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?

(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?

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.