Essential University Physics Global Edition

Richard Wolfson

Chapter 24

Electric Current - all with Video Answers

Educators

+ 7 more educators

Chapter Questions

Problem 1

Explain the difference between current and current density.

Vishal Gupta

Vishal Gupta

Numerade Educator

Problem 1

Why does classical physics predict that atoms should collapse?

Shital Rijal

Numerade Educator

Problem 2

A constant electric field generally produces a constant drift velocity. How is this consistent with Newton's assertion that force results in acceleration, not velocity?

Vishal Gupta

Numerade Educator

Problem 2

Looking at the night sky, you see one star that appears red, another vellow, and another blue. Compare their temperatures.

Vysakh M

Numerade Educator

Problem 3

Good conductors of electricity are often good conductors of heat. Why might this be?

Mrinal Rana

Numerade Educator

Problem 3

What colors of visible light have the highest-energy photons?

Zachary Warner

Numerade Educator

Problem 4

Does an electric stove burner draw more current when it's first turned on or when it's fully hot?

Mrinal Rana

Numerade Educator

Problem 4

Why is the immediate ejection of electrons in the photoelectric effect surprising from a classical viewpoint?

Zachary Warner

Numerade Educator

Problem 5

A person and a cow are standing in a field when lightning strikes the ground nearby. Why is the cow more likely to be electrocuted?

Mrinal Rana

Numerade Educator

Problem 5

How are the uncertainty principle and wave-particle duality related?

Zachary Warner

Numerade Educator

Problem 6

You put a 1.5-V battery across a piece of material, and a 100-mA current flows. With a 9-V battery, the current increases to $400 \mathrm{~mA}$. Is the material ohmic or not?

Mrinal Rana

Numerade Educator

Problem 6

How many spectral lines are in the entire Balmer series?

Zachary Warner

Numerade Educator

Problem 7

The resistance of a metal increases with increasing temperature, while the resistance of a semiconductor decreases. Why the difference?

Vishal Gupta

Numerade Educator

Problem 7

Why are the lines of the Lyman series in the ultraviolet while some Balmer lines are in the visible?

Zachary Warner

Numerade Educator

Problem 8

The resistance of a metal increases with increasing temperature, while the resistance of a semiconductor decreases. Why the difference?

Vishal Gupta

Numerade Educator

Problem 8

Why does the photoelectric effect suggest that light has particle-like properties?

Zachary Warner

Numerade Educator

Problem 9

Equation $24.8$ a suggests that no power can be dissipated in a superconductor because $R=0 .$ But Equation $24.8 \mathrm{~b}$ suggests the power should be infinite. Which is right, and why?

Mrinal Rana

Numerade Educator

Problem 9

Does a cricket ball of $100 \mathrm{~g}$ have a minimum velocity inside a box with sides of $1 \mathrm{~m}$ ? Explain.

James Kiss

Numerade Educator

Problem 10

What's wrong with this news report: "A power-line worker was injured when 4000 volts passed through his body"?

Mrinal Rana

Numerade Educator

Problem 10

Why are the energies given by Equations $34.12$ negative?

Zachary Warner

Numerade Educator

Problem 11

A wire carries $1.4$ A. How many electrons pass through the wire in one second?

Narayan Hari

Numerade Educator

Problem 11

If you double a blackbody's temperature, by what factor does its radiated power increase?

Narayan Hari

Numerade Educator

Problem 12

A 12-V car battery is rated at 80 ampere-hours, meaning it can supply 80 A of current for I hour before it becomes discharged. If you accidentally leave the headlights on until the battery discharges, how much charge moves through the lights?

Narayan Hari

Numerade Educator

Problem 12

Biologists measure the total current due to potassium ions moving through the membrane of a rock crab neuron cell as $29 \mathrm{nA}$. How many ions pass through the membrane each second?

Narayan Hari

Numerade Educator

Problem 12

The surface temperature of the star Rigel is $10^{4} \mathrm{~K}$. Find (a) the power radiated per square meter of its surface, (b) its $\lambda_{\text {peak }}$, and (c) its $\lambda_{\text {median- }}$

Zachary Warner

Numerade Educator

Problem 13

Seen from space, Earth is approximately a $255-\mathrm{K}$ blackbody. Find (a) $\lambda_{\text {peak }}$ and (b) $\lambda_{\text {median }}$ for Earth. (c) In what part of the spectrum do these wavelengths lie?

CB

Christina Bauer

Numerade Educator

Problem 14

Biologists measure the total current due to potassium ions moving through the membrane of a rock crab neuron cell as $29 \mathrm{nA}$. How many ions pass through the membrane each second?

Vishal Gupta

Numerade Educator

Problem 14

Spacecraft instruments measure the radiation from an asteroid, and the data show that the power per unit wavelength peaks at $40 \mu \mathrm{m}$. Assuming the asteroid is a blackbody, find its surface temperature.

Krystal K

Numerade Educator

Problem 15

UK wiring regulations specify a maximum current of $13 \mathrm{~A}$ in 1.5-mm $^{2}$ cross-sectional area copper wire. What's the corresponding current density?

Vishal Gupta

Numerade Educator

Problem 15

The Sun approximates a blackbody at $5800 \mathrm{~K}$. (a) Find the wavelength of peak radiance on the per-unit-wavelength basis implicit in Equation $34.2 \mathrm{a}$. (b) Find the median wavelength, below which half the radiation is emitted (Equation $34.2 \mathrm{~b}$ ). Identify the spectral region of each.

Zachary Warner

Numerade Educator

Problem 16

What electric field is necessary to drive a $7.5$-A current through a $0.95-\mathrm{mm}$-diameter silver wire?

