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physics
modern physics

Questions and Answers of Modern Physics

A sample of radioactive material is initially found to have an activity of 115.0 decays/min. After 4 d 5 h, its activity is measured to be 73.5 decays/min.(a) Calculate the half-life of the
The rubidium isotope 87Rb is a β emitter with a half-life of 4.9 × 1010 y that decays into 87Sr. It is used to determine the age of rocks and fossils. Rocks containing the fossils of early
If there are N0 radioactive nuclei at time t = 0, the number that decay in some time interval dt at time t is dN = λN0e – λt dt. If we multiply this number by the
Using Table 40-1, find the Q values for the following reactions:(a) 1H + 3H → 3He + n + Q and(b) 2H + 2H → 3He + n + Q
Using Table 40-1, find the Q values for the following reactions:(a) 2H + 2H → 3H + 1H + Q,(b) 2H + 3He → 4He + 1H + Q, (c) 6Li + n → 3H + 4He + Q.
(a) Use the atomic masses m = 14.00324 u for 614C and m = 14.00307 u for714N to calculate the Q value (in MeV) for the β decay614C → 714N + β – + ve(b) Explain why you
(a) Use the atomic masses m = 13.00574 u for 713N and m = 13.003354 u for 613C to calculate the Q value (in MeV) for the β decay713N → 613C + β+ + ve(b) Explain why you need
Why is a moderator needed in an ordinary nuclear fission reactor?
Explain why water is more effective than lead in slowing down fast neutrons.
What is the advantage of a breeder reactor over an ordinary one? What are the disadvantages?
Assuming an average energy of 200 MeV per fission, calculate the number of fissions per second needed for a 500-MW reactor.
If the reproduction factor in a reactor is k = 1.1, find the number of generations needed for the power level to(a) Double,(b) Increase by a factor of 10, and(c) Increase by a factor of 100. Find the
Compute the temperature T for which kT = 10 keV, where k is Boltzmann's constant.
In 1989, researchers claimed to have achieved fusion in an electrochemical cell at room temperature. They claimed a power output of 4 W from deuterium fusion reactions in the palladium electrode of
A fusion reactor using only deuterium for fuel would have the two reactions in Problem 46 taking place in it. The 3H produced in the second reaction reacts immediately with another 2H to produce3H +
The fusion reaction between 2H and 3H is3H + 2H → 4He + n + 17.6 MeVUsing the given Q value, find the final energies of both the 4He nucleus and the neutron, assuming the initial kinetic energy of
Energy is generated in the sun and other stars by fusion. One of the fusion cycles, the proton–proton cycle, consists of the following reactions:1H + 1H → 2H + β+ + ve1H + 2H → 3He +
(a) Show that ke2 = 1.44 MeV · fm, where k is the Coulomb constant and e is the electron charge.(b) Show that hc = 1240 MeV · fm.
The counting rate from a radioactive source is 6400 counts/s. The half-life of the source is 10 s. Make a plot of the counting rate as a function of time for times up to 1 min. What is the decay
Find the energy needed to remove a neutron from(a) 4He (b) 7Li
The isotope 14C decays according to 14C → 14N + e – + ve . The atomic mass of 14N is 14.003074 u. Determine the maximum kinetic energy of the electron.
A neutron star is an object of nuclear density. If our sun were to collapse to a neutron star, what would be the radius of that object?
Nucleus A has a half-life that is twice that of nucleus B. At t = 0 the number of B nuclei in a sample is twice that of A nuclei. If the half-life of A is 1 h, will there ever be an instant when the
Calculate the nuclear radii of(a) 19F,(b) 145La, and(c) 246Cm.
The relative abundance of 40K (molecular mass 40.0 g/mol) is 1.2 × 10-4. The isotope 40K is radioactive with a halflife of 1.3 × 109 y. Potassium is an essential element of every living cell. In
A 0.05394-kg sample of 144Nd (atomic mass 143.91 u) emits an average of 2.36 α particles each second. Find the decay constant in s – 1 and the half-life in years.
