Physics
Physics
1st Edition
Walker
ISBN: 9780133256925
Table of contents
Textbook solutions

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Page 909: Standardized Test Prep

Exercise 1
Step 1
1 of 2
It does not allow for electrons to be radiating when in a fixed orbit.
Result
2 of 2
(C)
Exercise 2
Step 1
1 of 2
Thomson Pudding Model – a historical fact
Result
2 of 2
(A)
Exercise 3
Step 1
1 of 2
The orbital radius for an electron in Bohr’s theory $r_n$ is given by:

$$
begin{align}
r_n=(5.3times 10^{-11}text{m})n^2
end{align}
$$

where $n$ is the principal quantum number.

For the first orbit $n=1$, we denote the radius as $r_1=R$

$$
begin{align*}
r_1=5.3times 10^{-11}text{m}=R
end{align*}
$$

For the third orbit $n=3$, the corresponding radius $r_3$ is given by

$$
begin{align*}
boxed{r_3}=(5.3times 10^{-11}text{m})3^2=boxed{9R}
end{align*}
$$

In other words, Bohr’s radius for the third orbit is nine times greater than Bohr’s orbit for the first orbit.

Result
2 of 2
D) $9R$
Exercise 4
Step 1
1 of 2
In Bohr’s theory, the energy of an electron $E_n$ in a particular orbit which is characterized by the principal quantum number $n$ is given by

$$
begin{align*}
E_n=frac{k}{n^2}
end{align*}
$$

where $k$ is a constant. For the $n=1$ orbit, the energy of the electron $E_1$ is given by

$$
begin{align*}
E_1=E=frac{k}{1^2}=k
end{align*}
$$

Thus, we can write the energy of the electron in the $n$-th orbit $E_n$ as

$$
begin{align*}
boxed{E_n}=frac{k}{n^2}=boxed{frac{E}{n^2}}
end{align*}
$$

Result
2 of 2
D) $frac{E}{n^2}$
Exercise 5
Step 1
1 of 4
$textbf{Known}$

The frequency of the emitted light $nu$ when an electron jumps from an orbit $n_i$ to an orbit $n_f$ is given by

$$
begin{align}
nu=frac{-13.6text{eV}}{h} left( frac{1}{n_f^2}-frac{1}{n_i^2} right)
end{align}
$$

where $h=6.62times 10^{-34}text{Js}$ is Planck’s constant.

Step 2
2 of 4
$textbf{Given}$

The inital orbit $n_i$ is

$$
begin{align*}
n_i=4
end{align*}
$$

The final orbit $n_f$ is

$$
begin{align*}
n_f=3
end{align*}
$$

Step 3
3 of 4
$textbf{Calculation}$

In order to calculate the frequency of the photon $nu$, we just plug in the numerical values for the intial $n_i$ and final orbit $n_f$ into Eq. (1). But first, we will express the numerical value of Planck’s constant $h$ in the units of electron-volts using the relationship

$$
begin{align*}
1text{J}=6.24times 10^{18}text{eV}
end{align*}
$$

Finally, we calculate the frequency $nu$ as

$$
begin{align*}
boxed{nu}&=frac{-13.6text{eV}}{h} left( frac{1}{n_f^2}-frac{1}{n_i^2} right)\
&=frac{-13.6text{eV}}{6.62times 10^{34} times 6.24times 10^18 text{eV}} left( frac{1}{3^2}-frac{1}{4^2} right)\
&=boxed{1.6times 10^{14}text{Hz}}
end{align*}
$$

Result
4 of 4
D) $1.6times 10^{14}text{Hz}$
Exercise 6
Step 1
1 of 4
$textbf{Knowns}$

The wavelength of the emitted/absorbed photon $lambda$ occuring in a hydrogen atom electron transition is given by

$$
begin{align}
lambda=frac{hc}{triangle E}
end{align}
$$

where $h=41.31times 10^{-16}text{eV}$ is Planck’s constant, $c=3times 10^8frac{text{m}}{text{s}}$ is the speed of light in vacuum and $triangle E$ is the energy difference between two particular electron orbits.