Rashmi Sinha

Numerade Educator

Problem 16

Find the energy in electronvolts of (a) a $1.0-\mathrm{MHz}$ radio photon, (b) a $5.0 \times 10^{14}-\mathrm{Hz}$ optical photon, and (c) a $3.0 \times 10^{18}-\mathrm{Hz} \mathrm{X}$-ray photon.Find the energy in electronvolts of (a) a $1.0-\mathrm{MHz}$ radio photon, (b) a $5.0 \times 10^{14}-\mathrm{Hz}$ optical photon, and (c) a $3.0 \times 10^{18}-\mathrm{Hz} \mathrm{X}$-ray photon.

Vishal Gupta

Numerade Educator

Problem 17

A cylindrical tube of seawater carries $350 \mathrm{~mA}$ of current. If the electric field in the water is $21 \mathrm{~V} / \mathrm{m}$, what's the tube's diameter?

Sheh Lit Chang

University of Washington

Problem 17

The human eye is sensitive to wavelengths from about $400 \mathrm{~nm}$ to $700 \mathrm{~nm}$. What's the corresponding range of photon energies?

Zachary Warner

Numerade Educator

Problem 18

A $1.0$-cm-diameter rod carries a 50 -A current when the electric field in the rod is $1.4 \mathrm{~V} / \mathrm{m}$. What's the resistivity of the rod material?

Mrinal Rana

Numerade Educator

Problem 18

A cellphone transmits at $787 \mathrm{MHz}$ with a power of $0.600 \mathrm{~W}$. At what rate does it produce photons?

Narayan Hari

Numerade Educator

Problem 19

A $1.0$-cm-diameter rod carries a 50 -A current when the electric field in the rod is $1.4 \mathrm{~V} / \mathrm{m}$. What's the resistivity of the rod material?

Mrinal Rana

Numerade Educator

Problem 19

A red laser at $650 \mathrm{~nm}$ and a blue laser at $450 \mathrm{~nm}$ emit photons at the same rate. How do their total power outputs compare?

Zachary Warner

Numerade Educator

Problem 20

Find the resistance of a heating coil that draws $4.6 \mathrm{~A}$ when the voltage across it is $230 \mathrm{~V}$.

Narayan Hari

Numerade Educator

Problem 20

Find the maximum work function, in $\mathrm{eV}$, for a surface to emit electrons when illuminated with 990 -nm infrared light.

Narayan Hari

Numerade Educator

Problem 21

What voltage does it take to drive $200 \mathrm{~mA}$ through a $2.3-\mathrm{k} \Omega$ resistance?

Narayan Hari

Numerade Educator

Problem 21

Calculate the wavelengths of the first three lines in the Lyman series for hydrogen.

Mayukh Banik

Numerade Educator

Problem 22

What's the current in an $85-\mathrm{k} \Omega$ resistor with $220 \mathrm{~V}$ across it?

Vishal Gupta

Numerade Educator

Problem 22

Which spectral line of the hydrogen Paschen series $\left(n_{2}=3\right)$ has wavelength $954.7 \mathrm{~nm}$ ?

Narayan Hari

Numerade Educator

Problem 23

The "third rail" that carries electric power to a subway train is an iron bar whose rectangular cross section measures $10 \mathrm{~cm}$ by $15 \mathrm{~cm}$. Find the resistance of a $5.0-\mathrm{km}$ length of this rail.

Mrinal Rana

Numerade Educator

Problem 23

What's the maximum wavelength of light that can ionize hydrogen in its ground state? In what spectral region is this?

Zachary Warner

Numerade Educator

Problem 24

What current flows when a 45 -V potential difference is imposed across a $1.8-\mathrm{k} \Omega$ resistor?

Mrinal Rana

Numerade Educator

Problem 24

What's the maximum wavelength of light that can ionize hydrogen in its ground state? In what spectral region is this?

Zachary Warner

Numerade Educator

Problem 25

A uniform wire of resistance $R$ is stretched until its length doubles. Assuming its density and resistivity remain constant, what's its new resistance?

Mrinal Rana

Numerade Educator

Problem 25

Find the de Broglie wavelength of (a) Earth, orbiting the Sun at $30 \mathrm{~km} / \mathrm{s}$, and (b) an electron moving at $20 \mathrm{~km} / \mathrm{s}$.

Vishal Gupta

Numerade Educator

Problem 26

A car's starter motor draws 120 A with 11 V across ts termmals. What's its power consumption?

Narayan Hari

Numerade Educator

Problem 26

Find the de Broglie wavelength of (a) Earth, orbiting the Sun at $30 \mathrm{~km} / \mathrm{s}$, and (b) an electron moving at $20 \mathrm{~km} / \mathrm{s}$.

Vishal Gupta

Numerade Educator

Problem 27

A $4.5-\mathrm{W}$ flashlight bulb draws $750 \mathrm{~mA}$. (a) At what voltage does it operate? (b) What's its resistance?

Mrinal Rana

Numerade Educator

Problem 27

A proton and electron have the same de Broglie wavelength. How do their speeds compare, assuming $v \ll c$ for both?

Zachary Warner

Numerade Educator

Problem 28

A watch uses energy at the rate of $210 \mu \mathrm{W}$. What current does it draw from its $1.5-\mathrm{V}$ battery?

Narayan Hari

Numerade Educator

Problem 28

Find the de Broglie wavelength of electrons with kinetic energies (a) $50 \mathrm{eV}$, (b) $3.0 \mathrm{keV}$, and (c) $50 \mathrm{keV}$.

Vishal Gupta

Numerade Educator

Problem 29

A $35-\Omega$ electric stove burner consumes $1.5 \mathrm{~kW}$ of power. At what voltage does it operate?

