Quiz 42: Nuclear Physics

Consider two different isotopes of the same neutral element. Which statements about these isotopes are true? (There may be more than one correct choice.) A) Both isotopes contain the same number of neutrons. B) Both isotopes contain the same number of protons. C) Both isotopes contain the same number of nucleons. D) Both isotopes contain the same number of orbital electrons. E) The sum of the protons and neutrons is the same for both isotopes.

Consider the short-lived neutral isotope represented by X. Which of the following statements about this isotope are correct? (There may be more than one correct choice.) A) The isotope has 25 nucleons. B) The isotope has 25 protons. C) The isotope has 25 neutrons. D) The isotope has 15 orbital electrons. E) The isotope has 15 protons. F) The isotope has 10 neutrons.

Which of the following statements about the atomic nucleus is correct? (There may be more than one correct choice.) A) Large nuclei are denser than light nuclei. B) All nuclei have nearly the same density. C) The nucleus is held together more by the electrical force than by the gravitational force. D) A nucleus containing 20 nucleons will have approximately twice the radius as a nucleus containing 10 nucleons. E) As the number of nucleons increases the binding energy per nucleon always increases.

For a Nb atom, the number of protons, neutrons, and electrons in the atom is A) 41, 52, 93. B) 41, 52, 52. C) 41, 52, 41. D) 41, 52, 0. E) 52, 41, 0.

The iron nucleus has the greatest binding energy of any nucleus.

Going from medium mass nuclei to heavy nuclei, the average binding energy per nucleon A) decreases. B) behaves randomly with no clear pattern. C) does not change. D) increases. E) doubles.

Heavier stable nuclei tend to have A) half as many protons as neutrons. B) the same number of neutrons and protons. C) more neutrons than protons. D) no clear trend in the relative number of neutrons and protons. E) more protons than neutrons.

Which of the following statements about the strong nuclear force are correct? (There may be more than one correct choice.) A) It acts equally on protons and neutrons but not on electrons. B) It acts equally on protons, neutrons, and electrons. C) It has a much longer range than the electric force. D) It keeps electrons in their orbits around the nucleus. E) Because of its very short range, there is a limit to how large the nucleus can be.

If a nucleus decays by β^- decay to a daughter nucleus, which of the following statements about this decay are correct? (There may be more than one correct choice.) A) The daughter nucleus has more protons than the original nucleus. B) The daughter nucleus has more neutrons than the original nucleus. C) The daughter nucleus has the same number of nucleons as the original nucleus. D) The daughter nucleus has fewer protons than the original nucleus. E) The daughter nucleus has fewer neutrons than the original nucleus.

If a nucleus decays by alpha decay to a daughter nucleus, which of the following statements about this decay are correct? (There may be more than one correct choice.) A) The daughter nucleus has more protons than the original nucleus. B) The daughter nucleus has more neutrons than the original nucleus. C) The daughter nucleus has the same number of nucleons as the original nucleus. D) The daughter nucleus has fewer protons than the original nucleus. E) The daughter nucleus has fewer neutrons than the original nucleus.

If a nucleus decays by gamma decay to a daughter nucleus, which of the following statements about this decay are correct? (There may be more than one correct choice.) A) The daughter nucleus has more protons than the original nucleus. B) The daughter nucleus has more neutrons than the original nucleus. C) The daughter nucleus has the same number of nucleons as the original nucleus. D) The daughter nucleus has fewer protons than the original nucleus. E) The daughter nucleus has fewer neutrons than the original nucleus.

If a nucleus decays by β⁺ decay to a daughter nucleus, which of the following statements about this decay are correct? (There may be more than one correct choice.) A) The daughter nucleus has more protons than the original nucleus. B) The daughter nucleus has more neutrons than the original nucleus. C) The daughter nucleus has the same number of nucleons as the original nucleus. D) The daughter nucleus has fewer protons than the original nucleus. E) The daughter nucleus has fewer neutrons than the original nucleus.

Which of the following statements about β⁺ decay are correct? (There may be more than one correct choice.) During β⁺ decay A) an orbital electron is captured by the nucleus. B) a proton is emitted from the nucleus. C) a neutron in the nucleus decays to a proton and an electron. D) a proton in the nucleus decays to a positron and a neutron. E) the atomic number Z of the isotope increases by one unit but the atomic weight A remains unchanged.

