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physics
modern physics

Physics Principles with Applications 7th edition Douglas C. Giancoli - Solutions

Calculate the longest-wavelength photon that can cause an electron in silicon (Eg = 1.12eV) to jump from the valence band to the conduction band.
The band gap of silicon is 1.12 eV. (a) For what range of wavelengths will silicon be transparent? In what region of the electromagnetic spectrum does this transparent range begin? (b) If window glass is transparent for all visible wavelengths, what is the minimum possible band gap value for
The energy gap Eg in germanium is 0.72 eV. When used as a photon detector, roughly how many electrons can be made to jump from the valence to the conduction band by the passage of an 830-keV photon that loses all its energy in this fashion?
Suppose that a silicon semiconductor is doped with phosphorus so that one silicon atom in 1.5 × 106 is replaced by a phosphorus atom. Assuming that the "extra" electron in every phosphorus atom is donated to the conduction band, by what factor is the density of conduction electrons increased? The
At what wavelength will an LED radiate if made from a material with an energy gap Eg = 1.3eV?
If an LED emits light of wavelength λ = 730 nm, what is the energy gap (in eV) between valence and conduction bands?
A semiconductor diode laser emits 1.30-μm light. Assuming that the light comes from electrons and holes recombining, what is the band gap in this laser material?
A silicon diode, whose current-voltage characteristics are given in Fig. 29-30, is connected in series with a battery and a 960-Î© resistor. What battery voltage is needed to produce a 14-mA current?
An ac voltage of 120-V rms is to be rectified. Estimate very roughly the average current in the output resistor R (= 31 kÎ©) for(a) A half-wave rectifier (Fig. 29-31), and(b) A full-wave rectifier (Fig. 29-32) without capacitor.
Suppose that the diode of Fig. 29-30 is connected in series to a 180-Î©resistor and a 2.0-V battery. What current flows in the circuit?
The equilibrium distance r0 between two atoms in a molecule is called the bond length. Using the bond lengths of homogeneous molecules (like H2, O2 and N2), one can estimate the bond length of heterogeneous molecules (like CO, CN, and NO). This is done by summing half of each bond length of the
Draw a circuit diagram showing how a pnp transistor can operate as an amplifier, similar to Fig. 29-41 showing polarities, etc.
If the current gain of the transistor amplifier in Fig. 29-41 is Î² = iC/iB = 95, what value must RC have if a 1.0-Î¼A ac base current is to produce an ac output voltage of 0.42 V?
Suppose that the current gain of the transistor in Fig. 29-41 is Î² = iC/iB = 85. If RC = 3.8kÎ©, calculate the ac output voltage for an ac input current of 2.0Î¼A.
An amplifier has a voltage gain of 75 and a 25-kΩ load (output) resistance. What is the peak output current through the load resistor if the input voltage is an ac signal with a peak of 0.080 V?
A transistor, whose current gain Î² = iC/iB = 65, is connected as in Fig. 29-41 with RB = 3.8 kÎ© and RC = 7.8kÎ©.Calculate (a) The voltage gain, (b) The power amplification.
Use the uncertainty principle to estimate the binding energy of the H2 molecule by calculating the difference in kinetic energy of the electrons between (i) when they are in separate atoms and (ii) when they are in the molecule. Take ∆x for the electrons in the separated atoms to be the radius of
The average translational kinetic energy of an atom or molecule is about KE = 3/2kT (see Section 13-9), where k = 1.38 × 10-23 J/K is Boltzmann's constant. At what temperature T will KE be on the order of the bond energy (and hence the bond easily broken by thermal motion) for (a) A covalent bond
A diatomic molecule is found to have an activation energy of 1.3 eV. When the molecule is disassociated, 1.6 eV of energy is released. Draw a potential energy curve for this molecule.
The rotational absorption spectrum of a molecule displays peaks about 8.9 × 1011 Hz. apart. Determine the moment of inertia of this molecule.
Must we consider quantum effects for everyday rotating objects? Estimate the differences between rotational energy levels for a spinning baton compared to the energy of the baton. Assume the baton consists of a uniform 32-cm-long bar with a mass of 230 g and two small end masses, each of mass 380
The energy gap between valence and conduction bands in zinc sulfide is 3.6 eV. What range of wavelengths can a photon have to excite an electron from the top of the valence band into the conduction band?
Most of the Sun's radiation has wavelengths shorter than 1100 nm. For a solar cell to absorb all this, what energy gap ought the material have?
