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physics
modern physics

Questions and Answers of Modern Physics

In the ground state, the outermost shell (n = 1) of helium (He) is filled with electrons, as is the outermost shell (n = 2) of neon (Ne). The full outermost shells of these two elements distinguish
By using the Bohr model, decide which element is likely to emit a Ka X-ray with a wavelength of 4.5 x 10-9 m.
What is the minimum potential difference that must be applied to an X-ray tube to knock a K-shell electron completely out of an atom in a copper (Z = 29) target? Use the Bohr model as needed.
An X-ray tube is being operated at a potential difference of 52.0 kV. What is the Bremsstrahlung wavelength that corresponds to 35.0% of the kinetic energy with which an electron collides with the
In a Rutherford scattering experiment a target nucleus has a diameter of 1.4 x 10-14 m. The incoming a particle has a mass of 6.64 x 10-27 kg. What is the kinetic energy of a particle that has a de
In the X-ray spectrum of niobium (Z = 41), a Ka peak is observed at a wavelength of 7.462 x 10-11 m. (a) Determine the magnitude of the difference between the observed wavelength of the Ka X-ray for
The Bohr model, although not strictly applicable, can be used to estimate the minimum energy Emin that an incoming electron must have in an X-ray tube in order to knock a K-shell electron entirely
Multiple-Concept Example 9 reviews the concepts that are important in this problem. An electron, traveling at a speed of 6.00 x 107 m/s, strikes the target of an X-ray tube. Upon impact, the electron
The ultraviolet excimer laser used in the PRK technique (see Section 30.9) has a wavelength of 193 nm. A carbon dioxide laser produces a wavelength of 1.06 x 10-5 m. What is the minimum number of
A pulsed laser emits light in a series of short pulses, each having a duration of 25.0 ms. The average power of each pulse is 5.00 mW, and the wavelength of the light is 633 nm. Find the number of
The drawing shows three energy levels of a laser that are involved in the lasing action. These levels are analogous to the levels in the Ne atoms of a He-Ne laser. The E2 level is a metastable level,
A laser peripheral iridotomy is a procedure for treating an eye condition known as narrow-angle glaucoma, in which pressure buildup in the eye can lead to loss of vision. A neodymium YAG laser
Fusion is the process by which the sun produces energy. One experimental technique for creating controlled fusion utilizes a solid-state laser that emits a wavelength of 1060 nm and can produce a
Referring to Figure 30.16 for the order in which the subshells fill and following the style used in Table 30.3, determine the ground-state electronic configuration for cadmium Cd (Z = 48).
The nucleus of a copper atom contains 29 protons and has a radius of 4.8 x 10-15 m. How much work (in electron volts) is done by the electric force as a proton is brought from infinity, where it is
A singly ionized helium atom (He+) has only one electron in orbit about the nucleus. What is the radius of the ion when it is in the second excited state?
Using the Bohr model, determine the ratio of the energy of the nth orbit of a triply ionized beryllium atom (Be3+, Z = 4) to the energy of the nth orbit of a hydrogen atom (H).
Two samples contain different radioactive isotopes. Is it possible for these samples to have the same activity? (a) Yes, if they have the same number of nuclei but different half-lives. (b) Yes, if
The bones from an animal found at an archaeological dig have a activity of 0.10 Bq per gram of carbon. The half-life of the radioactive isotope is 5730 yr. Which one of the following best
A nucleus can undergo α, β–, or γ decay. For each type of decay, is the radius of the daughter nucleus greater than, less than, or about the same as the radius of the parent nucleus?
Suppose that you could pack neutrons (mass = 1.67 × 10-27 kg) inside a tennis ball (radius = 0.032 m) in the same way as neutrons and protons are packed together in the nucleus of an atom. (a)
The binding energy of a nucleus is 225.0 MeV. What is the mass defect of the nucleus in atomic mass units?
Determine the mass defect (in atomic mass units) for (a) helium, which has an atomic mass of 3.016030 u, and (b), which has an atomic mass of 3.016050 u. (c) On the basis of your answers to parts (a)
A 245-kg boulder is dropped into a mine shaft that is 3.0 × 103 m deep. During the boulder's fall, the system consisting of the earth and the boulder loses a certain amount of gravitational
For lead (atomic mass = 205.974 440 u) obtain(a) The mass defect in atomic mass units,(b) The binding energy (in MeV), and(c) The binding energy per nucleon (in MeV/nucleon).
