Exam 34: Geometric Optics

Radioactivity: 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.)

Radioactivity: 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

Nuclear fission: How much energy is released in the total fission of of The average energy per fission is 200.0 MeV. (1 u = 931.5 MeV/c² = 1.6605 × 10^-27 kg, 1 eV = 1.60 × 10^-19 J)

Radioactive decay: 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?

Biomedicine: A 57-kg researcher absorbs 6.3 × 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?

Radioactivity: 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.)

Nuclear reactions: In the nuclear reaction B + He → H + X, which of the following is the missing nuclear product X?

Nuclear binding energy: 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)

Radioactive dating: 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)?

Radioactive decay: _{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%?}

Radioactive dating: 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?

Reaction energy: The detonation of a certain nuclear device results in a mass decrease of between the initial and the final ingredients. How much energy is released by this detonation? (c = 3.00 × 10⁸ m/s)

Nuclear fission: An excited U^* nucleus undergoes fission into two fragments, as shown: U* → Ba + Kr The following atomic masses are known: Kr: 91.926270 u Ba: 143.922845 u U*: 236.045563 u Assume, at a given instant, that the two fission fragments are spherical, just barely in contact, and carry spherically symmetric charge distributions. At that instant, what is the electrostatic interaction energy of the two fragments, in MeV? (1 u = 1.6605 × 10^-27 kg = 931.5 MeV/c², 1/4πε₀ = 9.0 × 10⁹ N * m²/C²)

Reaction energy: The reaction energy (Q value) for a particular reaction is -2.4 MeV, and the reaction's threshold energy is 9.60 MeV. What is the ratio of the mass of the incident particle to the mass of the stationary target nucleus?

Nuclear fusion: In massive stars, three helium nuclei fuse together, forming a carbon nucleus. This reaction heats the core of the star. The net mass of the three helium nuclei must therefore be

Radioactive decay: 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 × 10^-27 kg) (a) What mass of ²³⁴Th was initially present? (b) What is the decay rate after 68 days?

Reaction energy: Find the reaction energy (Q value) of the reaction N + He → O + H, given the following masses: N: 14.003074 u He: 4.002603 u O : 16.999131 u H: 1.007825 u (1 u = 931.5 MeV/c²)

Radioactive dating: 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?

Nuclear binding energy: 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)

Nuclear binding energy: Heavier stable nuclei tend to have