A TV remote control emits IR light. If the detector on the TV set is not to react to visible light, could it make use of silicon as a "window" with its energy gap Eg = 1.12eV? What is the shortest-wavelength light that can strike silicon without causing electrons to jump from the valence band to
Green and blue LEDs became available many years after red LEDs were first developed. Approximately what energy gaps would you expect to find in green (525 nm) and in blue (465 nm) LEDs?
Consider a monatomic solid with a weakly bound cubic lattice, with each atom connected to six neighbors, each bond having a binding energy of 3.4 Ã— 10-3 eV. When this solid melts, its latent heat of fusion goes directly into breaking the bonds between the atoms. Estimate the latent heat of
(a) Calculate the "characteristic rotational energy," h2/2I, for the O2 molecule whose bond length is 0.121 nm.(b) What are the energy and wavelength of photons emitted in an ℓ = 3 to ℓ = 2 transition?
The "characteristic rotational energy," h2/2I, for N2 is 2.48 × 10-4 eV. Calculate the N2 bond length.
(a) Why are weak bonds important in cells? (b) Explain why heating proteins too much may cause them to denature-that is, lose the specific shape they need to function. (c) What is the strongest weak bond, and why? (d) If this bond, and the other weak bonds, were stronger (that is, too strong),
Assume conduction electrons in a semiconductor behave as an ideal gas. (This is not true for conduction electrons in a metal.) (a) Taking mass m = 9 × 10-31 kg and temperature T = 300 K, determine the de Broglie wavelength of a semiconductor's conduction electrons. (b) Given that the spacing
A strip of silicon 1.6 cm wide and 1.0 mm thick is immersed in a magnetic field of strength 1.5 T perpendicular to the strip (Fig. 29-45). When a current of 0.28 mA is run through the strip, there is a resulting Hall effect voltage of 18 mV across the strip (Section 20-4). How many electrons per
Fill in the missing particle or nucleus:
What are the elements represented by the X in the following: (a) 23292X; (b) 187X; (c) 11X; (d) 8638X; (e) 252100X;
Explain the absence of β+ emitters in the radioactive decay series of Fig. 30-11.
As 22286Rndecays into 20682Pb, how many alpha and beta particles are emitted? Does it matter which path in the decay series is chosen? Why or why not?
A 238U nucleus (initially at rest) decays into a 234Th nucleus and an alpha particle. Which has the greater (i) Momentum, (ii) Velocity, (iii) Kinetic energy? Explain. (a) The 234Th nucleus. (b) The alpha particle. (c) Both the same.
1. Elements of the Periodic Table are distinguished by (a) The number of protons in the nucleus. (b) The number of neutrons in the nucleus. (c) The number of electrons in the atom. (d) Both (a) and (b). (e) (a), (b), and (c). 2. A nucleus has (a) More energy than its component neutrons and protons
1. Which of the following will generally create a more stable nucleus?(a) Having more nucleons.(b) Having more protons than neutrons.(c) Having a larger binding energy per nucleon.(d) Having the same number of electrons as protons.(e) Having a larger total binding energy.2. There are 82 protons in
1. The half-life of a radioactive nucleus is (a) Half the time it takes for the entire substance to decay. (b) The time it takes for half of the substance to decay. (c) The same as the decay constant. (d) Both (a) and (b) (they are the same). (e) All of the above. 2. As a radioactive sample
1. If the half-life of a radioactive sample is 10 years, then it should take _____ years for the sample to decay completely. (a) 10. (b) 20. (c) 40. (d) Cannot be determined. 2. A sample's half-life is 1 day. What fraction of the original sample will have decayed after 3 days? (a) 1/8, (b)
1. After three half-lives, what fraction of the original radioactive material is left? (a) None. (b) 1/16, (c) 1/8, (d) 1/4, (e) 3/4, (f) 7/8. 2. Technetium 9843 has a half-life of 4.2 × 106yr. Strontium has a half-life of 28.79 yr. Which statements are true? (a) The decay constant of Sr is
1. A material having which decay constant would have the shortest half-life?(a) 100 second.(b) 5 year.(c) 8 century.(d)2. Uranium-238 decays to lead-206 through a series of(a) Alpha decays.(b) Beta decays.(c) Gamma decays.(d) Some combination of alpha, beta, and gamma decays.