(a) Energy is required to separate a nucleus into its constituent nucleons, as Figure 31.3 indicates; this energy is the total binding energy of the nucleus. In a similar way one can speak of the
Copper penny has a mass of 3.0 g. Determine the energy (in MeV) that would be required to break all the copper nuclei into their constituent protons and neutrons. Ignore the energy that binds the
A nucleus contains 18 protons and 22 neutrons. What is the radius of this nucleus?
Write the β– decay process for carbon 146C, including the chemical symbols as well as the values of Z and A for the parent and daughter nuclei and the β– particle.
Find the energy that is released when a nucleus of lead 21182Pb (atomic mass = 210.988 735 u) undergoes β– decay to become bismuth 21183Bi (atomic mass = 210.987 255 u).
Find the energy (in MeV) released when a decay converts radium 22688Ra (atomic mass = 226.025 40 u) into radon 22286Rn (atomic mass = 222.017 57 u). The atomic mass of an a particle is 4.002 603 u.
Lead is a stable daughter nucleus that can result from either an a decay or a β– decay. Write the decay processes, including the chemical symbols and values for Z and A of the parent nuclei,
In the form AZX, identify the daughter nucleus that results when(a) Plutonium 24294Pu undergoes α decay,(b) Sodium 2411Na undergoes β– decay,(c) Nitrogen 137N undergoes β+ decay.
When uranium 23592U decays, it emits (among other things) a g ray that has a wavelength of 1.14 × 10–11 m. Determine the energy (in MeV) of this γ ray.
Polonium 21084Po (atomic mass = 209.982 848 u) undergoes a decay. Assuming that all the released energy is in the form of kinetic energy of the a particle (atomic mass = 4.002 603 u) and ignoring the
Radon 22086Rn produces a daughter nucleus that is radioactive. The daughter, in turn, produces its own radioactive daughter, and so on. This process continues until lead 20882Pbis reached. What are
Review Conceptual Example 5 as background for this problem. The a decay of uranium 23892U produces thorium 23490TH (atomic mass = 234.0436 u). In Example 4, the energy released in this decay is
In each of the following cases, what element does the symbol X represent and how many neutrons are in the nucleus? Use the periodic table on the inside of the back cover as needed.(a) (b) (c) (d) (e)
An isotope of beryllium (atomic mass = 7.017 u) emits a g ray and recoils with a speed of 2.19 × 104 m/s. Assuming that the beryllium nucleus is stationary to begin with, find the wavelength of the
In 9.0 days the number of radioactive nuclei decreases to one-eighth the number present initially. What is the half-life (in days) of the material?
The 3215P isotope of phosphorus has a half-life of 14.28 days. What is its decay constant in units of s–1?
Strontium 9038Sr has a half-life of 29.1 yr. It is chemically similar to calcium, enters the body through the food chain, and collects in the bones. Consequently, 9038Sr is a particularly serious
Two radioactive waste products from nuclear reactors are strontium 9038Sr (T1/2 5 29.1 yr) and cesium 13455Cs (T1/2 = 2.06 yr). These two species are present initially in a ratio of N0,Sr /N0,Cs =
Iodine 13153I is used in diagnostic and therapeutic techniques in the treatment of thyroid disorders. This isotope has a half-life of 8.04 days. What percentage of an initial sample of 13153I remains
One day, a cell phone company sends a text message to each of its 5800 subscribers, announcing that they have been automatically enrolled as contestants in a promotional lottery modeled on nuclear
A device used in radiation therapy for cancer contains 0.50 g of cobalt 6027Co (59.933 819 u). The half-life of 6027Co is 5.27 yr. Determine the activity of the radioactive material.
A one-gram sample of radium 22486Ra (atomic mass = 224.020 186 u, T1/2 = 3.66 days) contains 2.69 3 1021 nuclei and undergoes a decay to produce radon 22086Rn (atomic mass 5 220.011 368 u). The
The isotope 19879Au (atomic mass = 197.968 u) of gold has a half-life of 2.69 days and is used in cancer therapy. What mass (in grams) of this isotope is required to produce an activity of 315 Ci?