Mrinal Rana

Numerade Educator

Problem 29

A proton is confined to a space $1 \mathrm{fm}$ wide (about the size of an atomic nucleus). What's the minimum uncertainty in its velocity?

Narayan Hari

Numerade Educator

Problem 30

An incandescent lightbulb draws $261 \mathrm{~mA}$, while an LED with the same light output draws $34.8 \mathrm{~mA}$. Both operate on standard $230-\mathrm{V}$ household power. (a) Determine their energy-consumption rates. (b) Suppose you've been operating the incandescent bulb for 3 hours a day and that your electrical energy costs $13.5$ pence per kWh. How much money will you save on your electric bills over a year if you replace the incandescent with the LED? Note than an incandescent lightbulb costs about $£ 0.7$, while you might pay $£ 7$ for an LED-and the LED will last many years.

Vishal Gupta

Numerade Educator

Problem 30

Is it possible to determine an electron's velocity accurate to $\pm 1 \mathrm{~m} / \mathrm{s}$ while simultaneously finding its position to within $\pm 1 \mu \mathrm{m}$ ? What about a proton?

Zachary Warner

Numerade Educator

Problem 31

Though rare, electrocution has been reported under wet conditions with voltages as low as $40 \mathrm{~V}$. What resistance would be necessary for this voltage to drive a fatal current of $120 \mathrm{~mA}$ ?

Narayan Hari

Numerade Educator

Problem 31

Is it possible to determine an electron's velocity accurate to $\pm 1 \mathrm{~m} / \mathrm{s}$ while simultaneously finding its position to within $\pm 1 \mu \mathrm{m}$ ? What about a proton?

Zachary Warner

Numerade Educator

Problem 32

You touch a defective appliance while standing on the ground, and you feel the tingle of a $2.5-\mathrm{mA}$ current. What's your resistance, assuming you're touching the "hot" side of the $230-\mathrm{V}$ household wiring?

Vishal Gupta

Numerade Educator

Problem 32

An electron is moving in the $+x$-direction with speed measured at $50 \mathrm{Mm} / \mathrm{s}$, accurate to $\pm 10 \%$. What's the minimum uncertainty in its position?

Zachary Warner

Numerade Educator

Problem 33

You have a typical resistance of $100 \mathrm{k} \Omega$. (a) How much current could a 12 -V car battery pass through you? (b) Would you feel this?

Mrinal Rana

Numerade Educator

Problem 33

The heaviest element known is element 118, oganesson $(\mathrm{Og})$, with nuclear diameter $15 \mathrm{fm}$. Find the minimum kinetic energy for an alpha particle (a helium-4 nucleus, with mass $6.64 \times 10^{-27} \mathrm{~kg}$ ) confined within this nucleus.

Raj Bala

Numerade Educator

Problem 34

: Modern houses are often equipped with 200-amp service, meaning that $200 \mathrm{~A}$ is the maximum current that can be supplied to the house. Such service requires $9.3 \mathrm{~mm}$ diameter copper wires bringing power to the house. Find (a) the current density and (b) the electric field in such a wire when it's carrying the full $200 \mathrm{~A}$.

Vishal Gupta

Numerade Educator

Problem 34

A Rydberg hydrogen atom is in the $n=36$ state. Find (a) its diameter and (b) the wavelength of the photon emitted when it drops to the $n=35$ state.

James Kiss

Numerade Educator

Problem 35

The maximum current rating for a certain solid copper wire is $24 \mathrm{~A}$. If the maximum allowed current density in this wire is $12 \mathrm{MA} / \mathrm{m}^{2}$, what are (a) the wire diameter and (b) the electric field in the wire at the maximum current density?

Vishal Gupta

Numerade Educator

Problem 35

A Rydberg hydrogen atom is in the $n=21$ state when it emits a photon of wavelength $\lambda=76.44 \mu \mathrm{m}$. What state is it in after the photon emission?

Vishal Gupta

Numerade Educator

Problem 36

An electrolyzer passes electric current through water, dissociating some of the water molecules and thus producing hydrogen $\left(\mathrm{H}_{2}\right)$ and oxygen $\left(\mathrm{O}_{2}\right)$ gas. Electrolyzers powered by renewable wind and solar energy sources could produce hydrogen for fuel-cell vehicles. In an experimental electrolyzer, current flows through a cylindrical tube of diameter $6.85 \mathrm{~cm}$. The tube contains an alkaline solution that decreases the resistivity to $0.0466 \Omega \cdot \mathrm{m}$. If the tube carries $18.7 \mathrm{~A}$, what are (a) the current density and (b) the electric field in the solution?

Vishal Gupta

Numerade Educator

Problem 36

Doubly ionized lithium $\left(\mathrm{Li}^{2+}\right)$ is a singleelectron species, like hydrogen except for the greater charge on its nucleus. That results in a Rydberg constant that's greater than hydrogen's by a factor of the square of the ratio of the nuclear charges. Find the wavelength of the spectral line associated with the transition from $n=3$ to $n=2$ in doubly ionized lithium.

Dominador Tan

Numerade Educator

Problem 37

The solar corona is the Sun's hot $(\sim 1 \mathrm{MK})$ outer atmosphere. It's so hot that it's essentially fully ionized and is therefore an excellent electrical conductor. A cylindrical section of the corona has resistivity $1.62 \times 10^{-8} \Omega \cdot \mathrm{m}$ (slightly better than copper at room temperature) and carries a current of $464 \mathrm{kA}$ along the long dimension of the cylindrical region. Given that the current density in the region is $1.18 \mathrm{~mA} / \mathrm{m}^{2}$, find (a) the diameter of the region and (b) the electric field in the region.

