Two protons, each having a speed of $0.985 c$ in the laboratory, are moving toward each other. Determine $(c)$ the momentum of one proton as seen by the other proton.

How much energy would be required to break a helium nucleus into its constituents, two protons and two neutrons? The rest masses of a proton (including an electron), a neutron, and neutral helium are, respectively, $1.00783 \mathrm{u}$, $1.00867 \mathrm{u}$, and $4.00260 \mathrm{u}$. (This energy difference is called the total binding energy of the ${ }_2^4 \mathrm{He}$ nucleus.)

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 mass.

The Sun radiates energy at a rate of about $4 \times 10^{26} \mathrm{~W}$. Estimate how long the Sun could last if it radiated constantly at this rate.

The Sun radiates energy at a rate of about $4 \times 10^{26} \mathrm{~W}$. How long does it take for the Sun to lose a mass equal to that of Earth?

If a 5.1-eV photon is absorbed by an atom of this substance, in which state was the atom before absorbing the photon? What will be the energies of the photons that can subsequently be emitted by this atom?

The Sun radiates energy at a rate of about $4 \times 10^{26} \mathrm{~W}$. At what rate is the Sun's mass decreasing?

If $E$ is the total energy of a particle with zero potential energy, show that $d E / d p=v$, where $p$ and $v$ are the momentum and velocity of the particle, respectively.

If E is the total energy of a particle with zero potential energy, show that dE/dp=v, where p and v are the momentum and velocity of the particle, respectively.

What minimum amount of electromagnetic energy is needed to produce an electron and a positron together? A positron is a particle with the same mass as an electron, but has the opposite charge. (Note that electric charge is conserved in this process.)

A young-looking woman astronaut has just arrived home from a long trip. She rushes up to an old gray-haired man and in the ensuing conversation refers to him as her son. How might this be possible ?

At what speed $v$ will the length of a $1.00~\mathrm{m}$ stick look $10.0 \%$ shorter $(90.0 \mathrm{~cm})$ ?

As a rough rule, anything traveling faster than about $0.1 c$ is called relativistic - that is, special relativity is a significant effect. Determine the speed of an electron in a hydrogen atom (radius $0.53 \times 10^{-10} \mathrm{~m}$ ) and state whether or not it is relativistic. (Treat the electron as though it were in a circular orbit around the proton.)

State one piece of evidence supporting the wave model of light and one piece of evidence supporting the particle model of light.