Step 2
2 of 4
$textbf{Calculation}$

A) From the given diagram, we read the energy difference $triangle E$ between the orbits $n=4$ and $n=2$

$$
begin{align*}
triangle E=2.55text{eV}
end{align*}
$$

From Eq. (1), we calculate the wavelength of the photon $lambda$

$$
begin{align*}
boxed{lambda}&=frac{hc}{triangle E}\
&=frac{41.31times 10^{-16}text{eV} times 3 times 10^8frac{text{m}}{text{s}}}{2.55text{eV}}\
&=boxed{486text{nm}}
end{align*}
$$

The wavelength correspoding to this electron transition belongs to the region of visible light.

B) From the given diagram, we read the energy difference $triangle E$ between the orbits $n=4$ and $n=1$

$$
begin{align*}
triangle E=12.75text{eV}
end{align*}
$$

From Eq. (1), we calculate the wavelength of the photon $lambda$

$$
begin{align*}
boxed{lambda}&=frac{hc}{triangle E}\
&=frac{41.31times 10^{-16}text{eV} times 3 times 10^8frac{text{m}}{text{s}}}{12.75text{eV}}\
&=boxed{97.2text{nm}}
end{align*}
$$

The wavelength correspoding to this electron transition does not belong to the region of visible light.

Step 3
3 of 4
C) From the given diagram, we read the energy difference $triangle E$ between the orbits $n=3$ and $n=1$

$$
begin{align*}
triangle E=12.09text{eV}
end{align*}
$$

From Eq. (1), we calculate the wavelength of the photon $lambda$

$$
begin{align*}
boxed{lambda}&=frac{hc}{triangle E}\
&=frac{41.31times 10^{-16}text{eV} times 3 times 10^8frac{text{m}}{text{s}}}{12.09text{eV}}\
&=boxed{102.5text{nm}}
end{align*}
$$

The wavelength correspoding to this electron transition does not belong to the region of visible light.

D) From the given diagram, we read the energy difference $triangle E$ between the orbits $n=3$ and $n=2$

$$
begin{align*}
triangle E=1.89text{eV}
end{align*}
$$

From Eq. (1), we calculate the wavelength of the photon $lambda$

$$
begin{align*}
boxed{lambda}&=frac{hc}{triangle E}\
&=frac{41.31times 10^{-16}text{eV} times 3 times 10^8frac{text{m}}{text{s}}}{1.89text{eV}}\
&=boxed{655.7text{nm}}
end{align*}
$$

The wavelength correspoding to this electron transition belongs to the region of visible light.

Result
4 of 4
A) $n=4$ to $n=2$

D) $n=2$ to $n=3$

Exercise 7
Step 1
1 of 2
The energy difference $E$ between two energy levels characterized by the principal quantum numbers $n_i$ and $n_f$ ($n_i$ denotes the initial orbit and $n_f$ denotes the final orbit) in the hydrogen atom is given by

$$
begin{align}
E=(-13.6text{eV}) left( frac{1}{n_f^2}-frac{1}{n_i^2} right)
end{align}
$$

In our case, $n_i$ is the ground state, ie.

$$
begin{align*}
n_i=1
end{align*}
$$

and $n_f$ is the principal quantum number that corresponds to the state of the electron when the atom is ionized, ie.

$$
begin{align*}
n_f rightarrow infty Rightarrow frac{1}{n_f} rightarrow 0
end{align*}
$$

Plugging these values into Eq. (1) gives us the amount of energy that an electron in the ground state of a hydrogen atom needs to absorbed in order to be ionized $E$

$$
begin{align*}
boxed{E}&=(-13.6text{eV}) left( frac{1}{n_f^2}-frac{1}{n_i^2} right)\
&=(-13.6text{eV}) (0-1)\
&=boxed{13.6text{eV}}
end{align*}
$$

Result
2 of 2
D) $13.6text{eV}$
Exercise 8
Step 1
1 of 2
Exercise scan
Step 2
2 of 2
Hence from the figure, allowed orbit is $nlambda = 2pi r$.

But $lambda = h/mv$ from de-Broglie formula. Hence $nh/mv=2pi r$.

Hence we get $L=mvr_n = nh/2pi$.

