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 10 W laser emits a beam of light 4.0 mm in diameter. The laser is aimed at the Moon. By the time it reaches the Moon, the beam has spread out to a diameter of 85 km. Ignoring absorption by the atmosphere, what is the intensity of the light (a) just ou
> (a) Find the magnitude of the orbital angular momentum L for an electron with n = 2 and I = 1 in terms of ħ. (b) What are the allowed values for Lz? (c) What are the angles between the positive z-axis and / so that the quantized components, Lz, have a
> Energy carried by an EM wave coming through the air can be used to light a bulb that is not connected to a battery or plugged into an electric outlet. Suppose a receiving antenna is attached to a bulb and the bulb is found to dissipate a maximum power of
> An electron in a hydrogen atom has quantum numbers: n = 8; mℓ = 4. What are the possible values for the orbital angular momentum quantum number ℓ of the electron?
> A sinusoidal EM wave has an electric field amplitude Em = 32.0 mV/m. What are the intensity and average energy density? [Hint: Recall the relationship between amplitude and rms value for a quantity that varies sinusoidally.]
> What is the electronic configuration of the ground state of the carbon atom? Write it in the following ways: (a) using spectroscopic notation (1s2 …); (b) listing the four quantum numbers for each of the electrons. Note that there may be more than one
> An unpolarized beam of light (intensity I0) is moving in the x- direction. The light passes through three ideal polarizers whose transmission axes are (in order) at angles 0.0°, 45.0°, and 30.0° counterclockwise from the y-axis in the yz-plane. (a) What
> A muon and an antimuon, each with a mass that is 207 times greater than an electron, were at rest when they annihilated and produced two photons of equal energy. What is the wavelength of each of the photons?
> Polarized light of intensity I0 is incident on a pair of ideal polarizing sheets. Let θ1 and θ2 be the angles between the direction of polarization of the incident light and the transmission axes of the first and second sheets, respectively. Show that th
> A photon passes near a nucleus and creates an electron and a positron, each with a total energy of 8.0 MeV. What was the wavelength of the photon?
> Yolanda, whose mass is 64.2 kg, is riding in an elevator that has an upward acceleration of 2.13 m/s2. What force does she exert on the floor of the elevator?
> The range of wavelengths allotted to the radio broadcast band is from about 190 m to 550 m. If each station needs exclusive use of a frequency band 10 kHz wide, how many stations can operate in the broadcast band?
> A positron emission tomography (PET) scanner detects 511 keV photons emitted when positrons and electrons annihilate each other. What is the wavelength of the photons?
> A 2.0 mW laser pointer has a beam diameter of 1.5 mm. When it is accidentally pointed at a person’s eye, the beam is focused to a spot of diameter 20.0 µm on the retina and the retina is exposed for 80 ms. (a) What is the intensity of the laser beam? (b
> A photon with a wavelength in the visible region (between 400 and 700 nm) causes a transition from the n to the (n + 1) state in doubly ionized lithium (Li2+). What is the lowest value of n for which this could occur?
> (a) What is the total energy of a single pulse? (b) What is the intensity during a pulse?
> (a) Find the energies of the first four levels of doubly ionized lithium (Li2+), starting with n = 1. (b) What are the energies of the photons emitted or absorbed when the electron makes a transition between these levels? (c) Are any of the photons in t
> a) In what part of the EM spectrum is the laser pulse? (b) How long (in centimeters) is a single pulse of the laser in air? (c) How many wavelengths fit in one pulse?
> Find the energy in electron-volts required to remove the remaining electron from a doubly ionized lithium (Li2+) atom.
> Two identical television signals are sent between two cities that are 400.0 km apart. One signal is sent through the air, and the other signal is sent through a fiber optic network. The signals are sent at the same time, but the one traveling through air
> Find the Bohr radius of doubly ionized lithium (Li2+).
> What’s the quickest way to make a U-turn at constant speed? Suppose that you need to make a 180° turn on a circular path. The minimum radius (due to the car’s steering system) is 5.0 m, while the maximum (due to the width of the road) is 20.0 m. Your acc
> The antenna on a wireless router radiates microwaves at a frequency of 5.0 GHz. What is the maximum length of the antenna if it is not to exceed half of a wavelength?
> (a) What is the difference in radius between the n = 1 state and the n = 2 state for hydrogen? (b) What is the difference in radius between the n = 100 state and the n = 101 state for hydrogen? How do the neighboring orbital separations compare for larg
> Astronauts on the Moon communicated with mission control in Houston via EM waves. There was a noticeable time delay in the conversation due to the round-trip transit time for the EM waves between the Moon and Earth. How long was the time delay?
> 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
> 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?
> The diffraction pattern of a small circular object has minima at the same angles as the diffraction pattern of a circular hole of the same diameter. By shining a laser on a sample of human blood, one can observe the diffraction pattern from red blood cel
> 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
