How many protons and how many neutrons are there in a nucleus of the most common isotope of (a) silicon, ${}_{\phantom{0}14}^{28}Si$; (b) rubidium, ${}_{\phantom{0}37}^{85}Rb$; (c) thallium, ${}_{\phantom{0}81}^{205}Tl$?

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?

The most common isotope of uranium, ${}_{92}^{238}U$, has atomic mass $238.050788$ u. Calculate (a) the mass defect; (b) the binding energy (in MeV); (c) the binding energy per nucleon.

(a) Is the decay $n\to p+{\beta }^{-}+\overline{v_e}$ energetically possible? If not, explain why not. If so, calculate the total energy released.

(b) Is the decay $n\to p+{\beta }^{+}+\overline{v_e}$ energetically possible? If not, explain why not. If so, calculate the total energy released.

What nuclide is produced in the following radioactive decays?

(a) $\alpha$ decay of ${}_{94}^{239}Pu$

(b) ${\beta }^{-}$ decay of ${}_{11}^{24}Na$

(c) ${\beta }^{+}$ decay of ${}_8^{15}O$

The atomic mass of $14C$ is $14.003242$ u. Show that the ${\beta }^{-}$ decay of $14C$ is energetically possible, and calculate the energy released in the decay.

What particle (a particle, electron, or positron) is emitted in the following radioactive decays?

(a) ${}_{14}^{27}Si{\to }_{13}^{27}Al$

(b) ${}_{92}^{238}U{\to }_{90}^{234}Th$

(c) ${}_{33}^{74}As{\to }_{34}^{74}Se$

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 ${}^{60}Co$ 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 ${}^{60}Co$ 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 ${}^{60}Co$ is $5.271$ years.

The common isotope of uranium, ${}^{238}U$, has a half-life of $4.47\times {10}^9$ years, decaying to ${}^{234}Th$ 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?

The unstable isotope ${}^{40}K$ 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 ${}^{40}K$?

(b) What is the activity of the sample in curies?

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?

At an archeological site, a sample from timbers containing $500$ g of carbon provides $2690$ decays/min. What is the age of the sample?

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?

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?

In a diagnostic x-ray procedure, $5.00\times {10}^{10}$ photons are absorbed by tissue with a mass of $0.600$ kg. The x-ray wavelength is $0.0200$ nm.

(a) What is the total energy absorbed by the tissue?

(b) What is the equivalent dose in rem?

Calculate the energy released in the fusion reaction: ${}_2^{3}He{+}_1^{2}H{\to }_2^{4}He{+}_1^{1}H$