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20.7 End-of-Chapter Material

Application Problems

  1. Until the 1940s, uranium glazes were popular on ceramic dishware. One brand, Fiestaware, had bright orange glazes that could contain up to 20% uranium by mass. Although this practice is less common today due to the negative association of radiation, it is still possible to buy Depression-era glassware that is quite radioactive. Aqueous solutions in contact with this “hot” glassware can reach uranium concentrations up to 10 ppm by mass. If 1.0 g of uranium undergoes 1.11 × 107 decays/s, each to an α particle with an energy of 4.03 MeV, what would be your exposure in rem and rad if you drank 1.0 L of water that had been sitting for an extended time in a Fiestaware pitcher? Assume that the water and contaminants are excreted only after 18 h and that you weigh 70.0 kg.

  2. Neutrography is a technique used to take the picture of an object using a beam of neutrons. How does the penetrating power of a neutron compare with alpha, beta, and gamma radiation? Do you expect similar penetration for protons? How would the biological damage of each particle compare with the other types of radiation? (Recall that a neutron’s mass is approximately 2000 times the mass of an electron.)

  3. Spent fuel elements in a nuclear reactor contain radioactive fission products in addition to heavy metals. The conversion of nuclear fuel in a reactor is shown here:

    Neglecting the fission products, write balanced nuclear reactions for the conversion of the original fuel to each product.

  4. The first atomic bomb used 235U as a fissile material, but there were immense difficulties in obtaining sufficient quantities of pure 235U. A second fissile element, plutonium, was discovered in 1940, and it rapidly became important as a nuclear fuel. This element was produced by irradiating 238U with neutrons in a nuclear reactor. Complete the series that produced plutonium, all isotopes of which are fissile:

    U 92 238 + n 0 1 U Np  →  Pu
  5. Boron neutron capture therapy is a potential treatment for many diseases. As the name implies, when boron-10, one of the naturally occurring isotopes of boron, is bombarded with neutrons, it absorbs a neutron and emits an α particle. Write a balanced nuclear reaction for this reaction. One advantage of this process is that neutrons cause little damage on their own, but when they are absorbed by boron-10, they can cause localized emission of alpha radiation. Comment on the utility of this treatment and its potential difficulties.

  6. An airline pilot typically flies approximately 80 h per month. If 75% of that time is spent at an altitude of about 30,000 ft, how much radiation is that pilot receiving in one month? over a 30 yr career? Is the pilot receiving toxic doses of radiation?

  7. At a breeder reactor plant, a 72 kg employee accidentally inhaled 2.8 mg of 239Pu dust. The isotope decays by alpha decay and has a half-life of 24,100 yr. The energy of the emitted α particles is 5.2 MeV, and the dust stays in the employee’s body for 18 h.

    1. How many plutonium atoms are inhaled?
    2. What is the energy absorbed by the body?
    3. What is the physical dose in rads?
    4. What is the dose in rems? Will the dosage be fatal?
  8. For many years, the standard source for radiation therapy in the treatment of cancer was radioactive 60Co, which undergoes beta decay to 60Ni and emits two γ rays, each with an energy of 1.2 MeV. Show the sequence of nuclear reactions. If the half-life for beta decay is 5.27 yr, how many 60Co nuclei are present in a typical source undergoing 6000 dps that is used by hospitals? The mass of 60Co is 59.93 amu.

  9. It is possible to use radioactive materials as heat sources to produce electricity. These radioisotope thermoelectric generators (RTGs) have been used in spacecraft and many other applications. Certain Cold War–era Russian-made RTGs used a 5.0 kg strontium-90 source. One mole of strontium-90 releases β particles with an energy of 0.545 MeV and undergoes 2.7 × 1013 decays/s. How many watts of power are available from this RTG (1 watt = 1 J/s)?

  10. Potassium consists of three isotopes (potassium-39, potassium-40, and potassium-41). Potassium-40 is the least abundant, and it is radioactive, decaying to argon-40, a stable, nonradioactive isotope, by the emission of a β particle with a half-life of precisely 1.25 × 109 yr. Thus the ratio of potassium-40 to argon-40 in any potassium-40–containing material can be used to date the sample. In 1952, fragments of an early hominid, Meganthropus, were discovered near Modjokerto in Java. The bone fragments were lying on volcanic rock that was believed to be the same age as the bones. Potassium–argon dating on samples of the volcanic material showed that the argon-40-to-potassium-40 molar ratio was 0.00281:1. How old were the rock fragments? Could the bones also be the same age? Could radiocarbon dating have been used to date the fragments?


  1. 6.6 × 10−3 rad; 0.13 rem


    U 92 235 + n 0 1 U 92 236 + γ U 92 238 + n 0 1 U 92 239 + γ U 92 239 N 93 239 p + β 1 0 N 93 239 p P 94 239 u + β 1 0 P 94 239 u A 95 239 m + β 1 0 A 95 239 m C 96 239 m + β 1 0
    1. 7.1 × 1018 atoms of Pu
    2. 0.35 J
    3. 0.49 rad
    4. 9.8 rem; this dose is unlikely to be fatal.
  3. 130 W