1. Intro to Physics Units

The earth's circumference is approximately 40.1 Mm (megameters). What is this circumference in kilometers?

Astronomers often detect radio waves with wavelengths of 3,000,000,000 nm. What is this wavelength expressed in decameters (dam)?

Rewrite 0.00016 kg in scientific notation.

Rewrite 299,800,000 m/s in scientific notation.

Rewrite 3.41 × 10⁻⁴ in standard form:

1459

Rewrite 9.98 × 10⁷ in standard form.

1498

Which of the following quantities is an acceleration?

The position of an object is given by 𝓍 = At + Bt², where 𝓍 is in meters and t is in seconds.

(a) What are the units of A and B?

131

Write the following numbers in powers of 10 notation:

(e) 0.219

153

Write out the following numbers in full with the correct number of zeros:

114

(b) Is this particle curving upward, curving downward, or moving in a straight line?

Time intervals measured with a physical stopwatch typically have an uncertainty of about 0.2 s, due to human reaction time at the start and stop moments. What is the percent uncertainty of a hand-timed measurement of 4.5 min?

121

A watch manufacturer claims that its watches gain or lose no more than 9 seconds in a year. How accurate are these watches, expressed as a percentage?

122

Write the following as full (decimal) numbers without prefixes on the units:

(e) 22.5 nm

113

Express the following using the prefixes of Table 1–4: 18 x 10² bucks and

114

A demented scientist creates a new temperature scale, the 'Z scale.' He decides to call the boiling point of nitrogen 0°Z and the melting point of iron 1000°Z. b. Convert 500°Z to degrees Celsius and to kelvins.

176

The lowest and highest natural temperatures ever recorded on earth are −129°F in Antarctica and 134°F in Death Valley. What are these temperatures in °C and in K?

225

The age of the universe is thought to be about 14 billion years. Assuming two significant figures, write this in powers of 10 in :

(a) years

122

The Sun, on average, is 93 million miles from Earth. How many meters is this? Express

(b) using a metric prefix (km).

An alien spacecraft is flying overhead at a great distance as you stand in your backyard. You see its searchlight blink on for 0.150 s. The first officer on the spacecraft measures that the searchlight is on for 12.0 ms. (a) Which of these two measured times is the proper time? (b) What is the speed of the spacecraft relative to the earth, expressed as a fraction of the speed of light c?

147

The positive muon (µ+), an unstable particle, lives on average 2.20 * 10^-6 s (measured in its own frame of reference) before decaying. (b) What average distance, measured in the laboratory, does the particle move before decaying?

143

The positive muon (µ+), an unstable particle, lives on average 2.20 * 10^-6 s (measured in its own frame of reference) before decaying. (a) If such a particle is moving, with respect to the laboratory, with a speed of 0.900c, what average lifetime is measured in the laboratory?

171

(b) A force is applied to a particle along its direction of motion. At what speed is the magnitude of force required to produce a given acceleration twice as great as the force required to produce the same acceleration when the particle is at rest? Express your answer in terms of the speed of light

A proton has momentum with magnitude p0 when its speed is 0.400c. In terms of p0, what is the magnitude of the proton's momentum when its speed is doubled to 0.800c?

223

Suppose the two lightning bolts shown in Fig. 37.5a are simultaneous to an observer on the train. Show that they are not simultaneous to an observer on the ground. Which lightning strike does the ground observer measure to come first?

229

X rays with initial wavelength 0.0665 nm undergo Compton scattering. What is the longest wavelength found in the scattered x rays? At which scattering angle is this wavelength observed?

259

The cathode-ray tubes that generated the picture in early color televisions were sources of x rays. If the acceleration voltage in a television tube is 15.0 kV, what are the shortest-wavelength x rays produced by the television?

137

The photoelectric work function of potassium is 2.3 eV. If light that has a wavelength of 190 nm falls on potassium, find (b) the kinetic energy, in electron volts, of the most energetic electrons ejected

303

The photoelectric work function of potassium is 2.3 eV. If light that has a wavelength of 190 nm falls on potassium, find (a) the stopping potential in volts

129

What would the minimum work function for a metal have to be for visible light (380–750 nm) to eject photoelectrons?