A radioactive isotope decays by β^- emission with a half-life of 1.0 min. During the first 1.0 min, a particular sample emits 1000 β^- particles. During the next 1.0 min, the number of β^- particles this sample will emit will be closest to A) 250. B) 500. C) 1000. D) 1500. E) 2000.

A radioisotope has a half-life of τ at a temperature of 150 K. If its temperature is increased to 300 K, what will its half-life be? A) 4τ B) 2 τ C) τ D) τ/2 E) τ/4

The decay rate of an isotope is initially R₀, but after one half-life has gone by, the rate is R₀/2. At the end of the NEXT half-life, what will the decay rate be? A) 0 B) R₀/16 C) R₀/e D) R₀/4 E) R₀/e²

The half-life of cobalt-60 is 5.3 years, while that of strontium-90 is 28 years. Suppose you have a sample of each, such that they initially contain equal numbers of atoms of these nuclides. How will the activities (number of decays per second) of the samples compare? A) The activity of the cobalt-60 sample will be greater. B) The activities cannot be compared without more information. C) The activities will be equal. D) The activity of the strontium-90 sample will be greater.

The half-life of cobalt-60 is 5.3 years, while that of strontium-90 is 28 years. Suppose that samples of cobalt-60 and strontium-90 are such that they initially have the same activity (number of decays per second). What is true about the initial numbers of cobalt-60 and strontium-90 nuclei in these samples? A) There are more strontium-90 than cobalt-60 nuclei. B) There are equal numbers of cobalt-60 and strontium-90 nuclei. C) There are more cobalt-60 than strontium-90 nuclei. D) It is not possible to compare numbers of nuclei without knowing the masses of the samples.

A radioactive nuclide of atomic number Z emits an electron, then the daughter nuclide emits a gamma ray. What is the atomic number of the resulting nuclide after both processes? A) Z + 1 B) Z - 1 C) Z - 2 D) Z - 3 E) Z + 2

Modern nuclear bomb tests have created an extra high level of ¹⁴C in our atmosphere. Suppose that future archaeologists date samples from our era, but do not know about this testing. Will their dates be too young, too old, or still correct? If correct they are correct, why? A) too young B) too old C) correct, because ¹⁴C from bomb tests is different from that produced naturally D) correct, because modern biological materials do not gather ¹⁴C from bomb tests

A certain nucleus containing 8 protons and 7 neutrons has a radius R. Which of the following values would be closest to the expected value of the radius of a nucleus having 51 protons and 69 neutrons? A) 1.85R B) 2.00R C) 2.14R D) 6.38R E) 8.00R

A certain nucleus containing 8 protons and 7 neutrons has a density ρ. Which of the following values would be closest to the expected value of the density of a nucleus having 51 protons and 69 neutrons? A) 1.00 ρ B) 1.85 ρ C) 2.00 ρ D) 2.14 ρ E) 8.00 ρ

What would be the expected radius of a nucleus having 82 protons and 125 neutrons? A) 5.2 fm B) 5.9 fm C) 6.0 fm D) 7.1 fm E) 17 fm

What would be the expected radius of the nucleus of Sr? A) 4.0 fm B) 1.2 fm C) 5.4 fm D) 0.11 pm E) 0.54 pm

If a nucleus had a diameter of 8.0 fm, what would be its expected mass, in atomic mass units? A) 7 u B) 296 u C) 37 u D) 64 u E) 128 u

Two identical nuclei of mass 18 u are made to unite to make a single nucleus of mass 36 u. What is the radius of the result of this fusion? A) 4.0 fm B) 6.3 fm C) 4.5 fm D) 7.2 fm

The following masses are known: n (neutron) 1.008665 u H 1.007825 u Fe 56.935399 u What is the binding energy of Fe, in MeV? (1 u = 1.6605 × 10^-27 kg = 931.5 MeV/c²) A) 500 MeV B) 550 MeV C) 610 MeV D) 660 MeV E) 710 MeV

The neutral deuterium atom, H, has a mass of 2.014102 u; a neutral hydrogen atom has a mass of 1.007825 u; a neutron has a mass of 1.008665 u; and a proton has a mass of 1.007277 u. What is the binding energy of the H nucleus? (1 u = 931.494 MeV/c²) A) 1.1 MeV B) 1.7 MeV C) 2.2 MeV D) 2.9 MeV E) 3.4 MeV

