29.4 Photon Momentum

The mass of a proton is 1.67 × 10^–27 kg. If a proton has the same momentum as a photon with a wavelength of 325 nm, what is its speed?

1. 2.73 × 10^–3 m/s
2. 0.819 m/s
3. 1.22 m/s
4. 2.71 × 10⁴ m/s

In an experiment in which the Compton effect is observed, a “gamma ray” photon with a wavelength of 5.00 × 10^–13 m scatters from an electron. If the change in the electron energy is 1.60 × 10^–15 J, what is the wavelength of the photon after the collision with the electron?

1. 4.95 × 10^–13 m
2. 4.98 × 10^–13 m
3. 5.02 × 10^–13 m
4. 5.05 × 10^–13 m

(a) Find the momentum of a 4.00-cm-wavelength microwave photon. (b) Discuss why you expect the answer to (a) to be very small.

(a) What is the wavelength of a photon that has a momentum of $5 . \text{00} \times \text{10}^{- \text{29}} \text{kg} \cdot \text{m}/\text{s}$? (b) Find its energy in eV.

(a) Calculate the momentum of a photon having a wavelength of $2 . \text{50 }\mu\text{m}$. (b) Find the velocity of an electron having the same momentum. (c) What is the kinetic energy of the electron, and how does it compare with that of the photon?

(a) Calculate the wavelength of a photon that has the same momentum as a proton moving at 1.00% of the speed of light. (b) What is the energy of the photon in MeV? (c) What is the kinetic energy of the proton in MeV?

Take the ratio of relativistic rest energy, $E = γmc^{2} \text{mc}^{2}$, to relativistic momentum, $p = \gamma \text{mu}$, and show that in the limit that mass approaches zero, you find $E / p = c$.

A car feels a small force due to the light it sends out from its headlights, equal to the momentum of the light divided by the time in which it is emitted. (a) Calculate the power of each headlight, if they exert a total force of $2 . \text{00} \times \text{10}^{- 2} \text{ N}$ backward on the car. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?