Vishal Gupta

Numerade Educator

Problem 37

Doubly ionized lithium $\left(\mathrm{Li}^{2+}\right)$ is a singleelectron species, like hydrogen except for the greater charge on its nucleus. That results in a Rydberg constant that's greater than hydrogen's by a factor of the square of the ratio of the nuclear charges. Find the wavelength of the spectral line associated with the transition from $n=3$ to $n=2$ in doubly ionized lithium.

Dominador Tan

Numerade Educator

Problem 38

:You've got a $1.5$-m length of a wire that has diameter $0.51 \mathrm{~mm}$ and is rated for a maximum current of $3.5 \mathrm{~A}$. Find (a) the resistance of the wire and (b) the voltage from one end to the other when it's carrying its maximum rated current.

Vishal Gupta

Numerade Educator

Problem 38

Find the minimum kinetic energy for a proton confined inside a uranium-238 nucleus, whose diameter is $15 \mathrm{fm}$.

Ankur S

Numerade Educator

Problem 39

A potential difference of $235 \mathrm{mV}$ is imposed across a $2.25-\mathrm{m}$ length of a wire whose diameter is $0.640 \mathrm{~mm}$. As a result, a $1.27-\mathrm{A}$ current flows in the wire. (a) Is the wire made of aluminum or copper? (b) What would be the current if the wire were made of the other of those two materials?

Vishal Gupta

Numerade Educator

Problem 39

The outermost electrons in boron have kinetic energy on the order of $8 \mathrm{eV}$. Use this value (a crude estimate based partly on classical physics) to make an uncertainty-principle estimate of the diameter of the boron atom.

Jake Rempel

Numerade Educator

Problem 40

Find the length of the electrolyzer tube in Example Variation Problem 36 , if the voltage driving current through the tube is $162 \mathrm{~V}$.

Jake Rempel

Numerade Educator

Problem 40

An experimental transistor confines an electron in a region $1.45 \mathrm{~nm}$ wide. Find the minimum kinetic energy for this electron, expressed in eV.

Narayan Hari

Numerade Educator

Problem 41

Find the length of the electrolyzer tube in Example Variation Problem 36 , if the voltage driving current through the tube is $162 \mathrm{~V}$.

Jake Rempel

Numerade Educator

Problem 41

Thermal energy at room temperature is about 25 meV. You're designing an electronic device to operate at room temperature, and you want the kinetic energy associated with the uncertainty principle not to exceed the thermal energy. What's the minimum width in which your device can confine an electron?

Jake Rempel

Numerade Educator

Problem 42

An ion channel in a cell membrane carries $2.4 \mathrm{pA}$ when it's open, which is only $20 \mathrm{~s}$ of the time. (a) What's the average current in the channel? (b) If the channel opens for $1.0 \mathrm{~ms}$, how many singly ionized ions pass through in this time?

Sheh Lit Chang

University of Washington

Problem 42

Find the power per unit area emitted by a $2780-\mathrm{K}$ incandescent lightbulb filament in a wavelength interval $0.100 \mathrm{~nm}$ wide centered on $645 \mathrm{~nm}$. (This interval is narrow enough that you don't need to integrate to apply Equation 34.3.)

Jake Rempel

Numerade Educator

Problem 43

A lightbulb filament has diameter $0.046 \mathrm{~mm}$ and carries $0.326 \mathrm{~A}$. Find the current density (a) in the filament and (b) in the $1.5-\mathrm{mm}^{2}$ cross-sectional area wire supplying current to the lightbulb.

Vishal Gupta

Numerade Educator

Problem 43

Treating the Sun as a $5800-\mathrm{K}$ blackbody, compare its UV radiance at $200 \mathrm{~nm}$ with its visible radiance at its $500-\mathrm{nm}$ peak wavelength.

Zachary Warner

Numerade Educator

Problem 44

A gold film in an integrated circuit measures $1.85 \mu \mathrm{m}$ thick by $0.120 \mathrm{~mm}$ wide. It carries a current density of $0.482 \mathrm{MA} / \mathrm{m}^{2}$. What's the total current?

Mrinal Rana

Numerade Educator

Problem 44

wavelength.
For a 2.0-kK blackbody, by what percentage is the Rayleigh-Jeans law in error at wavelengths of (a) $1.0 \mathrm{~mm}$, (b) $10 \mu \mathrm{m}$, and (c) $1.0 \mu \mathrm{m}$ ?

Jake Rempel

Numerade Educator

Problem 45

A copper wire joins an aluminum wire whose diameter is twice that of the copper. The same current flows in both wires. The density of conduction electrons in copper is $1.1 \times 10^{29} \mathrm{~m}^{-3}$; in aluminum it's $2.1 \times 10^{29} \mathrm{~m}^{-3}$. Compare (a) the drift speeds and (b) the current densities in each wire.

Mrinal Rana

Numerade Educator

Problem 46

In Fig. 24.17, a 100-mA current flows through a copper wire $0.10 \mathrm{~mm}$ in diameter, a salt solution in a $1.0$-cm-diameter glass tube, and a vacuum tube where the current is carried by an electron beam $1.0 \mathrm{~mm}$ in diameter. The density of conduction electrons in copper is $1.1 \times 10^{29} \mathrm{~m}^{-3}$. The current in the solution is carried equally by positive and negative ions with charges $\pm 2 e$; the density of each ion species is $6.5 \times 10^{23} \mathrm{~m}^{-3}$. The electron density in the beam is $2.1 \times 10^{16} \mathrm{~m}^{-3}$. Find the drift speed in each region.
Vacuum

Penny Riley

Numerade Educator

Problem 46

Earth's surface approximates a blackbody at $288 \mathrm{~K}$. Find the power emitted by Earth's entire surface (a) in the visible wavelength interval from $0.550$ to $0.551 \mu \mathrm{m}$ and (b) in the infrared between $10.000 \mu \mathrm{m}$ and $10.001 \mu \mathrm{m}$. Your answer helps explain why greenhouse gases, which strongly absorb infrared radiation at around $10 \mu \mathrm{m}$, have such a significant effect on Earth's climate. (Note: The wavelength interval here is so small that, for the point this problem is making, you don't need to integrate to apply Equation 34.3.)