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Chapter 1: Introduction to Physics
Section 1.1: Physics and the Scientific Method
Section 1.2: Physics and Society
Section 1.3: Units and Dimensions
Section 1.4: Basic Math for Physics
Page 38: Assessment
Page 41: Standardized Test Prep
Chapter 2: Introduction to Motion
Section 2.1: Describing Motion
Section 2.2: Speed and Velocity
Section 2.3: Position-Time Graphs
Section 2.4: Equation of Motion
Page 66: Assessment
Page 71: Standardized Test Prep
Page 45: Practice Problems
Page 47: Practice Problems
Page 47: Lesson Check
Page 49: Practice Problems
Page 52: Practice Problems
Page 53: Lesson Check
Page 56: Practice Problems
Page 57: Lesson Check
Page 59: Practice Problems
Page 60: Practice Problems
Page 62: Practice Problems
Page 62: Lesson Check
Chapter 3: Acceleration and Acceleration Motion
Section 3.1: Acceleration
Section 3.2: Motion with Constant Acceleration
Section 3.3: Position-Time Graphs for Constant Acceleration
Section 3.4: Free Fall
Page 105: Assessment
Page 111: Standardized Test Prep
Chapter 4: Motion in Two Dimensions
Section 4.1: Vectors in Physics
Section 4.2: Adding and Subtracting Vectors
Section 4.3: Relative Motion
Section 4.4: Projectile Motion
Page 144: Assessment
Page 149: Standardized Test Prep
Chapter 5: Newton’s Laws of Motion
Section 5.1: Newton’s Laws of Motion
Section 5.2: Applying Newton’s Laws
Section 5.3: Friction
Page 180: Assessment
Page 187: Standardized Test Prep
Chapter 6: Work and Energy
Section 6.1: Work
Section 6.2: Work and Energy
Section 6.3: Conservation of Energy
Section 6.4: Power
Page 220: Assessment
Page 227: Standardized Test Prep
Page 191: Practice Problems
Page 193: Practice Problems
Page 196: Lesson Check
Page 196: Practice Problems
Page 199: Practice Problems
Page 201: Practice Problems
Page 203: Practice Problems
Page 204: Practice Problems
Page 205: Practice Problems
Page 206: Lesson Check
Page 209: Practice Problems
Page 211: Lesson Check
Page 213: Practice Problems
Page 214: Practice Problems
Page 215: Practice Problems
Page 216: Lesson Check
Chapter 7: Linear Momentum and Collisions
Section 7.1: Momentum
Section 7.2: Impulse
Section 7.3: Conservation of Momentum
Section 7.4: Collisions
Page 260: Assessment
Page 265: Standardized Test Prep
Chapter 8: Rotational Motion and Equilibrium
Section 8.1: Describing Angular Motion
Section 8.2: Rolling Motion and the Moment of Inertia
Section 8.3: Torque
Section 8.4: Static Equilibrium
Page 300: Assessment
Page 305: Standardized Test Prep
Page 269: Practice Problems
Page 271: Practice Problems
Page 272: Practice Problems
Page 275: Practice Problems
Page 275: Lesson Check
Page 277: Practice Problems
Page 280: Lesson Check
Page 284: Practice Problems
Page 286: Practice Problems
Page 287: Practice Problems
Page 289: Lesson Check
Page 294: Practice Problems
Page 295: Practice Problems
Page 296: Lesson Check
Chapter 9: Gravity and Circular Motion
Section 9.1: Newton’s Law of Universal Gravity
Section 9.2: Applications of Gravity
Section 9.3: Circular Motion
Section 9.4: Planetary Motion and Orbits
Page 336: Assessment
Page 341: Standardized Test Prep
Chapter 10: Temperature and Heat
Section 10.1: Temperature, Energy, and Heat
Section 10.2: Thermal Expansion and Energy Transfer
Section 10.3: Heat Capacity
Section 10.4: Phase Changes and Latent Heat
Page 378: Assessment
Page 383: Standardized Test Prep
Chapter 11: Thermodynamics
Section 11.1: The First Law of Thermodynamics
Section 11.2: Thermal Processes
Section 11.3: The Second and Third Laws of Thermodynamics