Outside the nucleus, the neutron itself is radioactive and decays into a proton, an electron, and an antineutrino. The half-life of a neutron (mass = 1.675 × 10227 kg) outside the nucleus is 10.4
(a) Find the age of the sample, assuming that the activity per gram of carbon in a living organism has been constant at a value of 0.23 Bq.(b) Evidence suggests that the value of 0.23 Bq might have
The half-life for the a decay of uranium 23892U is 4.47 × 109 yr. Determine the age (in years) of a rock specimen that contains 60.0% of its original number of 23892U atoms.
Review Conceptual Example 11 before starting to solve this problem. The number of unstable nuclei remaining after a time t = 5.00 yr is N, and the number present initially is N0. Find the ratio N/N0
Multiple-Concept Example 10 reviews most of the concepts that are needed to solve this problem. Material found with a mummy in the arid highlands of southern Peru has a 146C activity per gram of
(a) A sample is being dated by the radiocarbon technique. If the sample were uncontaminated, its activity would be 0.011 Bq per gram of carbon. Find the true age (in years) of the sample.(b) Suppose
Use the plot of binding energy per nucleon in Figure 31.5 to determine the mass defect for the oxygen 168O nucleus. Express your answer in kilograms.
In a nucleus, each proton experiences a repulsive electrostatic force from each of the other protons. In a nucleus of gold 19779Au, what is the magnitude of the least possible electrostatic force of
When a sample from a meteorite is analyzed, it is determined that 93.8% of the original mass of a certain radioactive isotope is still present. Based on this finding, the age of the meteorite is
The b2 decay of phosphorus 3215P (atomic mass 5 31.973 907 u) produces a daughter nucleus that is sulfur 3216S (atomic mass = 31.972 070 u), a β– particle, and an antineutrino. The kinetic energy
Complete the following decay processes by stating what the symbol X represents (X = α, β–, β+, or γ):(a) (b) (c) (d)
To see why one curie of activity was chosen to be 3.7 × 1010 Bq, determine the activity (in disintegrations per second) of one gram of radium 22688Ra (T1/2 = 1.6 × 103 yr).
The largest stable nucleus has a nucleon number of 209, and the smallest has a nucleon number of 1. If each nucleus is assumed to be a sphere, what is the ratio (largest/smallest) of the surface
A sample of ore containing radioactive strontium 9038Sr has an activity of 6.0 × 105 Bq. The atomic mass of strontium is 89.908 u, and its half-life is 29.1 yr. How many grams of strontium are in
In a radioactive decay series similar to that shown in Figure 31.15, thorium (atomic mass = 228.028 715 u) undergoes four successive a decays, producing a daughter nucleus.Figure 31.15:(a)
What is the wavelength (in vacuum) of the 0.186-MeV g-ray photon emitted by 22688Ra?
Thorium h produces a daughter nucleus that is radioactive. The daughter, in turn, produces its own radioactive daughter, and so on. This process continues until bismuth is
A one-gram sample of thorium contains 2.64 × 1021 atoms and undergoes a decay with a half-life of 1.913 yr (1.677 × 104 h). Each disintegration releases an energy of 5.52 MeV (8.83 × 10–13
The ratio rX/rT of the radius of an unknown nucleus AZX to the radius of a tritium nucleus 31T is rX/rT = 1.10. Both nuclei contain the same number of neutrons. Identify the unknown nucleus in the
An unknown nucleus contains 70 neutrons and has twice the volume of the nickel 6028Ni nucleus. Identify the unknown nucleus in the form AZX. Use the periodic table on the inside of the back cover as
The drawings show four possibilities for hadrons in the quark theory. In each of the possibilities, the symbols for the quarks are shown together with the corresponding electric charges. Note that e
Which one of the following statements is not accepted as a part of the current picture of the universe? (a) The universe is expanding. (b) Early in the history of the universe, there was only one
Determine the unknown nuclear species in the following nuclear reaction:(a) (b) (c) γ(d)
The fission of can occur via many different reactions. In general, they can be written as follows:where X and Y refer to the identities of the fission fragments and η is the number of neutrons
In each of the following three nuclear fusion reactions, the masses of the nuclei are given beneath each nucleus. Rank the energy produced by each reaction in descending order (greatest first).(a) I,
Multiple-Concept Example 1 uses an approach similar to that needed in this problem, except here the temperature remains constant while a phase change occurs. A sample of liquid water at 100 °C and 1
What is the atomic number Z, the atomic mass number A, and the element X in the reaction 105B (α, p) AZX?