Dominador Tan

Numerade Educator

Problem 47

The single most important use of the element gold is for wires that join integrated circuits to the conducting pads that then connect microelectronic chips with external circuitry. A typical application uses gold wires $1.0 \mathrm{mil}(0.001$ inch) in diameter and $50 \mathrm{mil}$ long. Although the current under normal conditions is much less, such a wire will fuse (that is, melt and interrupt the current) when the current exceeds some $600 \mathrm{~mA}$. Find (a) the current density in the wire, (b) the electric field in the wire, and (c) the voltage between the ends of the wire, all when this maximum current is flowing.

Vishal Gupta

Numerade Educator

Problem 47

Find the rate of photon production by (a) a radio antenna broadcasting $1.5 \mathrm{~kW}$ at $89.5 \mathrm{MHz}$, (b) a laser producing $1.4 \mathrm{~mW}$ of $633-\mathrm{nm}$ light, and $(\mathrm{c})$ an $\mathrm{X}$-ray machine producing $0.10-\mathrm{nm}$ $\mathrm{X}$-rays with total power $2.6 \mathrm{~kW}$.

Nishant Kumar

Numerade Educator

Problem 48

The single most important use of the element gold is for wires that join integrated circuits to the conducting pads that then connect microelectronic chips with external circuitry. A typical application uses gold wires $1.0 \mathrm{mil}(0.001$ inch $)$ in diameter and $50 \mathrm{mil}$ long. Although the current under normal conditions is much less, such a wire will fuse (that is, melt and interrupt the current) when the current exceeds some $600 \mathrm{~mA}$. Find (a) the current density in the wire, (b) the electric field in the wire, and (c) the voltage between the ends of the wire, all when this maximum current is flowing.

Vishal Gupta

Numerade Educator

Problem 48

Electrons in a photoelectric experiment emerge from an aluminum surface with maximum kinetic energy $1.3 \mathrm{eV}$. Find the wavelength of the illuminating radiation.

Zachary Warner

Numerade Educator

Problem 49

The maximum safe current in a $2.5-\mathrm{mm}^{2}$ cross-sectional area copper wire is $20 \mathrm{~A}$. Find (a) the current density and (b) the electric field under these conditions.

Vishal Gupta

Numerade Educator

Problem 49

(a) Find the cutoff frequency for the photoelectric effect in copper. (b) Find the maximum energy of the ejected electrons if the copper is illuminated with light of frequency $2.1 \times 10^{15} \mathrm{~Hz}$.

Ankur S

Numerade Educator

Problem 50

Silver and iron wires of the same length and diameter carry the same current. How do the voltages across the two compare?

Mrinal Rana

Numerade Educator

Problem 50

The stopping potential in a photoelectric experiment is $1.8 \mathrm{~V}$ when the illuminating radiation has wavelength $365 \mathrm{~nm}$. Determine (a) the work function of the emitting surface and (b) the stopping potential for $280-n m$ radiation.

Vishal Gupta

Numerade Educator

Problem 51

You have a cylindrical piece of material $2.4 \mathrm{~cm}$ long and $2.0 \mathrm{~mm}$ in diameter. When you attach a 9-V battery to its ends, a 2.6-mA current flows. Which material from Table $24.1$ do you have?

Mrinal Rana

Numerade Educator

Problem 51

Chlorophyll is a photosynthetic molecule common in green plants. On a per-unit-wavelength basis, its ability to absorb visible light has two peaks, at $430 \mathrm{~nm}$ and $662 \mathrm{~nm}$. (a) Find the corresponding photon energies. (b) Use these peak wavelengths to explain why plants appear green.

Dominador Tan

Numerade Educator

Problem 52

How must the diameters of copper and aluminum wire be related if they're to have the same resistance per unit length?

Mrinal Rana

Numerade Educator

Problem 52

Find the initial wavelength of a photon that loses half its energy when it Compton-scatters from an electron and emerges at $90^{\circ}$ to its initial direction.

Zachary Warner

Numerade Educator

Problem 53

You're writing the instruction manual for a power saw, and you have to specify the maximum permissible length for an extension cord made from $1.5-\mathrm{mm}^{2}$ cross-sectional area copper wire. The saw draws $13.0 \mathrm{~A}$ and needs a minimum of $225 \mathrm{~V}$ across its motor when the outlet supplies $230 \mathrm{~V}$. What do you specify for the maximum length extension cord, given that they come in 5 -meter increments?

Vishal Gupta

Numerade Educator

Problem 53

its initial direction.
When light shines on potassium, the photoelectrons' maximum speed is $5.0 \times 10^{5} \mathrm{~m} / \mathrm{s}$. Find the light's wavelength.

Narayan Hari

Numerade Educator

Problem 54

An implanted pacemaker supplies the heart with 72 pulses per minute, each pulse providing $6.8 \mathrm{~V}$ for $0.68 \mathrm{~ms}$. The resistance of the heart muscle between the pacemaker's electrodes is $550 \Omega$. Find (a) the current that flows during a pulse, (b) the energy delivered in one pulse, and (c) the average power supplied by the pacemaker.