198

The photoelectric threshold wavelength of a tungsten surface is 272 nm. Calculate the maximum kinetic energy of the electrons ejected from this tungsten surface by ultraviolet radiation of frequency 1.45 * 10^15 Hz. Express the answer in electron volts.

157

A photon has momentum of magnitude 8.24 * 10-28 kg # m>s. (b) What is the wavelength of this photon? In what region of the electromagnetic spectrum does it lie?

135

A laser used to weld detached retinas emits light with a wavelength of 652 nm in pulses that are 20.0 ms in duration. The average power during each pulse is 0.600 W. (a) How much energy is in each pulse in joules? In electron volts?

127

A photon of green light has a wavelength of 520 nm. Find the photon's frequency, magnitude of momentum, and energy. Express the energy in both joules and electron volts.

509

(a) The energy of the 2s state of lithium is -5.391 eV. Calculate the value of Zeff for this state.

118

(b) Estimate the energy of the least strongly bound level in the L shell of N2+.

150

(a) The doubly charged ion N2+ is formed by removing two electrons from a nitrogen atom. What is the ground-state electron configuration for the N2+ ion?

115

The energies of the 4s, 4p, and 4d states of potassium are given in Example 41.10. Calculate Zeff for each state. What trend do your results show? How can you explain this trend?

135

The 5s electron in rubidium (Rb) sees an effective charge of 2.771e. Calculate the ionization energy of this electron.

357

A hydrogen atom in a particular orbital angular momentum state is found to have j quantum numbers 7 2 and 9 2 . (b) If n = 5, what is the energy difference between the j = 7 2 and j = 9 2 levels?

149

Calculate the energy difference between the ms = 1 2 ('spin up') and ms = - 1 2 ('spin down') levels of a hydrogen atom in the 1s state when it is placed in a 1.45-T magnetic field in the negative z@direction. Which level, ms = 1 2 or ms = - 1 2 , has the lower energy?

334

The hyperfine interaction in a hydrogen atom between the magnetic dipole moment of the proton and the spin magnetic dipole moment of the electron splits the ground level into two levels separated by 5.9 * 10-6 eV. (a) Calculate the wavelength and frequency of the photon emitted when the atom makes a transition between these states, and compare your answer to the value given at the end of Section 41.5. In what part of the electromagnetic spectrum does this lie? Such photons are emitted by cold hydrogen clouds in interstellar space; by detecting these photons, astronomers can learn about the number and density of such clouds.

186

(a) If you treat an electron as a classical spherical object with a radius of 1.0 * 10-17 m, what angular speed is necessary to produce a spin angular momentum of magnitude 23 4 U? (b) Use v = rv and the result of part (a) to calculate the speed v of a point at the electron's equator. What does your result suggest about the validity of this model?

156

A hydrogen atom in the 5g state is placed in a magnetic field of 0.600 T that is in the z@direction. (a) Into how many levels is this state split by the interaction of the atom's orbital magnetic dipole moment with the magnetic field?

214

A hydrogen atom in a 3p state is placed in a uniform external magnetic field B S . Consider the interaction of the magnetic field with the atom's orbital magnetic dipole moment. (a) What field magnitude B is required to split the 3p state into multiple levels with an energy difference of 2.71 * 10-5 eV between adjacent levels?

294

Pure germanium has a band gap of 0.67 eV. The Fermi energy is in the middle of the gap. (a) For temperatures of 250 K, 300 K, and 350 K, calculate the probability f(E) that a state at the bottom of the conduction band is occupied.

294

At the Fermi temperature T_F, E_F = kT_F (see Exercise 42.22). When T = T_F, what is the probability that a state with energy E = 2E_F is occupied?

128

CP Silver has a Fermi energy of 5.48 eV. Calculate the electron contribution to the molar heat capacity at constant volume of silver, CV, at 300 K. Express your result (a) as a multiple of R and

126

Calculate the density of states g(E) for the free-electron model of a metal if E = 7.0 eV and V = 1.0 cm^3 . Express your answer in units of states per electron volt.

221

The maximum wavelength of light that a certain silicon photocell can detect is 1.11 mm. (b) Explain why pure silicon is opaque.

The maximum wavelength of light that a certain silicon photocell can detect is 1.11 mm. (a) What is the energy gap (in electron volts) between the valence and conduction bands for this photocell?