The isotope 24Na is a β emitter with a half-life of 15 h. A saline solution containing this radioactive isotope with an activity of 600 kBq is injected into the bloodstream of a patient. Ten hours
Determine the closest distance of approach of an 8-MeV α particle in a head-on collision with a nucleus of 197Au and a nucleus of 10B,(a) Neglecting the recoil of the struck nuclei.(b) Repeat the
Twelve nucleons are in a one-dimensional infinite square well of length L = 3 fm.(a) Using the approximation that the mass of a nucleon is 1 u, find the lowest energy of a nucleon in the well.
The helium nucleus or α particle is a very tightly bound system. Nuclei with N = Z = 2n, where n is an integer, such as 12C, 16O, 20Ne, and 24Mg, may be thought of as
Radioactive nuclei with a decay constant of λ are produced in an accelerator at a constant rate Rp. The number of radioactive nuclei N then obeys the equation dN/dt = Rp – λN.(a)
The total energy consumed in the United States in 1 y is about 7.0 × 1019 J. How many kilograms of 235U would be needed to provide this amount of energy if we assume that 200 MeV of energy is
(a) Find the wavelength of a particle in the ground state of a one-dimensional infinite square well of length L = 2 fm.(b) Find the momentum in units of MeV/c for a particle with this wavelength.(c)
(a) How many a decays and how many β decays must a 222Rn nucleus undergo before it becomes a 210Pb nucleus?(b) Calculate the total energy released in the decay of one 222Rn nucleus to
Assume that a neutron decays into a proton plus an electron without the emission of a neutrino. The energy shared by the proton and electron is then 0.782 MeV. In the rest frame of the neutron, the
Consider a neutron of mass m moving with speed vL and making an elastic head-on collision with a nucleus of mass M that is at rest in the laboratory frame of reference.(a) Show that the speed of the
(a) Use the result of part (e) of Problem 72 (Equation 40-23) to show that after N head-on collisions of a neutron with carbon nuclei at rest, the energy of the neutron is approximately (0.714)NE0,
On the average, a neutron loses 63% of its energy in a collision with a hydrogen atom and 11% of its energy in a collision with a carbon atom. Calculate the number of collisions needed to reduce the
Frequently, the “daughter” of a radioactive “parent” is itself radioactive. Suppose the parent, designated by A has a decay constant λA, while the daughter, designated B has a decay constant
Suppose isotope A decays to isotope B with a decay constant λA, and isotope B in turn decays with a decay constant λB. Suppose a sample contains, at t = 0, only isotope A. Derive an expression for
An example of the situation discussed in Problem 75 is the radioactive isotope 229Th, an a emitter with a half-life of 7300 years. Its daughter, 225Ra, is a β emitter with a half-life of 14.8 d. In
Multiples choice(1)True or false:(a) The atomic nucleus contains protons, neutrons, and electrons.(b) The mass of 2H is less than the mass of a proton plus a neutron.(c) After two half-lives, all the
1. Why is the decay series A = 4n + 1 not found in nature?2. A decay by a emission is often followed by b decay. When this occurs, it is by β – and not β+ decay. Why?
1. The half-life of 14C is much less than the age of the universe, yet 14C is found in nature. Why?2. What happens to the neutrons produced in fission that do not produce another fission?
1. What effect would a long-term variation in cosmic -ray activity have on the accuracy of 14C dating?2. Why isn't there an element with Z = 130?3. Why does fusion occur spontaneously in the sun
1. Why do extreme changes in the temperature or pressure of a radioactive sample have little or no effect on the radioactivity?2. The stable isotope of sodium is 23Na. What kind of radioactivity
The mean lifetime of stationary muons is measured to be 2.2000 µs. The mean lifetime of high-speed muons in a burst of cosmic rays observed from Earth is measured to be 16.000 µs. To five
Figure is a graph of intensity versus wavelength for light reaching Earth from galaxy NGC 7319, which is about 3 × 108 light-years away. The most intense light is emitted by the oxygen in NGC 7319.
In the reaction p + 19F → a + 16O, the masses arem(p) = 1.007825 u, m(a) = 4.002603 u,m(F) = 18.998405 u, m(O) = 15.994915 u.Calculate the Q of the reaction from these data.