What is the binding energy per nucleon for Al? The neutral Al atom has a mass of 26.981539 u; a neutral hydrogen atom has a mass of 1.007825 u; a neutron has a mass of 1.008665 u; and a proton has a mass of 1.007277 u. (1 u = 931.494 MeV/c²) A) 8.3 MeV B) 6.7 MeV C) 5.4 MeV D) 3.4 MeV E) 2.8 MeV

Uranium-238 decays into thorium-234 plus an alpha particle. How much energy is released in this process? 1 u = 931.494 MeV/c², and the relevant mass values are He: 4.002603 u Th: 234.043583 u U: 238.050786 u A) 4.28 MeV B) 3.76 MeV C) 3.18 MeV D) 2.89 MeV E) 5.05 MeV

Radium-226 decays into radon-222 plus an alpha particle. How much energy is released in this process? 1 u = 931.494 MeV/c², and the relevant mass values are He: 4.002603 u Rn: 222.017570 u Ra: 226.025402 u A) 4.24 MeV B) 3.76 MeV C) 4.87 MeV D) 5.05 MeV E) 5.39 MeV

Plutonium-239 decays into uranium-235 plus an alpha particle. The energy released in the process is 5.24 MeV. Given the following mass values He: 4.002603 u U: 235.043924 u What is the mass of Pu in atomic mass units? (1 u = 931.494 MeV/c²) A) 239.05215 u B) 239.02775 u C) 239.00189 u D) 238.99919 u E) 238.98884 u

A stationary plutonium-239 nucleus decays into a uranium-235 nucleus plus an alpha particle. The energy released in the process is 5.24 MeV. Given the following mass values He: 4.002603 u U: 235.043924 u What is the kinetic energy of the U nucleus? (1 u =931.494 MeV/c²) A) 0.0829 MeV B) 0.0837 MeV C) 0.0852 MeV D) 0.0863 MeV E) 0.0877 MeV

The carbon in your body was formed in nuclear reactions in long-dead stars. How much energy was released when three ⁴He nuclei combined to make ¹²C? The mass of ⁴He is 4.002603 u, the mass of ¹²C is 12.0000 u, and 1 u = 931.494 MeV/c². A) 7.274 MeV B) 3716 MeV C) 8.424 MeV D) 2.106 MeV

How much energy is released when 1.40 μg of ³H have decayed to ³He? The mass of ³He is 3.016029 u, the mass of ³H is 3.016049 u, and 1 u = 931.494 MeV/c². A) 830 J B) 11,900 J C) 7970 J D) 71,700 J E) 23,900 J

The set of nuclear reactions that power our sun can be summarized a 4p⁺ → ⁴He⁺² + 2e⁺. The masses of the particles involved are 938.272 MeV/c² (proton, p⁺), 3727.38 MeV/c² (alpha particle, ⁴He⁺²), and 0.511 MeV/c² (positron, e⁺). How much energy is released by each set of these reactions? A) 24.69 MeV B) 28.3 MeV C) 2790 MeV D) 279 MeV

A sphere made of a radioactive isotope initially has a mass of 6.88 kg. The half-life of this isotope is 1.34 h, and it decays by β^- emission. At the end of 2.68 h, what is the mass of this sphere? A) 6.88 kg B) 3.44 kg C) 1.72 kg D) 2.53 kg

A radioactive atom has 98 protons and 249 nucleons. If it undergoes alpha decay, what are the number of protons and nucleons, respectively, in the daughter nucleus? A) 100, 245 B) 94, 247 C) 96, 245 D) 96, 247 E) 100, 249

Scandium, Sc, decays by emitting a positron. What is the nuclide that is the product of the decay? A) Sc B) Sc C) Ca D) Ca E) Sc

The stability of C with respect to alpha, β⁺, and β^- decay is to be determined. Do not consider the possibility of decay by electron capture. The following atomic masses are known: He: 4.002603 u Be: 7.016928 u B: 11.009305 u C: 11.011433 u N: 11.026742 u The C nuclide is A) not subject to alpha, β⁺, or β^- decay. B) subject to alpha decay only. C) subject to β⁺ decay only. D) subject to β^- decay only. E) subject to β⁺ or β^- decay, but not to alpha decay.

The stability of Sc with respect to alpha, β⁺, and β^- decay is to be determined. Do not consider the possibility of decay by electron capture. The following atomic masses are known: He: 4.002603 u K: 42.960717 u Ca: 46.954543 u Sc 46.952409 u Ti: 46.951764 u The Sc nuclide is A) not subject to alpha, β⁺, or β^- decay. B) subject to alpha decay only. C) subject to β⁺ decay only. D) subject to β^- decay only. E) subject to β⁺ or β^- decay, but not to alpha decay.

