Determine the mass defect (in atomic mass units) for (a)

For 208 82 Pb fi nd (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.

A nucleus contains 18 protons and 22 neutrons. What is the radius of this nucleus?

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) 195 78X (b) 32 16X (c) 63 29X (d) 11 5 X (e) 239 94X

By what factor does the nucleon number of a nucleus have to increase in order for the nuclear radius to double?

In electrically neutral atoms, how many (a) protons are in the uranium 238 92U nucleus, (b) neutrons are in the mercury 202 80Hg nucleus, and (c) electrons are in orbit about the niobium 93 41 Nb nucleus?

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 areas of these spheres?

The ratio rX/rT of the radius of an unknown nucleus A ZX to the radius of a tritium nucleus 3 1T is rX rT 5 1.10. Both nuclei contain the same number of neutrons. Identify the unknown nucleus in the form A ZX. Use the periodic table on the inside of the back cover as needed.

An unknown nucleus contains 70 neutrons and has twice the volume of the nickel 60 28Ni nucleus. Identify the unknown nucleus in the form A ZX. Use the periodic table on the inside of the back cover as needed.

Refer to Conceptual Example 1 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 a neutron star whose mass is 0.40 times the mass of the sun?

Suppose that you could pack neutrons (mass 5 1.67 3 10227 kg) inside a tennis ball (radius 5 0.032 m) in the same way as neutrons and protons are packed together in the nucleus of an atom. (a) Approximately how many neutrons would fi t inside the tennis ball? (b) A small object is placed 2.0 m from the center of the neutron-packed tennis ball, and the tennis ball exerts a gravitational force on it. When the object is released, what is the magnitude of the acceleration that it experiences? Ignore the gravitational force exerted on the object by the earth.

Find the binding energy (in MeV) for lithium 7 3 Li (atomic mass 5 7.016 003 u).

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 3 2He, which has an atomic mass of 3.016 030 u, and (b) the isotope of hydrogen known as tritium 3 1T, which has an atomic mass of 3.016 050 u. (c) On the basis of your answers to parts (a) and (b), state which nucleus requires more energy to disassemble it into its separate and stationary constituent nucleons. Give your reasoning.

A 245-kg boulder is dropped into a mine shaft that is 3.0 3 103 m deep. During the boulders fall, the system consisting of the earth and the boulder loses a certain amount of gravitational potential energy. It would take an equal amount of energy to free the boulder from the shaft by raising it back to the top, so this can be considered the systems binding energy. (a) Determine the binding energy (in joules) of the earthboulder system. (b) How much mass does the earthboulder system lose when the boulder falls to the bottom of the shaft?

For lead 206 82Pb (atomic mass 5 205.974 440 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 energy that binds a single nucleon to the remainder of the nucleus. For example, separating nitrogen 14 7N into nitrogen 13 7 N and a neutron takes energy equal to the binding energy of the neutron, as shown below: 14 7N 1 Energy 13 7N 1 1 0n Find the energy (in MeV) that binds the neutron to the 14 7N nucleus by considering the mass of 13 7 N (atomic mass 5 13.005 738 u) and the mass of 1 0n (atomic mass 5 1.008 665 u), as compared to the mass of 14 7N (atomic mass 5 14.003 074 u). (b) Similarly, one can speak of the energy that binds a single proton to the 14 7N nucleus: 14 7N 1 Energy 13 6C 1 1 1H Following the procedure outlined in part (a), determine the energy (in MeV) that binds the proton (atomic mass 5 1.007 825 u) to the 14 7 N nucleus. The atomic mass of carbon 13 6C is 13.003 355 u. (c) Which nucleon is more tightly bound, the neutron or the proton?

Two isotopes of a certain element have binding energies that diff er by 5.03 MeV. The isotope with the larger binding energy contains one more neutron than the other isotope. Find the diff erence in atomic mass between the two isotopes.

A 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 electrons to the nucleus and the energy that binds one atom to another in the structure of the metal. For simplicity, assume that all the copper nuclei are 63 29Cu (atomic mass 5 62.939 598 u).

Write the b1 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) 18 9 F (b) 15 8 O

Write the b2 decay process for carbon 14 6C, including the chemical symbols as well as the values of Z and A for the parent and daughter nuclei and the b2 particle.

Write the b2 decay process for carbon 14 6C, including the chemical symbols as well as the values of Z and A for the parent and daughter nuclei and the b2 particle.

Find the energy that is released when a nucleus of lead 211 82 Pb (atomic mass 5 210.988 735 u) undergoes b2 decay to become bismuth 211 83Bi (atomic mass 5 210.987 255 u).

Find the energy (in MeV) released when a decay converts radium 226 88 Ra (atomic mass 5 226.025 40 u) into radon 222 86 Rn (atomic mass 5 222.017 57 u). The atomic mass of an a particle is 4.002 603 u.

Find the energy (in MeV) released when a decay converts radium 226 88 Ra (atomic mass 5 226.025 40 u) into radon 222 86 Rn (atomic mass 5 222.017 57 u). The atomic mass of an a particle is 4.002 603 u.