Another approach to velocity transformations. In Figure, reference frames B and C move past reference frame A in the common direction of their x axes. Represent the x components of the velocities of
Continuation of Problem 65. Use the result of part (b) in Problem 65 for the motion along a single axis in the following situation. Frame A in Figure is attached to a particle that moves with
Suppose a spinless particle is bound to a fixed center by a potential V(x) so asymmetrical that no energy level is degenerate. Using time-reversal invariance prove ? 0 For any energy eigenstate.
The Hamiltonian for a spin 1 system is given by H = AS2z + B (S2x – S2v).Solve this problem exactly to find the normalized energy eigenstates and eigenvalues. (A spin-dependent Hamiltonian of
a. What is the time-reversed state corresponding to D(R)|j, m>?b. Using the properties of time reversal and rotations, provec. Prove θ |j, m> = i2m|j, – m>.
A particle known as a pion lives for a short time before breaking apart into other particles. Suppose that a pion is moving at a speed of 0.990c, and an observer who is stationary in a laboratory
Suppose that you are planning a trip in which a spacecraft is to travel at a constant velocity for exactly six months, as measured by a clock on board the spacecraft, and then return home at the same
How fast must a meter stick be moving if its length is observed to shrink to one-half of a meter?
A tourist is walking at a speed of 1.3 m/s along a 9.0-km path that follows an old canal. If the speed of light in a vacuum were 3.0 m/s, how long would the path be, according to the tourist?
A woman is 1.6m tall and has a mass of 55kg. She moves past an observer with the direction of the motion parallel to her height. The observer measures her relativistic momentum to have a magnitude of
Starting from rest, two skaters push off against each other on smooth level ice, where friction is negligible. One is a woman and one is a man. The woman moves away with a velocity of +2.5 m/s
How much work must be done on an electron to accelerate it from rest to a speed of 0.990c?
Determine the ratio of the relativistic kinetic energy (½ mυ2) to the nonrelativistic kinetic energy when a particle has a speed of(a) 1.00 × 10-3c and(b) 0.970c.
A spacecraft approaching the earth launches an exploration vehicle. After the launch, an observer on earth sees the spacecraft approaching at a speed of 0.50c and the exploration vehicle approaching
Refer to Conceptual Example as an aid in solving this problem. An intergalactic cruiser has two types of guns: a photon cannon that fires a beam of laser light and an ion gun that shoots ions at a
A space traveler moving at a speed of 0.70c with respect to the earth makes a trip to a distant star that is stationary relative to the earth. He measures the length of this trip to be 6.5
The crew of a rocket that is moving away from the earth launches an escape pod, which they measure to be 45m long. The pod is launched toward the earth with a speed of 0.55c relative to the rocket.
The nucleus of the hydrogen atom has a radius of about 1 × 10-15 m. The electron is normally at a distance of about 5.3 × 10-11 m from the nucleus. Assuming that the hydrogen atom is a sphere with
There are Z protons in the nucleus of an atom, where Z is the atomic number of the element. An α particle carries a charge of +2e. In a scattering experiment, an α particle, heading directly toward
For a doubly ionized lithium atom Li2+ (Z = 3), what is the principal quantum number of the state in which the electron has the same total energy as a ground-state electron has in the hydrogen atom?
Find the energy (in joules) of the photon that is emitted when the electron in a hydrogen atom undergoes a transition from the n = 7 energy level to produce a line in the Paschen series.
A wavelength of 410.2 nm is emitted by the hydrogen atoms in a high-voltage discharge tube. What are the initial and final values of the quantum number n for the energy level transition that produces
For atomic hydrogen, the Paschen series of lines occurs when nf = 3, whereas the Brackett series occurs when nf = 4 in. Using this equation, show that the ranges of wavelengths in these two series
The maximum value for the magnetic quantum number in state A is mℓ = 2, while in state B it is mℓ = 1. What is the ratio LA/LB of the magnitudes of the orbital angular moment of an electron in
For an electron in a hydrogen atom, the z component of the angular momentum has a maximum value of Lz = 4.22 × 10-34 J · s. Find the three smallest possible values (the most negative) for the total
When an electron makes a transition between energy levels of an atom, there are no restrictions on the initial and final values of the principal quantum number n. According to quantum mechanics,
When a certain element is bombarded with high-energy electrons, Kα X-rays that have energy of 9890 eV are emitted. Determine the atomic number Z of the element, and identify the element. Use the
An X-ray tube contains a silver (Z = 47) target. The high voltage in this tube is increased from zero. Using the Bohr model, find the value of the voltage at which the Kα X-ray just appears in the
A laser is used in eye surgery to weld a detached retina back into place. The wavelength of the laser beam is 514 nm, and the power is 1.5 W. During surgery, the laser beam is turned on for 0.050 s.