The stability of Fe with respect to alpha, β⁺, and β^- decay is to be determined. Do not consider the possibility of decay by electron capture. The following atomic masses are known: He: 4.002603 u Cr: 51.944768 u Mn: 55.938907 u Fe: 55.934939 u Co: 55.939841 u The Fe nuclide is A) not subject to alpha, β⁺, or β^- decay. B) subject to alpha decay only. C) subject to β⁺decay only. D) subject to β^- decay only. E) subject to β⁺ or β^- decay, but not to alpha decay.

A certain substance has a half-life of 5.0 hours. How many nuclei of the substance are required to give an initial activity of 6.0 μCi? 1 Ci = 3.7 × 10¹⁰ Bq. A) 5.8 × 10⁹ B) 8.5 × 10⁸ C) 6.3 × 10⁸ D) 3.2 × 10⁹ E) 2.4 × 10⁹

What mass of ¹⁴C (having a half-life of 5730 years) do you need to provide a decay rate of 280.0 Bq? (1 u = 1.6605 × 10^-27 kg) A) 1.70 × 10^-12 kg B) 5.38 × 10^-19 kg C) 3.84 × 10^-20 kg D) 8.68 × 10^-13 kg

How many days are required for a radioactive sample, with a half-life of 5.7 d and an initial activity of 1.07 × 10⁵ Bq, to decay to an activity of 100 Bq? A) 57 d B) 46 d C) 68 d D) 39 d

A hospital patient has been given some ¹³¹I (half-life = 8.04 d) which decays at 4.2 times the acceptable level for exposure to the general public. How long must the patient wait for the decay rate to reach the acceptable level? Assume that the material merely decays and is not excreted by the body. A) 17 d B) 12 d C) 8.0 d D) 7.2 d

The material used in certain nuclear bombs is ²³⁹Pu, which has a half-life of about 20,000 years. How long must we wait for a buried stockpile of this substance to decay to 4.0% of its original ²³⁹Pu mass? A) 93,000 y B) 64,000 y C) 45,000 y D) 800 y

An air sample is contaminated with ¹⁵O, which has a half-life of 2.03 min. One possible way to minimize its hazard is to pass it through a long pipe to allow it to decay inside the pipe until it can be safely released into the atmosphere. If the oxygen moves at a speed of 1.1 m/s in the pipe, how long must the pipe be for the sample to have decayed to 3.0% of its original activity just as it leaves the pipe? A) 680 m B) 8.0 m C) 7.0 m D) 2.0 m

Rutherfordium-261 has a half-life of 1.08 min. How long will it take for a sample of rutherfordium to lose one-third of its nuclei? A) 1.02 min B) 1.62 min C) 0.632 min D) 2.70 min E) 3.24 min

A radioactive sample has a half-life of 10 min. What fraction of the sample is left after 40 min? A) 1/2 B) 1/4 C) 1/8 D) 1/16 E) 1/32

Fermium-253 has a half-life of 3.00 d. A sample of fermium contains 7.37 × 10⁷ nuclei. How long will it take for there to be only 3.36 × 10⁶ fermium nuclei in this sample? A) 2.75 d B) 9.80 d C) 13.4 d D) 15.7 d E) 58.6 d

In a laboratory accident a work area is contaminated with radioactive material. Health physicists monitor the area during a 30-day period and, after correcting for the background rate, obtain the data shown in the table. The accident occurred at t = 0. They determine that it will not be safe for workers to enter the area until the radioactivity level has dropped to 133 counts per minute. Of the choices listed below, which one is the earliest time that workers could safely return? A) 38 days B) 44 days C) 50 days D) 32 days E) 24 days

The unstable isotope ²³⁴Th decays by β emission with a half-life of 24.5 days. The initial decay rate of the sample was 9.9 × 10¹³ Bq. (1 u = 1.6605 x 10^-27 kg) (a) What mass of ²³⁴Th was initially present? (b) What is the decay rate after 68 days?

