# Collision involving an electron and a photon

An electron moving to the left at 0.8c collides with an incoming photon moving to the right. After the collision, the electron is moving to the right at 0.6c and an outgoing photon moves to the left. What was the wavelength of the incoming photon?

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#### Solution Preview

This problem can actually be solved most easily in the elementary way, i.e. by simply writing down conservation of energy and momentum and solving these equations. So, perhaps you need to study some other problems, I'll suggest a few after finishing this problem.

Let's introduce the following four-vectors:

P1 = four-momentum of electron before collision

P2 = four-momentum of electron after collision

Pf1 = four-momentum of photon before collision

Pf2 = four-momentum of photon after collision

Then we have:

P1 + Pf1 = P2 + Pf2 (1)

Let's first solve this equation without using four-vector algebra. We just rewrite it as:

P1 - P2 = Pf2 - Pf1 (2)

In c = 1 units we have:

P1 = (m gamma1, -m gamma1 v1)

P2 = (m gamma2, m gamma2 v2)

Pf1 = (E1, E1)

Pf2 = (E2, -E2)

where v1 = 0.8 and v2 = 0.6 are the ...

#### Solution Summary

A detailed solution is given.

Millikan experiment, Compton effect, photoelectric effect

1. In a Millikan oil drop experiment the terminal velocity of the droplet is observed to be vt = 1.5 mm/s. The density of the oil is = 830 kg/m3 and the viscosity of air is = 1.82 10-5 kg/m s. Use the following equations to find the values below.

Calculate the droplet radius.

µm

(b) Calculate the mass of the droplet.

kg

(c) Calculate the coefficient of friction.

kg/s

12. A gamma ray of 630 keV energy Compton scatters from an electron. Find the energy of the photon scattered at 89°, the kinetic energy of the scattered electron, and the recoil angle of the electron.

keV (photon)

keV (electron)

°

3. What is the threshold frequency for the photoelectric effect of barium ( = 2.5 eV)?

Hz

What is the stopping potential if the wavelength of the incident light is 420 nm?

eV

4. Light from a slit passes through a transmission diffraction grating of 330 lines/mm, which is located 2.2 m from a screen. What are the distances on the screen (from the unscattered slit image) of the three brightest visible (first-order) hydrogen lines?

Red cm

Blue-green cm

Violet cm

3. In a Millikan oil drop experiment the terminal velocity of the droplet is observed to be vt = 1.5 mm/s. The density of the oil is = 830 kg/m3 and the viscosity of air is = 1.82 10-5 kg/m s. Use the following equations to find the values below.

(b) Calculate the droplet radius.

µm

(b) Calculate the mass of the droplet.

kg

(c) Calculate the coefficient of friction.

kg/s

4. Light from a slit passes through a transmission diffraction grating of 330 lines/mm, which is located 2.2 m from a screen. What are the distances on the screen (from the unscattered slit image) of the three brightest visible (first-order) hydrogen lines?

Red cm

Blue-green cm

Violet cm

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