In the line spectrum of atomic hydrogen, there is also a group of lines known as the Fund series. These lines are produced when electrons, excited to high energy levels, make transitions to the n = 5
The Bohr model can be applied to singly ionized helium He+ (Z = 2). Using this model, consider the series of lines that is produced when the electron makes a transition from higher energy levels into
A certain species of ionized atoms produces an emission line spectrum according to the Bohr model, but the number of protons Z in the nucleus is unknown. A group of lines in the spectrum forms a
For 20882Pbfind:(a) The net electrical charge of the nucleus,(b) The number of neutrons,(c) The number of nucleons,(d) The approximate radius of the nucleus, and(e) The nuclear density.
In electrically neutral atoms, how many(a) Protons are in the uranium 23892U nucleus,(b) Neutrons are in the mercury 20280Hg nucleus, and(c) Electrons are in orbit about the niobium 9341Nb nucleus?
Refer to Conceptual Example for a discussion of nuclear densities. A neutron star is composed of neutrons and has a density that is approximately the same as that of a nucleus. What is the radius of
Find the binding energy (in MeV) for lithium 73Li (atomic mass = 7.016 003 u).
Two isotopes of a certain element have binding energies that differ by 5.03 MeV. The isotope with the larger binding energy contains one more neutron than the other isotope. Find the difference in
Write the β+ decay process for each of the following nuclei, being careful to include Z and A and the proper chemical symbol for each daughter nucleus:(a) 189F(b) 158 O
Osmium 19176Os (atomic mass = 190.960 920 u) is converted into iridium 19177Ir (atomic mass = 190.960 584 u) via β- decay. What is the energy (in MeV) released in this process?
Find the energy (in MeV) released when β+ decay converts sodium 2211Na (atomic mass = 21.994 434 u) into neon (atomic mass = 21.991 383 u). Notice that the atomic mass for 2211Ne includes the mass
The half-lives in two different samples, A and B, of radioactive nuclei are related according to T½,B = ½T1/2,A · In a certain period, the number of radioactive nuclei in samples A decreases to
Suppose that the activity of a radioactive substance is initially 398 disintegrations/min and two days later, it is 285 disintegrations/min. What is the activity four days later still, or six days
The number of radioactive nuclei present at the start of an experiment is 4.60 × 1015. The number present twenty days later is 8.14 × 1014. What is the half-life (in days) of the nuclei?
Two radioactive nuclei A and B are present in equal numbers to begin with. Three days later, there are three times as many A nuclei as there are B nuclei. The half-life of species B is 1.50 days.
Review Multiple-Concept Example for help in approaching this problem. An archaeological specimen containing 9.2 g of carbon has an activity of 1.6 Bq. How old (in years) is the specimen?
When any radioactive dating method is used, experimental error in the measurement of the sample’s activity leads to error in the estimated age. In an application of the radiocarbon dating technique
The photomultiplier tube in a commercial scintillation counter contains 15 of the special electrodes, or dynodes. Each dynode produces 3 electrons for every electron that strikes it. One
Neutrons (RBE = 2.0) and α particles have the same biologically equivalent dose. However, the absorbed dose of the neutrons is six times the absorbed dose of the α particles. What is the RBE for
A beam of particles is directed at a 0.015-kg tumor. There are 1.6 × 1010 particles per second reaching the tumor, and the energy of each particle is 4.0 MeV. The RBE for the radiation is 14. Find
A beam of nuclei is used for cancer therapy. Each nucleus has an energy of 130 MeV, and the relative biological effectiveness (RBE) of this type of radiation is 16. The beam is directed onto a
Write the equation for the reaction 178O (γ, αn) 126C. The notation “αn” means that an α particle and a neutron are produced by the reaction.

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