Vishal Gupta

Numerade Educator

Problem 54

The maximum electron energy in a photoelectric experiment is $2.8 \mathrm{eV}$. When the wavelength of the illuminating radiation is increased by $50 \%$, the maximum energy drops to $1.1 \mathrm{eV}$. Find (a) the work function of the emitting surface and (b) the original wavelength.

Zachary Warner

Numerade Educator

Problem 55

A rectangular pad made of gold is used as a bonding site for wires connecting to an integrated circuit. The pad measures $0.254 \mathrm{~mm}$ by $0.186 \mathrm{~mm}$ by $2.00 \mu \mathrm{m}$ thick. Find the resistance between each of the three pairs of faces, assuming the faces are equipotentials. List in order from lowest to highest resistance.

Jake Rempel

Numerade Educator

Problem 55

A 160 -pm X-ray photon Compton-scatters off an electron and emerges at $135^{\circ}$ to its original direction. Find (a) the wavelength of the scattered photon and (b) the electron's kinetic energy.

Jake Rempel

Numerade Educator

Problem 56

Each pulse produced by the Taser described in the Application on page 476 typically delivers $100 \mu \mathrm{C}$ of charge to the victim. Use this value, along with other quantities given in the Application, to find (a) the instantaneous current during a pulse, (b) the average current, and (c) the effective resistance of the victim between the points where the probes make contact.

Mrinal Rana

Numerade Educator

Problem 56

Find the kinetic energy of an initially stationary electron after a $0.40-\mathrm{nm}$ X-ray photon scatters from it at $90^{\circ}$.

Narayan Hari

Numerade Educator

Problem 57

The Nissan Leaf is an all-electric car powered by a 107 -hp electric motor and a lithium-ion battery that stores $24 \mathrm{kWh}$ and produces $394 \mathrm{~V}$ at its terminals when fully charged. The Leaf's battery can charge at the rate of $6.3 \mathrm{~kW}$ from a standard $230-\mathrm{V}$ power outlet and at $44 \mathrm{~kW}$ using a special $480-\mathrm{V}$ charger. The Leaf's fuel economy is $3.38$ miles per $\mathrm{kWh}$, the equivalent of 114 miles per gallon in a gasoline-powered car. Find (a) the range of the Leaf, assuming the battery can be fully depleted, (b) the charging time for each mode, and (c) the current delivered by the fully charged battery when the motor is operating at full power.

Penny Riley

Numerade Educator

Problem 57

An electron is known to be somewhere inside a carbon nanotube that's $370 \mathrm{~nm}$ long and $1.2 \mathrm{~nm}$ in diameter. Find the minimum uncertainties in the components of its velocity (a) along the tube and (b) perpendicular to the tube's long dimension.

Rashmi Sinha

Numerade Educator

Problem 58

An electric heater is tested by immersing it in $0.500 \mathrm{~kg}$ of water and measuring the time $\Delta t$ it takes to raise the water temperature by $10.0^{\circ} \mathrm{C}$. The experiment is repeated for different currents $I$ through the heater, and the results are tabulated below. Determine two quantities, based on heating time and current, which, when plotted, will give a straight line. Make your plot, determine a bestfit line, and use it to find the heater's resistance.

Narayan Hari

Numerade Educator

Problem 58

A scanning electron microscope accelerates electrons through a potential difference of $3.35 \mathrm{kV}$. What's the electrons' wavelength?

Vishal Gupta

Numerade Educator

Problem 59

(a) Determine the power associated with the Io-to-Jupiter current described in Example Variation Problem 41 . (b) Compare your answer in (a) with humankind's electrical energy consumption rate, approximately $22,000 \mathrm{TWh}$ per year.

Narayan Hari

Numerade Educator

Problem 59

A scanning electron microscope accelerates electrons through a potential difference of $3.35 \mathrm{kV}$. What's the electrons' wavelength?

Vishal Gupta

Numerade Educator

Problem 60

At a particular point in a material with resistivity $\rho$ the current density has magnitude $J$. Show that the power per unit volume dissipated at this point is $J^{2} \rho$.

Mrinal Rana

Numerade Educator

Problem 60

(a) Find the highest possible energy for a photon emitted as the electron jumps between two adjacent energy levels in the Bohr hydrogen atom. (b) Which energy levels are involved?

Zachary Warner

Numerade Educator

Problem 61

A thermally insulated container of seawater carries a uniform current density of $75 \mathrm{~mA} / \mathrm{cm}^{2}$. How long does it take for its temperature to increase from $15^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$ ? Use the result of the preceding problem and any other information you might look up.

James Kiss

Numerade Educator

Problem 61

(a) Find the highest possible energy for a photon emitted as the electron jumps between two adjacent energy levels in the Bohr hydrogen atom. (b) Which energy levels are involved?

Zachary Warner

Numerade Educator

Problem 62

Two cylindrical resistors are made from the same material and have the same length. When connected across the same battery, one dissipates twice as much power as the other. How do their diameters compare?

Mrinal Rana

Numerade Educator

Problem 62

The wavelengths of a spectral line series tend to a limit as $n_{1} \rightarrow \infty$. Evaluate the series limit for (a) the Lyman series and (b) the Balmer series in hydrogen.

Zachary Warner

Numerade Educator

Problem 63

Two cylindrical resistors are made from the same material and have the same length. When connected across the same battery, one dissipates twice as much power as the other. How do their diameters compare?

Mrinal Rana

Numerade Educator

Problem 63

A Rydberg hydrogen atom makes a downward transition to the $n=225$ state, emitting a $9.32-\mu \mathrm{eV}$ photon. What was the original state?