_{An isotope of Tc having a half-life of 6.0 h is used in bone scans. If a certain amount of this Tc is injected into the body, how long does it take for its initial decay rate to decrease BY 99%?} A) _{0.060 h} B) _{3.3 h} C) _{33 h} D) _{40 h} E) _{slightly more than a month}

The radioactivity due to carbon-14 measured in a piece of a wood from an ancient site was found to produce 20 counts per minute from a given sample, whereas the same amount of carbon from a piece of living wood produced 160 counts per minute. The half-life of carbon-14, a beta emitter, is 5730 y. The age of the artifact is closest to A) 5700 y B) 12,000 y C) 15,000 y D) 17,000 y E) 23,000 y

Carbon-14 has a half-life of 5730 y. A sample of wood has been recovered by an archaeologist. The sample is sent to a laboratory, where it is determined that the activity of the sample is 0.144 Bq/g. By comparing this activity with the activity of living organic matter, 0.230 Bq/g, the scientist determines how old the wood sample is, or more precisely, when the tree that the sample came from died. How old is the sample of wood? A) 3870 y B) 4250 y C) 4590 y D) 2630 y E) 2940 y

Living matter has 1.3 × 10^-10 % of its carbon in the form of ¹⁴C which has a half-life of 5730 y. A mammoth bone has a 300-g sample of carbon separated from it, and the sample is found to have an activity of 20 decays per second. How old is the bone? A) 15,000 y B) 10,900 y C) 11,500 y D) 7600 y E) 6400 y

An archaeologist finds the ¹⁴C in a sample of 3.10 g of material to be decaying at 107 counts per second. A modern 1.00-g sample of the same material decays at 151 counts per second. The half-life of ¹⁴C is 5730 y. How old is the sample? A) 12,200 y B) 8460 y C) 25,100 y D) 12,600 y

An ancient rock is found to contain ⁴⁰Ar gas, indicating that 77% of the ⁴⁰K in the rock has decayed since the rock solidified. Any argon would have boiled out of liquid rock. The half-life of ⁴⁰K is 1.25 billion years. How long ago did the rock solidify? A) 2.6 billion years B) 0.50 billion years C) 1.8 billion years D) 0.30 billion years

Today, the uranium found on Earth contains 0.720% ²³⁵U (with a half-life of 0.700 billion years) and 99.28% ²³⁸U (with a half-life of 4.50 billion years). At a time 2.20 billion years ago, what percent of the uranium on Earth was ²³⁸U (assuming that no other uranium isotopes were present)? A) 95.6% B) 2.18% C) 6.29% D) 8.68% E) 4.53%

A certain isotope has a half-life of 32.4 hr and a relative biological effectiveness of 3.50. A sample of this isotope initially delivers an absorbed dose of 0.240 Gy to 250 g of tissue. (a) What was the initial equivalent dose to the tissue in rem and in sieverts? (b) How many joules of energy did the 250-g sample initially receive from the isotope?

The maximum permissible workday dose for occupational exposure to radiation is 26 mrem. A 55-kg laboratory technician absorbs 3.3 mJ of 0.40-MeV gamma rays in a workday. The relative biological efficiency (RBE) for gamma rays is 1.00. What is the ratio of the equivalent dosage received by the technician to the maximum permissible equivalent dosage? A) 0.23 B) 0.25 C) 0.28 D) 0.30 E) 0.32

A 70-kg laboratory technician absorbs 2.9 mJ of 0.50-MeV gamma rays in a workday. How many gamma-ray photons does the technician absorb in a workday? A) 3.6 × 10¹⁰ B) 3.6 × 10⁹ C) 3.6 × 10⁸ D) 1.0 × 10⁹ E) 1.0 × 10⁸

A 57-kg researcher absorbs 6.3 × 10⁸ neutrons in a workday. The energy of the neutrons is 2.6 MeV. The relative biological efficiency (RBE) for fast neutrons is 10. What is the equivalent dosage of the radiation exposure, in mrem, of this worker? A) 4.6 mrem B) 1.4 mrem C) 2.9 mrem D) 14 mrem E) 46 mrem

The radioactive nuclei ⁶⁰Co is widely used in medical applications. It undergoes beta decay, and the total energy of the decay process is 2.82 MeV per decay event. The half-life of this nucleus is 272 days. Suppose that a patient is given a dose of 6.9 µCi of ⁶⁰Co. If all of this material decayed while in the patient's body, what would be the total energy deposited there? (1 Ci = 3.70 × 10¹⁰ decays/s) A) 11 J B) 8.6 GJ C) 3.9 J D) 24 J E) 4.15 MJ