignore air resistance. At the location of the bridge g has been measured to be 9.83 m/s2. (a) If you drop the stone, how long does it take for it

> An ideal solenoid (N1 turns, length ℓ1, radius r1) is placed inside another ideal solenoid (N2 turns, length ℓ2 > ℓ1, radius r2 > r1) such that the axes of the two coincide. If the current in the outer solenoid is changing at a rate ΔI2/Δt, what is the m

> A grating is made of exactly 8000 slits; the slit spacing is 1.50 µm. Light of wavelength 0.600 µm is incident normally on the grating. (a) How many maxima are seen in the pattern on the screen? (b) Sketch the pattern that would appear on a screen 3.0

> An ideal inductor of inductance L is connected to an ac power supply, which provides an emf ℰ(t) = ℰm sin ωt. (a) Write an expression for the current in the inductor as a function of time. (b) What is the ratio of the maximum emf to the maximum current

> A grating has 5000.0 slits/cm. How many orders of violet light of wavelength 412 nm can be observed with this grating?

> The magnetic field between the poles of an electromagnet is 2.6 T. A coil of wire is placed in this region so that the field is parallel to the axis of the coil. The coil has electrical resistance 25 Φ and radius 1.8 cm. When the current supply to the el

> Red light of 650 nm appears in orders 1, 2 and 3 using a particular grating. What are the minimum and maximum possible number of slits per centimeter in this grating?

> A bar magnet is initially far from a circular loop of wire. The magnet is moved at constant speed along the axis of the loop. It moves toward the loop, proceeds to pass through it, and then continues until it is far away on the right side of the loop. Sk

> A red line (wavelength 630 nm) in the third order overlaps with a blue line in the fourth order for a particular grating. What is the wavelength of the blue line?

> A 50 turn coil with a radius of 10.0 cm is mounted so the coil’s axis can be oriented in any horizontal direction. Initially the axis is oriented so the magnetic flux from Earth’s field is maximized. If the coil’s axis is rotated through 90.0° in 0.080 s

> A refracting telescope is 45.0 cm long, and the caption states that the telescope magnifies images by a factor of 30.0. Assuming these numbers are for viewing an object an infinite distance away with minimum eyestrain, what is the focal length of each of

> An electron is confined in a one-dimensional box of length L. Another electron is confined in a box of length 2L. Both are in the ground state. What is the ratio of their energies E2L/EL?

> A flip coil is a device used to measure a magnetic field. A coil of radius r, N turns, and electrical resistance R is initially perpendicular to a magnetic field of magnitude B. The coil is connected to a special kind of galvanometer that measures the to

> You have a set of converging lenses with focal lengths 1.00 cm, 10.0 cm, 50.0 cm, and 80.0 cm. (a) Which two lenses would you select to make a telescope with the largest magnifying power? What is the angular magnification of the telescope when viewing a

> A CRT requires a 20.0 kV amplitude power supply. (a) What is the turns ratio of the transformer that raises the 170 V amplitude household voltage to 20.0 kV? (b) If the tube draws 82 W of power, find the currents in the primary and secondary windings.

> What is the distance between the objective and eyepiece in the Yerkes telescope? (See Example 24.8.)