1. Carbon dating is useful only for determining the age of objects less than about _____ years old. (a) 4.5 million. (b) 1.2 million. (c) 600,000. (d) 60,000. (e) 6000. 2. Radon has a half-life of about 1600 years. The Earth is several billion years old, so why do we still find radon on this
1. How does an atom's nucleus stay together and remain stable? (a) The attractive gravitational force between the protons and neutrons overcomes the repulsive electrostatic force between the protons. (b) Having just the right number of neutrons overcomes the electrostatic force between the
Estimate the total binding energy for 6329Cu, using Fig. 30-1.
Calculate the binding energy per nucleon for a 157 N nucleus, using Appendix B.
Determine the binding energy of the last neutron in a 2311 Na nucleus.
Calculate the total binding energy, and the binding energy per nucleon, for(a) 73 Li,(b) 19578 PtUse Appendix B.
How much energy is required to remove (a) A proton, (b) A neutron, from 157N? Explain the difference in your answers.
The 73Li nucleus has an excited state 0.48 MeV above the ground state. What wavelength gamma photon is emitted when the nucleus decays from the excited state to the ground state?
Give the result of a calculation that shows whether or not the following decays are possible:
Calculate the maximum kinetic energy of the particle emitted during the decay of 6027Co.
By what % is the radius of 23892U greater than the radius of 23592U?
The isotope 21884Po can decay by either or β- emission. What is the energy release in each case? The mass of 21884Po is 218.008973 u.
A photon with a wavelength of 1.15 × 10-13m is ejected from an atom. Calculate its energy and explain why it is a ray from the nucleus or a photon from the atom.
When 23892U decays, the particle emitted has 4.20 MeV of kinetic energy. Calculate the recoil kinetic energy of the daughter nucleus and the Q-value of the decay
(a) What is the decay constant of 23892U whose half-life is 4.5 × 109 yr? (b) The decay constant of a given nucleus is 3.2 × 10-5 s-1. What is its half-life?
A radioactive material produces 1120 decays per minute at one time, and 3.6 h later produces 140 decays per minute. What is its half-life?
(a) What is the approximate radius of a 11248Cd nucleus? (b) Approximately what is the value of A for a nucleus whose radius is 3.7 × 10-15 m?
What fraction of a sample of 6832Ge, whose half-life is about 9 months, will remain after 2.5 yr?
Gallery What is the activity of a sample of 146C that contains 6.5 × 1020 nuclei?
What fraction of a radioactive sample is left after exactly 5 half-lives?
The iodine isotope 13153I is used in hospitals for diagnosis of thyroid function. If 782 μg are ingested by a patient, determine the activity(a) Immediately,(b) 1.50 h later when the thyroid is being tested,(c) 3.0 months later. Use Appendix B.
How many nuclei of 23892U remain in a rock if the activity registers 420 decays per second?
Calculate the mass of a sample of pure 4019K with an initial decay rate of 2.4 × 105 s-1. The half-life of 4019K is 1.248 × 109 yr.
Calculate the activity of a pure 6.7-μg sample of 3215P (T ½ = 1.23 × 106s).
A sample of 23392 U (T ½ 1.59 × 105 yr) contains 4.50 × 1018 nuclei. (a) What is the decay constant? (b) Approximately how many disintegrations will occur per minute?
The activity of a sample drops by a factor of 6.0 in 9.4 minutes. What is its half-life?
The rubidium isotope 8737Rb, a β emitter with a half-life 4.75 × 1010yr, of is used to determine the age of rocks and fossils. Rocks containing fossils of ancient animals contain a ratio of 8737Sr to 8737Rb of 0.0260. Assuming that there was no 8738Sr present when the rocks were formed, estimate
Two of the naturally occurring radioactive decay sequences start with 23290Th and with 23592U. The first five decays of these two sequences are: α, β, β, α, α α, β, α, β, α and Determine the resulting intermediate daughter nuclei in each case.
An ancient wooden club is found that contains 73 g of carbon and has an activity of 7.0 decays per second. Determine its age assuming that in living trees the ratio of 14C/12C atoms is about 1.3 × 10-12.
The activity of a radioactive source decreases by 5.5% in 31.0 hours. What is the half-life of this source?
Suppose two alpha particles were held together so they were just "touching" (use Eq. 30-1). Estimate the electrostatic repulsive force each would exert on the other. What would be the acceleration of an alpha particle subjected to this force?
Which radioactive isotope of lead is being produced if the measured activity of a sample drops to 1.050% of its original activity in 4.00 h?
An old wooden tool is found to contain only 4.5% of the 146C that an equal mass of fresh wood would. How old is the tool?