Page 410: Assessment
Page 413: Standardized Test Prep
Chapter 12: Gases, Liquids, and Solids
Section 12.1: Gases
Section 12.2: Fluids at Rest
Section 12.3: Fluids in Motion
Section 12.4: Solids
Page 446: Assessment
Page 451: Standardized Test Prep
Chapter 13: Oscillations and Waves
Section 13.1: Oscillations and Periodic Motion
Section 13.2: The Pendulum
Section 13.3: Waves and Wave Properties
Section 13.4: Interacting Waves
Page 486: Assessment
Page 491: Standardized Test Prep
Chapter 14: Sound
Section 14.1: Sound Waves and Beats
Section 14.2: Standing Sound Waves
Section 14.3: The Doppler Effect
Section 14.4: Human Perception of Sound
Page 523: Assessment
Page 527: Standardized Test Prep
Page 495: Practice Problems
Page 496: Practice Problems
Page 500: Practice Problems
Page 501: Lesson Check
Page 503: Practice Problems
Page 504: Practice Problems
Page 506: Practice Problems
Page 506: Lesson Check
Page 510: Practice Problems
Page 511: Practice Problems
Page 512: Lesson Check
Page 514: Practice Problems
Page 516: Practice Problems
Page 517: Practice Problems
Page 519: Lesson Check
Chapter 15: The Properties of Lights
Section 15.1: The Nature of Light
Section 15.2: Color and the Electromagnetic Spectrum
Section 15.3: Polarization and Scattering of Light
Page 557: Assessment
Page 563: Standardized Test Prep
Chapter 16: Reflection and Mirrors
Section 16.1: The Reflection of Light
Section 16.2: Plane Mirrors
Section 16.3: Curved Mirrors
Page 590: Assessment
Page 595: Standardized Test Prep
Chapter 17: Refraction and Lenses
Section 17.1: Refraction
Section 17.2: Applications of Refraction
Section 17.3: Lenses
Section 17.4: Applications of Lenses
Page 629: Assessment
Page 635: Standardized Test Prep
Chapter 18: Interference and Diffraction
Section 18.1: Interference
Section 18.2: Interference in Thin Films
Section 18.3: Diffraction
Section 18.4: Diffraction Gratings
Page 668: Assessment
Page 673: Standardized Test Prep
Chapter 19: Electric Charges and Forces
Section 19.1: Electric Charge
Section 19.2: Electric Force
Section 19.3: Combining Electric Forces
Page 698: Assessment
Page 703: Standardized Test Prep
Chapter 20: Electric Fields and Electric Energy
Section 20.1: The Electric Field
Section 20.2: Electric Potential Energy and Electric Potential
Section 20.3: Capacitance and Energy Storage
Page 738: Assessment
Page 743: Standardized Test Prep
Chapter 21: Electric Current and Electric Circuits
Section 21.1: Electric Current, Resistance, and Semiconductors
Section 21.2: Electric Circuits
Section 21.3: Power and Energy in Electric Circuits
Page 775: Assessment
Page 781: Standardized Test Prep
Chapter 22: Magnetism and Magnetic Fields
Section 22.1: Magnets and Magnetic Fields
Section 22.2: Magnetism and Electric Currents
Section 22.3: The Magnetic Force
Page 810: Assessment
Page 815: Standardized Test Prep
Chapter 23: Electromagnetic Induction
Section 23.1: Electricity from Magnetism
Section 23.2: Electric Generators and Motors
Section 23.3: AC Circuits and Transformers
Page 844: Assessment
Page 849: Standardized Test Prep
Chapter 24: Quantum Physics
Section 24.1: Quantized Energy and Photons
Section 24.2: Wave-Particle Duality
Section 24.3: The Heisenberg Uncertainty Principle
Page 876: Assessment
Page 881: Standardized Test Prep
Chapter 26: Nuclear Physics
Section 26.1: The Nucleus
Section 26.2: Radioactivity
Section 26.3: Applications of Nuclear Physics
Section 26.4: Fundamental Forces and Elementary Particles
Page 944: Assessment
Page 947: Standardized Test Prep