In the form A ZX, identify the daughter nucleus that results when (a) plutonium 242 94 Pu undergoes a decay, (b) sodium 24 11Na undergoes b2 decay, and (c) nitrogen 13 7 N undergoes b1 decay.

When uranium 235 92U decays, it emits (among other things) a g ray that has a wavelength of 1.14 3 10211 m. Determine the energy (in MeV) of this g ray.

Polonium 210 84 Po (atomic mass 5 209.982 848 u) undergoes a decay. Assuming that all the released energy is in the form of kinetic energy of the a particle (atomic mass 5 4.002 603 u) and ignoring the recoil of the daughter nucleus (lead 206 82 Pb, 205.974 440 u), fi nd the speed of the a particle. Ignore relativistic eff ects.

Radon 220 86 Rn produces a daughter nucleus that is radioactive. The daughter, in turn, produces its own radioactive daughter, and so on. This process continues until lead 208 82 Pb is reached. What are the total number Na of a particles and the total number Nb of b2 particles that are generated in this series of radioactive decays?

Review Conceptual Example 5 as background for this problem. The a decay of uranium 238 92 U produces thorium 234 90 Th (atomic mass 5 234.0436 u). In Example 4, the energy released in this decay is determined to be 4.3 MeV. Determine how much of this energy is carried away by the recoiling 234 90 Th daughter nucleus and how much by the a particle (atomic mass 5 4.002 603 u). Assume that the energy of each particle is kinetic energy, and ignore the small amount of energy carried away by the g ray that is also emitted. In addition, ignore relativistic eff ects.

An isotope of beryllium (atomic mass 5 7.017 u) emits a g ray and recoils with a speed of 2.19 3 104 m/s. Assuming that the beryllium nucleus is stationary to begin with, fi nd the wavelength of the g ray.

Find the energy (in MeV) released when b1 decay converts sodium 22 11Na (atomic mass 5 21.994 434 u) into neon 22 10Ne (atomic mass 5 21.991 383 u). Notice that the atomic mass for 22 11Na includes the mass of 11 electrons, whereas the atomic mass for 22 10Ne includes the mass of only 10 electrons

In 9.0 days the number of radioactive nuclei decreases to oneeighth the number present initially. What is the half-life (in days) of the material?

In 9.0 days the number of radioactive nuclei decreases to oneeighth the number present initially. What is the half-life (in days) of the material?

The 32 15P isotope of phosphorus has a half-life of 14.28 days. What is its decay constant in units of s21 ?

Strontium 90 38Sr 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, 90 38Sr is a particularly serious health hazard. How long (in years) will it take for 99.9900% of the 90 38Sr released in a nuclear reactor accident to disappear?

Two radioactive waste products from nuclear reactors are strontium 90 38Sr (T1/2 5 29.1 yr) and cesium 134 55 Cs (T1/2 5 2.06 yr). These two species are present initially in a ratio of N0,Sr /N0,Cs 5 7.80 3 1023 . What is the ratio NSr /NCs fi fteen years later?

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 after the start? Give your answer in disintegrations/min.

Iodine 131 53 I 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 131 53 I remains after 30.0 days?

The number of radioactive nuclei present at the start of an experiment is 4.60 3 1015. The number present twenty days later is 8.14 3 1014. What is the half-life (in days) of the nuclei?

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 decay. On the fi rst day, 10% of the 5800 contestants are notifi ed by text message that they have been randomly eliminated from the lottery. The other 90% of the contestants automatically advance to the next round. On each of the following days, 10% of the remaining contestants are randomly eliminated, until fewer than 10 contestants remain. Determine (a) the activity (number of contestants eliminated per day) on the second day of the lottery, (b) the decay constant (in d21 ) of the lottery, and (c) the half-life (in d) of the lottery

A device used in radiation therapy for cancer contains 0.50 g of cobalt 60 27Co (59.933 819 u). The half-life of 60 27Co is 5.27 yr. Determine the activity of the radioactive material.

A one-gram sample of radium 224 88 Ra (atomic mass 5 224.020 186 u, T1/2 5 3.66 days) contains 2.69 3 1021 nuclei and undergoes a decay to produce radon 220 86 Rn (atomic mass 5 220.011 368 u). The atomic mass of an a particle is 4.002 603 u. The latent heat of fusion for water is 33.5 3 104 J/kg. With the energy released in 3.66 days, how many kilograms of ice could be melted at 0 8C?

The isotope 198 79Au (atomic mass 5 197.968 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 5 1.675 3 10227 kg) outside the nucleus is 10.4 min. On average, * * * * * over what distance (in meters) would a beam of 5.00-eV neutrons travel before the number of neutrons decreased to 75.0% of its initial value?

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. Find the halflife of species A.

A sample has a 14 6 C activity of 0.0061 Bq per gram of carbon. (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 been as much as 40% larger. Repeat part (a), taking into account this 40% increase

Review Multiple-Concept Example 10 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?