The 31H isotope of hydrogen, which is called tritium (because it contains three nucleons), has a half-life of 12.3 yr. It can be used to measure the age of objects up to about 100 yr. It is produced in the upper atmosphere by cosmic rays and brought to Earth by rain. As an application, determine
Some elementary particle theories (Section 32-11) suggest that the proton may be unstable, with a half-life ≥ 1033yr. (a) How long would you expect to wait for one proton in your body to decay (approximate your body as all water)? (b) Of the roughly 7 billion people on Earth, about how many
How long must you wait (in half-lives) for a radioactive sample to drop to 2.00% of its original activity?
If the potassium isotope 4019K gives 42decays/s in a liter of milk, estimate how much 4019K and regular 3019K are in a liter of milk. Use Appendix B.
The activity of a sample of 3516S (T12 = 87.37 days) is 4.28 × 104 decays per second. What is the mass of the sample?
(a) What would be the radius of the Earth if it had its actual mass but had the density of nuclei?(b) By what factor would the radius of a 23892U nucleus increase if it had the Earth's density?
Determine the activities of (a) 1.0 g of 13153I (T12 = 8.02 days) (b) 1.0 g of 23892U (T12 = 4.47 × 109 yr)
Use Fig. 30-1 to estimate the total binding energy for copper and then estimate the energy, in joules, needed to break a 3.0-g copper penny into its constituent nucleons.
Instead of giving atomic masses for nuclides as in Appendix B, some Tables give the mass excess, ∆, defined as ∆ = M - A, where A is the atomic mass number and M is the mass in u. Determine the mass excess, in u and in MeV/c2, for: (a) 42He; (b) 126C; (c) 8638Sr; (d) 23592U; (e) From a glance
When water is placed near an intense neutron source, the neutrons can be slowed down to almost zero speed by collisions with the water molecules, and are eventually captured by a hydrogen nucleus to form the stable isotope called deuterium, 21H, giving off a gamma ray. What is the energy of the
Using Section 30-2 and Appendix B, determine the energy required to remove one neutron from 42He. How many times greater is this energy than the binding energy of the last neutron in 136C?
(a) If all of the atoms of the Earth were to collapse and simply become nuclei, what would be the Earth's new radius? (b) If all of the atoms of the Sun were to collapse and simply become nuclei, what would be the Sun's new radius?
(a) A 72-gram sample of natural carbon contains the usual fraction of 146C. Estimate roughly how long it will take before there is only one 146C nucleus left.(b) How does the answer in (a) change if the sample is 340 grams? What does this tell you about the limits of carbon dating?
What stable nucleus has approximately half the radius of a uranium nucleus?
Almost all of naturally occurring uranium is with a 23892U half-life of 4.468 × 109 yr. Most of the rest of natural uranium is 23592U with a half-life of 7.04 × 108 yr. Today a sample contains 0.720% 23592U.(a) What was this percentage 1.0 billion years ago?(b) What percentage of uranium will be
A banana contains about 420 mg of potassium, of which a small fraction is the radioactive isotope 4019K (Appendix B). Estimate the activity of an average banana due to 4019K.
When 2310Ne (mass = 22.9947 u) decays to 2311Na (mass = 22.9898 u), what is the maximum kinetic energy of the emitted electron? What is its minimum energy? What is the energy of the neutrino in each case? Ignore recoil of the daughter nucleus.
If an alpha particle were released from rest near the surface of a 257100Fm nucleus, what would its kinetic energy be when far away?
Describe in detail why we think there is a strong nuclear force.
(a) Under what circumstances could a fermium nucleus decay into an einsteinium nucleus?(b) What about the reverse, an Es nucleus decaying into Fm?
Using the uncertainty principle and the radius of a nucleus, estimate the minimum possible kinetic energy of a nucleon in, say, iron. Ignore relativistic corrections.
In Fig. 30-17, a nucleus decays and emits a particle that enters a region with a uniform magnetic field of 0.012 T directed into the page. The path of the detected particle is shown.(a) What type of radioactive decay is this?(b) If the radius of the circular arc is 4.7 mm, what is the velocity of
In both internal conversion and β decay, an electron is emitted. How could you determine which decay process occurred?
In 1991, the frozen remains of a Neolithic-age man, nicknamed Otzi, were found in the Italian Alps by hikers. The body was well preserved, as were his bow, arrows, knife, axe, other tools, and clothing. The date of his death can be determined using carbon-14 dating.(a) What is the decay constant
Some radioactive isotopes have half-lives that are greater than the age of the universe (like gadolinium or samarium). The only way to determine these half-lives is to monitor the decay rate of a sample that contains these isotopes. For example, suppose we find an asteroid that currently contains

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