Prabhat Tyagi

Numerade Educator

Problem 64

You're working on a new high-speed rail system. It uses 6000 -horsepower electric locomotives, getting power from a single overhead wire with resistance $15 \mathrm{~m} \Omega / \mathrm{km}$, at $22 \mathrm{kV}$ potential relative to the track. Current returns through the track, whose resistance is negligible. Energy-efficiency standards call for no more than $3 \%$ power loss in the wire. How far from the power plant can the train go and still meet this standard?

James Kiss

Numerade Educator

Problem 64

A hydrogen atom is in its ground state when its electron absorbs a $50-\mathrm{eV}$ photon. What's the energy of the resulting free electron?

Vishal Gupta

Numerade Educator

Problem 65

A $100 \%$-efficient electric motor is lifting a $20-\mathrm{N}$ weight at $30 \mathrm{~cm} / \mathrm{s}$. How much current does it draw from a $6.0-\mathrm{V}$ battery?

Vishal Gupta

Numerade Educator

Problem 65

How much energy does it take to ionize a hydrogen atom in its first excited state?

Zachary Warner

Numerade Educator

Problem 66

A $100 \%$-efficient electric motor is lifting a $20-\mathrm{N}$ weight at $30 \mathrm{~cm} / \mathrm{s}$. How much current does it draw from a $6.0-\mathrm{V}$ battery?

Vishal Gupta

Numerade Educator

Problem 66

A cosmic ray particle passes through a 1 -cm-thick energymeasuring detector at very nearly the speed of light. What's the uncertainty in the particle's energy as measured in the detector's reference frame?

James Kiss

Numerade Educator

Problem 67

You're estimating costs for a new power line with your company's financial group. Engineering specifies a resistance of $50 \mathrm{~m} \Omega$ per kilometer for the line. The costs and densities of copper and aluminum are, respectively, \$6.86/kg and $8.9 \mathrm{~g} / \mathrm{cm}^{3}$, and \$2.23/kg and $2.7 \mathrm{~g} / \mathrm{cm}^{3}$. Determine the cost per meter of each type of wire. Which is more economical?

Vishal Gupta

Numerade Educator

Problem 67

Find the minimum electron speed that would make an electron microscope superior to an optical microscope using $460-\mathrm{nm}$ light.

Vishal Gupta

Numerade Educator

Problem 68

A $240-\mathrm{V}$ electric motor is $90 \%$ efficient, meaning that $90 \%$ of the energy supplied to it ends up as mechanical work. If the motor lifts a $200-\mathrm{N}$ weight at $3.4 \mathrm{~m} / \mathrm{s}$, how much current does it draw?

Vishal Gupta

Numerade Educator

Problem 68

You're a cell biologist who wants to image microtubules that form the "skeletons" of living cells. The microtubules are $25 \mathrm{~nm}$ in diameter, and, as Chapter 32 shows, you need to image with waves whose wavelength is at least this small. You can use either an inexpensive electron microscope that accelerates electrons to kinetic energies of $40 \mathrm{keV}$, or a more expensive unit that produces 100-keV electrons. Will the less expensive microscope work?

James Kiss

Numerade Educator

Problem 69

A metal bar has rectangular cross section $5.0 \mathrm{~cm}$ by $10 \mathrm{~cm}$, as shown in Fig. $24.18$. The bar has a nonuniform conductivity, and as a result the current density increases linearly from zero at the bottom to $0.10 \mathrm{~A} / \mathrm{cm}^{2}$ at the top. Find the total current in the bar.

Mrinal Rana

Numerade Educator

Problem 69

An electron is trapped in a "quantum well" $15 \mathrm{~nm}$ wide. Find its minimum possible speed.

James Kiss

Numerade Educator

Problem 70

An immersion-type heating
coil is connected to a $230-\mathrm{V}$
outlet and immersed in a $250-\mathrm{mL}$ cup of water initially at $10^{\circ} \mathrm{C}$.
The water comes to a boil in $89 \mathrm{~s}$. Assuming no heat loss, andneglecting the heater's mass, find (a) the power and (b) the heater's resistance.

Vishal Gupta

Numerade Educator

Problem 70

Typically, an atom remains in an excited state for about $10^{-8} \mathrm{~s}$ before it drops to a lower state, emitting a photon in the process. What's the uncertainty in the energy of this transition?

Zachary Warner

Numerade Educator

Problem 71

A circular pan of radius $b$ has a plastic bottom and metallic sidewall of height $h$. It's filled with a solution of resistivity $\rho$. A metal disk of radius $a$ and height $h$ is at the center, as shown in Fig. 24.19. The side and disk are essentially perfect conductors. Show that the resistance measured from side to disk is $R=\rho \ln (b / a) / 2 \pi h$.

Ajay Singhal

Numerade Educator

Problem 71

An electron is moving at $10^{6} \mathrm{~m} / \mathrm{s}$ and you wish to measure its energy to an accuracy of $\pm 0.01 \%$. What's the minimum time necessary for this measurement?

Zachary Warner

Numerade Educator

Problem 72

The current density in a particle beam with circular cross section of radius $a$ points along the beam axis with a magnitude that decreases linearly from $J_{0}$ at the center $(r=0)$ to half that value at the edge $(r=a)$. Find an expression for the total current in the beam.

Sheh Lit Chang

University of Washington

Problem 72

Use the series expansion for $e^{x}$ (Appendix A) to show that Planck's law (Equation $34.3$ ) reduces to the Rayleigh-Jeans law (Equation 34.5) when $\lambda \gg h c / k T$.

Ren Jie Tuieng

Numerade Educator

Problem 73

You work for an automobile manufacturer developing a new plug-in hybrid car. The car's mass is $1200 \mathrm{~kg}$, and it uses a 360 - V battery driving an electric motor that can handle a maximum current of 190 A. You're to specify the greatest slope the car can climb, maintaining $68 \mathrm{~km} / \mathrm{h}$, without its gasoline engine coming on to assist.