For each of the nuclear reactions listed below, determine the unknown particleAZX. Use the periodic table on the inside of the back cover as needed.(a) (b) (c) (d)
A neutron causes23290Th to change according to the reaction(a) Identify the unknown nucleus AZX, giving its atomic mass number A, its atomic number Z, and the symbol X for the element.(b) The AZX
Write the reactions below in the shorthand form discussed in the text.(a) (b) (c)
Complete the following nuclear reactions, assuming that the unknown quantity signified by the question mark is a single entity:(a) (n,α)?(b) (?, n)(c) (d)
During a nuclear reaction, an unknown particle is absorbed by a copper 6329Cu nucleus, and the reaction products are 6329Cu, a neutron, and a proton. What are the name, atomic number, and nucleon
Consider the induced nuclear reaction 21H + 147H → 126C + 42He. The atomic masses are 21H (2.014 102 u), 147N (14.003 074 u), 126C (12.000 000 u), and 42He (4.002 603 u). Determine the energy (in
What absorbed dose (in rads) of a particles (RBE = 15) causes as much biological damage as a 60-rad dose of protons (RBE = 10)?
Determine the atomic number Z, the atomic mass number A, and the element X for the unknown species in the following reaction for the fission of uranium :Consult the periodic table on the inside
How many neutrons are produced when 23592U fissions in the following Way 10n + 23592U → 13250Sn + 10142Mo + neutrons
Neutrons released by a fission reaction must be slowed by collisions with the moderator nuclei before the neutrons can cause further fissions. Suppose a 1.5-MeV neutron leaves each collision with 65%
The energy released by each fission within the core of a nuclear reactor is 2.0 × 102 MeV. The number of fissions occurring each second is 2.0 × 1019. Determine the power (in watts) that the
Uranium 23592U fissions into two fragments plus three neutrons: 10n + 23592U → (2 fragments) + 310n.. The mass of a neutron is 1.008 665 u and the mass of 23592U is 235.043 924 u. If 225.0 MeV of
When 1.0 kg of coal is burned, approximately 3.0 × 107 J of energy is released. If the energy released during each 23592U fission is 2.0 × 102 MeV, how many kilograms of coal must be burned to
Suppose that the 23994Pu nucleus fissions into two fragments whose mass ratio is 0.32:0.68. With the aid of Figure 32.8, estimate the energy (in MeV) released during this fission.
The water that cools a reactor core enters the reactor at 216 °C and leaves at 287 °C. (The water is pressurized, so it does not turn to steam.) The core is generating 5.6 × 109 W of power. Assume
Over a full course of treatment, two different tumors are to receive the same absorbed dose of therapeutic radiation. The smaller of the tumors (mass = 0.12 kg) absorbs a total of 1.7 J of energy.(a)
When a nuclear reactor is in a critical state, the neutrons released in each fission trigger an average of exactly one additional fission. If the average number of additional fissions triggered rises
Two deuterium atoms react to produce tritium and hydrogen according to the following fusion reaction:What is the energy (in MeV) released by this deuterium–deuterium reaction?
In one type of fusion reaction a proton fuses with a neutron to form a deuterium nucleus:The masses are (1.0078 u), (1.0087 u), and (2.0141 u). The g-ray photon is massless. How
The fusion of two deuterium nuclei (21H, mass = 2.0141 u) can yield a helium nucleus (32He, mass 5 3.0160 u) and a neutron (10n, mass 5 1.0087 u). What is the energy (in MeV) released in this
Tritium () is a rare isotope of hydrogen that can be produced by the following fusion reaction:(a) Determine the atomic mass number A, the atomic number Z, and the names X and Y of the unknown
In Example 6 it was determined that 17.6 MeV of energy is released when the following fusion reaction occurs:Ignore relativistic effects and determine the kinetic energies of the neutron and the Î±
Deuterium () is an attractive fuel for fusion reactions because it is abundant in the oceans, where about 0.015% of the hydrogen atoms in the water (H2O) are deuterium atoms.(a) How many deuterium
The proton–proton cycle thought to occur in the sun consists of the following sequence of reactions:(1) (2) (3) In these reactions is a positron (mass = 0.000 549 u), n is a neutrino (mass
The main decay mode for the negative pion is π– → μ– + v̅μ. Find the energy (in MeV) released in this decay. Consult Table 32.3 for rest energies and assume that the rest energy for

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