Exam 42: Nuclear Physics

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?

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)

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?

If a nucleus had a diameter of 8.0 fm, what would be its expected mass, in atomic mass units?

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 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?

Which of the following statements about the strong nuclear force are correct? (There may be more than one correct choice.)

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?

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)

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

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 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.

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 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)

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

Which of the following statements about the atomic nucleus is correct? (There may be more than one correct choice.)

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)

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 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?