Short on time? This page is the recap. For the collision diagram and the worked examples, use the full study guide.
Recap
- In Compton scattering a photon (usually an X-ray) collides with a free electron at rest and comes out at an angle θ to its original direction.
- The photon hands some energy to the electron, so it leaves with lower energy and a longer wavelength.
- The shift grows with the scattering angle and does not depend on the starting wavelength.
- A classical wave model predicts no change in wavelength. Treating the photon as a particle that obeys energy and momentum conservation explains the shift, so the effect is evidence for photons.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| E = hf = hc/λ | h = 6.63 × 10⁻³⁴ J·s | find photon energy |
| p = h/λ = E/c | kg·m/s | find photon momentum |
| hc/λ = hc/λ′ + K_e | J (or eV) | find the electron’s kinetic energy |
| Δλ = (h/m_e c)(1 − cos θ) | h/(m_e c) = 2.43 × 10⁻¹² m | relate the shift to the angle |
| Σp_x and Σp_y are each conserved | vector components | find the electron’s momentum and direction |
| θ | 0° | 90° | 180° |
|---|---|---|---|
| Δλ | 0 | 2.43 pm | 4.85 pm (the maximum) |
Mistakes to avoid
- Saying the photon slows down. Its speed stays at c.
- Using p = mv for a photon. Use p = h/λ.
- Thinking Δλ depends on λ. Only the fractional change does.
- Putting the electron on the same side as the scattered photon. The y-components of momentum must cancel.
- Rounding E and E′ before subtracting to find K_e.
- Calculator in radians mode when θ is in degrees, or writing 1 + cos θ instead of 1 − cos θ.
Quick self-check
- A photon scatters at 90°. What is Δλ? (2.43 pm)
- Which has the larger shift at the same angle: a 30 pm photon or a 60 pm photon? (Neither: the shift is the same. The 30 pm photon loses the larger fraction of its energy.)
- A photon scatters straight back (θ = 180°). In which direction does the electron move? (Forward, along the photon’s original direction.)
Next: practice questions.