Problem 26
As a health physicist, you are being consulted about a spill in a radiochemistry lab. The isotope spilled was 400 \(\mu\)Ci of \(^1$$^3$$^1\)Ba, which has a half-life of 12 days. (a) What mass of \(^1$$^3$$^1\)Ba was spilled? (b) Your recommendation is to clear the lab until the radiation level has fallen 1.00 \(\mu\)Ci. How long will the lab have to be closed?
Problem 27
Measurements on a certain isotope tell you that the decay rate decreases from 8318 decays/min to 3091 decays/min in 4.00 days. What is the half-life of this isotope?
Problem 28
A radioactive isotope has a half-life of 43.0 min. At \(t\) = 0 its activity is 0.376 Ci. What is its activity at \(t\) = 2.00 h?
Problem 29
The radioactive nuclide \(^1$$^9$$^9\)Pt has a half-life of 30.8 minutes. A sample is prepared that has an initial activity of 7.56 \(\times\) 10\(^1$$^1\) Bq. (a) How many \(^1$$^9$$^9\)Pt nuclei are initially present in the sample? (b) How many are present after 30.8 minutes? What is the activity at this time? (c) Repeat part (b) for a time 92.4 minutes after the sample is first prepared.
Problem 31
(a) If a chest x ray delivers 0.25 mSv to 5.0 kg of tissue, how many \(total\) joules of energy does this tissue receive? (b) Natural radiation and cosmic rays deliver about 0.10 mSv per year at sea level. Assuming an RBE of 1, how many rem and rads is this dose, and how many joules of energy does a 75-kg person receive in a year? (c) How many chest x rays like the one in part (a) would it take to deliver the same \(total\) amount of energy to a 75-kg person as she receives from natural radiation in a year at sea level, as described in part (b)?
Problem 32
\(\textbf{Radiation Overdose}\). If a person's entire body is exposed to 5.0 J/kg of x rays, death usually follows within a few days. (a) Express this lethal radiation dose in Gy, rad, Sv, and rem. (b) How much total energy does a 70.0-kg person absorb from such a dose? (c) If the 5.0 J/kg came from a beam of protons instead of x rays, what would be the answers to parts (a) and (b)?
Problem 33
A nuclear chemist receives an accidental radiation dose of 5.0 Gy from slow neutrons (RBE \(=\) 4.0). What does she receive in rad, rem, and J/kg?
Problem 34
A person exposed to fast neutrons receives a radiation dose of 300 rem on part of his hand, affecting 25 g of tissue. The RBE of these neutrons is 10. (a) How many rad did he receive? (b) How many joules of energy did he receive? (c) Suppose the person received the same rad dosage, but from beta rays with an RBE of 1.0 instead of neutrons. How many rem would he have received?
Problem 36
\(\textbf{To Scan or Not to Scan?}\) It has become popular for some people to have yearly whole-body scans (CT scans, formerly called CAT scans) using x rays, just to see if they detect anything suspicious. A number of medical people have recently questioned the advisability of such scans, due in part to the radiation they impart. Typically, one such scan gives a dose of 12 mSv, applied to the \(whole\) \(body\). By contrast, a chest x ray typically administers 0.20 mSv to only 5.0 kg of tissue. How many chest x rays would deliver the same total amount of energy to the body of a 75-kg person as one whole-body scan?
Problem 37
A 67-kg person accidentally ingests 0.35 Ci of tritium. (a) Assume that the tritium spreads uniformly throughout the body and that each decay leads on the average to the absorption of 5.0 keV of energy from the electrons emitted in the decay. The half-life of tritium is 12.3 y, and the RBE of the electrons is 1.0. Calculate the absorbed dose in rad and the equivalent dose in rem during one week. (b) The \(\beta$$^-\) decay of tritium releases more than 5.0 keV of energy. Why is the average energy absorbed less than the total energy released in the decay?
