1. Intro to Physics Units

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.

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

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 ${}_8^{15}O$

(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.

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.

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?

What is the speed of a proton that has total energy $1000$ GeV?

A high-energy beam of alpha particles collides with a stationary helium gas target. What must the total energy of a beam particle be if the available energy in the collision is $16.0$ GeV?

The magnetic field in a cyclotron that accelerates protons is $1.70$ T. How many times per second should the potential across the dees reverse? (This is twice the frequency of the circulating protons.)

Deuterons in a cyclotron travel in a circle with radius $32.0$ cm just before emerging from the dees. The frequency of the applied alternating voltage is $9.00$ MHz. Find the magnetic field.

An electron with a total energy of $30.0$ GeV collides with a stationary positron. What is the available energy?

A proton and an antiproton annihilate, producing two photons. Find the energy, frequency, and wavelength of each photon if the $p$ and $\bar{p}$ are initially at rest.

Two equal-energy photons collide head-on and annihilate each other, producing a ${\text{µ}}^{+}{\text{µ}}^{-}$ pair. The muon mass is given in terms of the electron mass in Section $44.1$. Calculate the maximum wavelength of the photons for this to occur. If the photons have this wavelength, describe the motion of the ${\text{µ}}^{+}$ and immediately after they are produced.

A neutral pion at rest decays into two photons. Find the energy, frequency, and wavelength of each photon. In which part of the electromagnetic spectrum does each photon lie? (Use the pion mass given in terms of the electron mass in Section $44.1$.)

"(I) Estimate the order of magnitude (power of 10) of: 86.30 x 10³"