153

The average kinetic energy of an ideal-gas atom or molecule is (3/2)kT, where T is the Kelvin temperature (Chapter 18). The rotational inertia of the H2 molecule is 4.6 * 10^-48 kg•m^2. What is the value of T for which (3/2)kT equals the energy separation between the l = 0 and l = 1 energy levels of H2? What does this tell you about the number of H2 molecules in the l = 1 level at room temperature?

255

CP The rotational energy levels of CO are calculated in Example 42.2. If the energy of the rotating molecule is described by the classical expression K = (1/2)Iω^2 , for the l = 1 level what are (b) the linear speed of each atom;

197

Measurements on a certain isotope tell you that the decay rate decreases from 8318 decays/min to 3091 decays/min in 4.00 days. What is the half-life of this isotope?

227

The unstable isotope 40K is used for dating rock samples. Its half-life is 1.28x10^9 y. (a) How many decays occur per second in a sample containing 1.63x10^-6 g of 40K? (b) What is the activity of the sample in curies?

125

The common isotope of uranium, 238U, has a halflife of 4.47x10^9 years, decaying to 234Th by alpha emission. (a) What is the decay constant? (b) What mass of uranium is required for an activity of 1.00 curie? (c) How many alpha particles are emitted per second by 10.0 g of uranium?

Radioactive isotopes used in cancer therapy have a 'shelf-life,' like pharmaceuticals used in chemotherapy. Just after it has been manufactured in a nuclear reactor, the activity of a sample of 60Co is 5000 Ci. When its activity falls below 3500 Ci, it is considered too weak a source to use in treatment. You work in the radiology department of a large hospital. One of these 60Co sources in your inventory was manufactured on October 6, 2011. It is now April 6, 2014. Is the source still usable? The half-life of 60Co is 5.271 years.

191

What particle (a particle, electron, or positron) is emitted in the following radioactive decays? (a) 27 14SiS 27 13 Al; (b) 238 92U S 234 90Th; (c) 74 33As S 7434Se.

171

The atomic mass of 14C is 14.003242 u. Show that the b- decay of 14C is energetically possible, and calculate the energy released in the decay.

118

What nuclide is produced in the following radioactive decays? (a) a decay of 239 94 Pu; (b) b- decay of 24 11Na; (c) b+ decay of 15 8O.

130

(a) Is the decay nS p + b- + ve energetically possible? If not, explain why not. If so, calculate the total energy released. (b) Is the decay pS n + b+ + ve energetically possible? If not, explain why not. If so, calculate the total energy released.

118

The most common isotope of uranium, 238 92U, has atomic mass 238.050788 u. Calculate (a) the mass defect; (b) the binding energy (in MeV); (c) the binding energy per nucleon.

743

Hydrogen atoms are placed in an external magnetic field. The protons can make transitions between states in which the nuclear spin component is parallel and antiparallel to the field by absorbing or emitting a photon. What magnetic-field magnitude is required for this transition to be induced by photons with frequency 22.7 MHz?

356

(a) What is the speed of a proton that has total energy 1000 GeV?

329

(a) A high-energy beam of alpha particles collides with a stationary helium gas target. What must the total energy of a beam particle be if the available energy in the collision is 16.0 GeV?

155

The magnetic field in a cyclotron that accelerates protons is 1.70 T. (a) How many times per second should the potential across the dees reverse? (This is twice the frequency of the circulating protons.)

132

Deuterons in a cyclotron travel in a circle with radius 32.0 cm just before emerging from the dees. The frequency of the applied alternating voltage is 9.00 MHz. Find (a) the magnetic field and

125

An electron with a total energy of 30.0 GeV collides with a stationary positron. (a) What is the available energy?

123

A proton and an antiproton annihilate, producing two photons. Find the energy, frequency, and wavelength of each photon (a) if the p and p are initially at rest and

180

CP Two equal-energy photons collide head-on and annihilate each other, producing a µ^+µ^- pair. The muon mass is given in terms of the electron mass in Section 44.1. (a) Calculate the maximum wavelength of the photons for this to occur. If the photons have this wavelength, describe the motion of the µ^+ and mimmediately after they are produced.

