Problem 1
How many protons and how many neutrons are there in a nucleus of the most common isotope of (a) silicon, \(^{28}_{14}Si\); (b) rubidium, \(^{85}_{37}Rb\); (c) thallium, \(^{205}_{81}Tl\)?
Problem 3
Hydrogen atoms are placed in an external magnetic field. The protons can make transitions between states in which the nuclear spin component is parallel and antiparallel to the field by absorbing or emitting a photon. What magnetic- field magnitude is required for this transition to be induced by photons with frequency 22.7 MHz?
Problem 13
What nuclide is produced in the following radioactive decays? (a) \(\alpha\) decay of \(^{239}_{94}Pu\); (b) \(\beta$$^-\) decay of \(^{24}_{11}Na\); (c) \(\beta$$^+\) decay of \(^{15}_{8}O\).
Problem 14
\(^2$$^3$$^8\)U decays spontaneously by \(\alpha\) emission to \(^2$$^3$$^4\)Th. Calculate (a) the total energy released by this process and (b) the recoil velocity of the \(^2$$^3$$^4\)Th nucleus. The atomic masses are 238.050788 u for \(^2$$^3$$^8\)U and 234.043601 u for \(^2$$^3$$^4\)Th.
Problem 16
What particle (a particle, electron, or positron) is emitted in the following radioactive decays? (a) \(^{27}_{14}Si\) \(\rightarrow\) \(^{27}_{13}Al\); (b) \(^{238}_{92}U\) \(\rightarrow\) \(^{234}_{90}Th\); (c) \(^{74}_{33}As\) \(\rightarrow\) \(^{74}_{34}Se\).
Problem 20
Radioactive isotopes used in cancer therapy have a "shelf-life," like pharmaceuticals used in chemotherapy. Just after it has been manufactured in a nuclear reactor, the activity of a sample of \(^6$$^0\)Co is 5000 Ci. When its activity falls below 3500 Ci, it is considered too weak a source to use in treatment. You work in the radiology department of a large hospital. One of these \(^6$$^0\)Co sources in your inventory was manufactured on October 6, 2011. It is now April 6, 2014. Is the source still usable? The half-life of \(^6$$^0\)Co is 5.271 years.
Problem 21
The common isotope of uranium, \(^2$$^3$$^8\)U, has a halflife of 4.47 \(\times\) 10\(^9\) years, decaying to \(^2$$^3$$^4\)Th by alpha emission. (a) What is the decay constant? (b) What mass of uranium is required for an activity of 1.00 curie? (c) How many alpha particles are emitted per second by 10.0 g of uranium?
Problem 22
\(\textbf{Radiation Treatment of Prostate Cancer}\). In many cases, prostate cancer is treated by implanting 60 to 100 small seeds of radioactive material into the tumor. The energy released from the decays kills the tumor. One isotope that is used (there are others) is palladium (\(^1$$^0$$^3\)Pd), with a half-life of 17 days. If a typical grain contains 0.250 g of \(^1$$^0$$^3\)Pd, (a) what is its initial activity rate in Bq, and (b) what is the rate 68 days later?
Problem 24
\(\textbf{Radioactive Tracers}\). Radioactive isotopes are often introduced into the body through the bloodstream. Their spread through the body can then be monitored by detecting the appearance of radiation in different organs. One such tracer is \(^1$$^3$$^1\)I, a \(\beta$$^-\) emitter with a half-life of 8.0 d. Suppose a scientist introduces a sample with an activity of 325 Bq and watches it spread to the organs. (a) Assuming that all of the sample went to the thyroid gland, what will be the decay rate in that gland 24 d (about 3 \\(\frac{1}{2}\\) weeks) later? (b) If the decay rate in the thyroid 24 d later is measured to be 17.0 Bq, what percentage of the tracer went to that gland? (c) What isotope remains after the I-131 decays?
Problem 25
The unstable isotope \(^4$$^0\)K is used for dating rock samples. Its half-life is 1.28 \(\times\) 10\(^9\) y. (a) How many decays occur per second in a sample containing 1.63 \(\times\) 10\(^-$$^6\) g of \(^4$$^0\)K? (b) What is the activity of the sample in curies?