Vishal Gupta

Numerade Educator

Problem 73

A photon's wavelength is equal to the Compton wavelength of a particle with mass $m$. Show that the photon's energy is equal to the particle's rest energy.

Zachary Warner

Numerade Educator

Problem 74

During the brownout, the current in conductors whose resistance is nearly independent of temperature
a. decreases by approximately $10 \%$.
b. decreases by approximately $20 \%$.
c. decreases by approximately $5 \%$.
d. You can't tell without knowing the resistance.

James Kiss

Numerade Educator

Problem 74

Show that the frequency range of the hydrogen spectral line series involving transitions ending at the $n$th level is $\Delta f=c R_{\mathrm{H}} /(n+1)^{2}$.

Zachary Warner

Numerade Educator

Problem 75

Which of the following occurs in the conductors of the preceding problem during the brownout?
a. Both the electric field and electron drift speed decrease.
b. The electric field decreases but the electron drift speed doesn't.
c. The current is carried by fewer electrons.
d. The electrons undergo more frequent collisions.

Mrinal Rana

Numerade Educator

Problem 75

A photon undergoes a $90^{\circ}$ Compton scattering off a stationary electron, and the electron emerges with total energy $\gamma m_{e} c^{2}$, where $\gamma$ is the relativistic factor introduced in Chapter 33 . Find an expression for the initial photon energy.

Zachary Warner

Numerade Educator

Problem 76

During the brownout, the power dissipated in conductors whose resistance is nearly independent of temperature
a. decreases by approximately $10 \%$.
b. decreases by approximately $20 \%$.
c. decreases by approximately $5 \%$.
d. You can't tell without knowing the resistance.

Mrinal Rana

Numerade Educator

Problem 76

Show that Wien's law (Equation $34.2 \mathrm{a}$ ) follows from Planck's law (Equation 34.3). Hint: Differentiate Planck's law with respect to wavelength.

Zachary Warner

Numerade Educator

Problem 77

Metallic conductors like lightbulb filaments and electric stove burners have resistance that increases with increasing temperature. During the brownout, the current in such devices
a. decreases by $10 \%$.
b. decreases by more than $10 \%$.
c. decreases by less than $10 \%$.
d. You can't tell without knowing more about how the resistance varies.

Mrinal Rana

Numerade Educator

Problem 77

Consider an elastic collision between a photon with initial wavelength $\lambda_{0}$ moving in the $x$-direction and a stationary electron, as depicted in Fig. $34.8 b$. Use relativistic expressions for energy and momentum from Chapter 33 to show that conservation of energy and momentum yield the equations $h c / \lambda_{0}+m c^{2}=h c / \lambda+\gamma m c^{2}, h / \lambda_{0}=(h / \lambda) \cos \theta+\gamma m u \cos \phi$, and $0=(h / \lambda) \sin \theta-\gamma m u \sin \phi$, where $\lambda$ is the post-collision photon wavelength and the angles $\theta$ and $\phi$ are as shown in Fig. $34.8 b$. Solve these equations to find the Compton shift (Equation 34.8).

Lainey Roebuck

Numerade Educator

Problem 78

Integrate Equation $34.3$ over all wavelengths to get the total power radiated per unit area. Show that your result is equivalent to Equation $34.1$, with the Stefan-Boltzmann constant given by $\sigma=2 \pi^{5} k^{4} / 15 c^{2} h^{3}$.

Dominador Tan

Numerade Educator

Problem 79

Perform a numerical integration of Equation $34.3$ to the wave$P$ length given by Equation $34.2 \mathrm{~b}$. Divide by the result of Problem 78 , and thus verify that Equation $34.2 \mathrm{~b}$ gives the wavelength above and below which a blackbody radiates half its energy.

Zachary Warner

Numerade Educator

Problem 80

Show that in the Bohr model, the frequency of a photon emitted in a transition between levels $n+1$ and $n$, in the limit of large $n$, is equal to the electron's orbital frequency. (This is an example of Bohr's correspondence principle.)

Zachary Warner

Numerade Educator

Problem 81

The table below lists the stopping potential as a function of wave-
length in a photoelectric effect experiment. Determine quantities
to plot that should yield a straight line. Make your plot, establish
a best-fit line, and use your line to determine (a) an experimental
value for Planck's constant and (b) the work function of the ma-
terial comprising the photocathode. (c) Use Table $34.1$ to identify
the material.

Dominador Tan

Numerade Educator

Problem 82

Which of the curves in Fig. $34.15$ represents the particle with the shortest lifetime?
a. $A$
b. B
c. $\mathrm{C}$
d. You can't tell from the graph.

Dominador Tan

Numerade Educator

Problem 83

An energy uncertainty of $1 \mathrm{MeV}$ corresponds to a particle lifetime closest to
a. $10^{-34} \mathrm{~s}$.
b. $10^{-21} \mathrm{~s}$.
c. $10^{-9} \mathrm{~s}$.

Ankur S

Numerade Educator

Problem 84

The converse approach is used for particles with longer lifetimes: Direct measurement of the lifetime yields, through energy-time uncertainty, a range of expected values for particle energies or masses. The longer the lifetime,
a. the wider the mass range and the narrower the energy range.
b. the wider the mass and energy ranges.
c. the narrower the mass range and the wider the energy range.
d. the narrower the mass and energy ranges.

Zachary Warner

Numerade Educator

Problem 85

For a particle with lifetime $10^{-7} \mathrm{~s}$, the corresponding mass range is closest to
a. $10^{-44} u$.
b. $10^{-27} \mathrm{u}$.
c. $10^{-17} \mathrm{u}$.
d. Iu.

Ankur S

Numerade Educator