121

A neutral pion at rest decays into two photons. Find the energy, frequency, and wavelength of each photon. In which part of the electromagnetic spectrum does each photon lie? (Use the pion mass given in terms of the electron mass in Section 44.1.)

411

"(I) Estimate the order of magnitude (power of 10) of: (b) 86.30 x 10³"

"(II) Use Table 1–3 to estimate the total number of protons or neutrons in :(c) the human body"

100

"(II) A typical atom has a diameter of about 1.0 x 10⁻¹⁰ m. (b) Approximately how many atoms are along a 1.0-cm line, assuming they just touch?"

162

(III) Many sailboats are docked at a marina 4.4 km away on the opposite side of a lake. You stare at one of the sailboats because, when you are lying flat at the water's edge, you can just see its deck but none of the side of the sailboat. You then go to that sailboat on the other side of the lake and measure that the deck is 1.5 m above the level of the water. Using Fig. 1–14, where h = 1.5 m , estimate the radius R of the Earth. <IMAGE>

122

Global positioning satellites (GPS) can be used to determine your position with great accuracy. If one of the satellites is 20,000 km from you, and you want to know your position to ±2 m, what percent uncertainty in the distance is required? How many significant figures are needed in the distance?

123

If you walked north along one of Earth's lines of longitude until you had changed latitude by 1 minute of arc (there are 60 minutes per degree), how far would you have walked (in miles)? This distance is a nautical mile (page 7).

129

Determine the percent uncertainty in θ, and in sin θ, when θ = 75.0° ± 0.5°.

105

Dimensional analysis. Waves on the surface of the ocean do not depend significantly on the properties of water such as density or surface tension. The primary 'return force' for water piled up in the wave crests is due to the gravitational attraction of the Earth. Thus the speed v (m/s) of ocean waves depends on the acceleration due to gravity g. It is reasonable to expect that υ might also depend on water depth h and the wave's wavelength λ. Assume the wave speed is given by the functional form v = Cgᵅ hᵝ λᵞ, where α , β , c and C are numbers without dimension.

(a) In deep water, the water deep below the surface does not affect the motion of waves at the surface. Thus υ should be independent of depth h (i.e., β = 0). Using only dimensional analysis (Section 1–7 and Appendix D), determine the formula for the speed of surface ocean waves in deep water.

108

(II) Estimate how many books can be shelved in a college library with 6500 m² of floor space. Assume 8 shelves high, having books on both sides, with corridors 1.5 m wide. Assume books are about the size of this one, on average.

144

(II) Estimate how long it would take one person to mow a football field using an ordinary home lawn mower (Fig. 1–12). (State your assumptions, such as the mower moves with a 1-km/h speed, and has a 0.5-m width.) <IMAGE>

138

(II) A hiking trail is 270 km long through varying terrain. A group of hikers cover the first 49 km in two and a half days. Estimate how much time they should allow for the rest of the trip.

102

(II) Estimate the number of jelly beans in the jar of Fig. 1–13.

<IMAGE>

104

Recent findings in astrophysics suggest that the observable universe can be modeled as a sphere of radius R = 13.7 x 10⁹ light-years = 13.0 x 10²⁵ m with an average total mass density of about 1 x 10⁻²⁶ kg/m³. Only about 4% of total mass is due to 'ordinary' matter (such as protons, neutrons, and electrons). Estimate how much ordinary matter (in kg) there is in the observable universe. (For the light-year, see Problem 25.)

101

(II) The diameter of the planet Mercury is 4879 km.

(a) What is the surface area of Mercury?

219

One mole of atoms consists of 6.02 x 10²³ individual atoms. If a mole of atoms were spread uniformly over the Earth's surface, how many atoms would there be per square meter?

114

Relativistic Baseball. Calculate the magnitude of the force required to give a 0.145-kg baseball an acceleration a = 1.00 m/s2 in the direction of the baseball's initial velocity when this velocity has a magnitude of (a) 10.0 m/s; (b) 0.900c; (c) 0.990c.

A proton (rest mass 1.67 * 10-27 kg) has total energy that is 4.00 times its rest energy. What are (a) the kinetic energy of the proton; (b) the magnitude of the momentum of the proton; (c) the speed of the proton?

347