The half-life for the a decay of uranium 238 92U is 4.47 3 109 yr. Determine the age (in years) of a rock specimen that contains 60.0% of its original number of 238 92U atoms.

Review Conceptual Example 11 before starting to solve this problem. The number of unstable nuclei remaining after a time t 5 5.00 yr is N, and the number present initially is N0. Find the ratio N/N0 for (a) 14 6 C (half-life 5 5730 yr), (b) 15 8 O (half-life 5 122.2 s; use t 5 1.00 h, since otherwise the answer is out of the range of your calculator), and (c) 3 1H (half-life 5 12.33 yr). Verify that your answers are consistent with the reasoning in Conceptual Example 11.

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 14 6 C activity per gram of carbon that is 78.5% of the activity present initially. How long ago (in years) did this individual die?

When any radioactive dating method is used, experimental error in the measurement of the samples activity leads to error in the estimated age. In an application of the radiocarbon dating technique to certain fossils, an activity of 0.100 Bq per gram of carbon is measured to within an accuracy of 610.0%. Find the age of the fossils and the maximum error (in years) in the value obtained. Assume that there is no error in the 5730-year half-life of 14 6 C nor in the value of 0.23 Bq per gram of carbon in a living organism.

(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 the sample is contaminated, so that only 98.0% of its carbon is ancient carbon. The remaining 2.0% is fresh carbon, in the sense that the 14 6 C it contains has not had any time to decay. Assuming that the lab technician is unaware of the contamination, what apparent age (in years) would be determined for the sample?

Use the plot of binding energy per nucleon in Figure 31.5 to determine the mass defect for the oxygen 16 8O 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 197 79 Au, what is the magnitude of the least possible electrostatic force of repulsion that one proton can exert on another?

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 fi nding, the age of the meteorite is calculated to be 4.51 3 109 yr. What is the half-life (in yr) of the isotope used to date the meteorite?

The b2 decay of phosphorus 32 15P (atomic mass 5 31.973 907 u) produces a daughter nucleus that is sulfur 32 16S (atomic mass 5 31.972 070u), a b2 particle, and an antineutrino. The kinetic energy of the b2 particle is 0.90 MeV. Find the maximum possible energy (in MeV) that the antineutrino could carry away

Complete the following decay processes by stating what the symbol X represents (X 5 a, b2, b1, or g): (a) 211 82 Pb B 211 83 Bi 1 X (c) 231 90 Th* B 231 90 Th 1 X (b) 11 6 C B 11 5 B 1 X (d) 210 84 Po B 206 82 Pb 1 X

To see why one curie of activity was chosen to be 3.7 3 1010 Bq, determine the activity (in disintegrations per second) of one gram of radium 226 88 Ra (T1/2 5 1.6 3 103 yr).

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 photoelectron strikes the fi rst dynode. What is the maximum number of electrons that strike the 15th dynode?

A sample of ore containing radioactive strontium 90 38Sr has an activity of 6.0 3 105 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 the sample?

Determine the symbol Z AX for the parent nucleus whose a decay produces the same daughter as the b2 decay of thallium 208 81 Tl.

In a radioactive decay series similar to that shown in Figure 31.15, thorium 228 90 Th (atomic mass 5 228.028 715 u) undergoes four successive a decays, producing a daughter nucleus. (a) Determine the symbol Z AX for the nucleus produced by four successive a decays of 228 90 Th. (b) What is the total amount of energy (in MeV) released in this series of a decays? The mass of the daughter nucleus can be obtained by using the result of part (a) and consulting Appendix F at the back of the book. The mass of a single a particle is 4.002 603 u.

What is the wavelength (in vacuum) of the 0.186-MeV g-ray photon emitted by 226 88Ra?

Thorium 228 90Th produces a daughter nucleus that is radioactive. The daughter, in turn, produces its own radioactive daughter, and so on. This process continues until bismuth 212 83Bi is reached. Concepts: (i) How many of the 90 protons in the thorium nucleus are carried off by the a particles? (ii) How many protons are left behind when the b2 particles are emitted? (iii) How many of the 228 nucleons in the thorium nucleus * are carried off by the a particles? (iv) Does the departure of a b2 particle alter the number of nucleons? Calculations: What are the total number Na of a particles and the total number Nb of b2 particles that are generated in this series of radioactive decays?

A one-gram sample of thorium 228 90 Th contains 2.64 3 1021 atoms and undergoes a decay with a half-life of 1.913 yr (1.677 3 104 h). Each disintegration releases an energy of 5.52 MeV (8.83 3 10213 J). Assume that all of the energy is used to heat a 3.8-kg sample of water. Concepts: (i) How much heat Q is needed to raise the temperature of a mass m of water by DT degrees? (ii) The energy released by each disintegration is E. What is the total energy Etotal released by a number n of disintegrations? (iii) What is the number n of disintegrations that occur during a time t? Calculations: Find the change in temperature of the 3.8-kg sample of water that occurs in one hour.