Exam 42: Nuclear Physics

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)?

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)

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 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 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?

Which of the following statements about β⁺ decay are correct? (There may be more than one correct choice.) During β⁺ decay

If a 2.0-MeV neutron released in a fission reaction loses half of its energy in each moderator collision, how many collisions are needed to reduce its energy to (1/25) eV?

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?

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.)

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.)

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

Which of the following descriptions best describes the process by which energy is released in a conventional nuclear reactor?

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?

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 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?

Going from medium mass nuclei to heavy nuclei, the average binding energy per nucleon

How much energy is released in the total fission of 2.0 g of ²³⁵U? 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)

Two deuterium nuclei, H, fuse to produce a helium nucleus, H, and a neutron. A neutral deuterium atom has a mass of 2.014102 u; a neutral helium atom has a mass of 3.016030 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 1.007276 u. How much energy is released in the process? (1 u = 931.494 MeV/c²)

A radioactive sample has a half-life of 10 min. What fraction of the sample is left after 40 min?

What would be the expected radius of a nucleus having 82 protons and 125 neutrons?