An unknown particle is measured to have a negative charge and a speed of $2.24 \times 10^{8} \mathrm{m} / \mathrm{s}$. Its momentum is determined to be $3.07 \times 10^{-22} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$. Identify the particle by finding its rest mass.

A negative muon traveling at 33 % the speed of light collides head on with a positive muon traveling at 50% the speed of light. The two muons (each of rest mass $105.7 \mathrm{MeV} / \mathrm{c}^{2})$ annihilate, and produce how much electromagnetic energy?

An electron $(m=9.11 \times 10^{-31} \mathrm{kg})$ enters a uniform magnetic field B = 1.8 T, and moves perpendicular to the field lines with a speed v = 0.92 c. What is the radius of curvature of its path?

What minimum amount of electromagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same rest mass as an electron, but has the opposite charge.

How many grams of matter would have to be totally destroyed to run a 100-W lightbulb for 1 year?

(I) A certain type of elementary particle travels at a speed of $2.70 \times 10^8 \mathrm{~m} / \mathrm{s}$. At this speed, the average lifetime is measured to be $4.76 \times 10^{-6} \mathrm{~s}$. What is the particle's lifetime at rest?

A certain type of elementary particle travels at a speed of $2.70 \times 10^{8} \mathrm{m} / \mathrm{s} .$ At this speed, the average lifetime is measured to be $4.76 \times 10^{-6} \mathrm{s}$. What is the particle's lifetime at rest?

If the electrons travel in the lab through a tube 3.0 km long (as at SLAC), how long is this tube in the electrons' reference frame? [Hint: use the binomial expansion.]

What is the speed v of an electron whose kinetic energy is 14,000 times its rest energy? You can state the difference, c - v. Such speeds are reached in the Stanford Linear Accelerator, SLAC.

As a rule of thumb, anything traveling faster than about 0.1 c is called relativistic-i.e., for which the correction using special relativity is a significant effect. Determine the speed of an electron in a hydrogen atom (radius $\left.0.5 \times 10^{-10} \mathrm{m}\right)$ and state if it is relativistic. (Treat the electron as though it were in a circular orbit around the proton.)

If you were on a spaceship traveling at 0.5c away from a star, at what speed would the starlight pass you?

What is the speed of a pion if its average lifetime is measured to be $4.10 \times 10^{-8} \mathrm{s} ?$ At rest, its average lifetime is $2.60 \times 10^{-8} \mathrm{s}$.

The nearest star to Earth is Proxima Centauri, 4.3 lightyears away. How long does the trip take according to Earth observers?

The nearest star to Earth is Proxima Centauri, 4.3 lightyears away. At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 4.0 years, as measured by travelers on the spacecraft?