1. Compton Effect Objective:
Discuss Compton effect and calculate Compton shift by solving problems.

2. Compton Effect
Arthur Holly Compton observed that x-rays increase in wavelength when scattered.
When an x-ray photon collides with a stationary target electron, the photon is scattered away from its original direction of motion while the electron receives an impulse and begins to move with kinetic energy K.

3. Compton Scattering

4. The energy lost by the photon equals the kinetic energy K gained by the electron.
gain in electron energy = loss in photon energy
K = Eincident photon – Escattered photon
= hf – Escattered photon
= hf – hf’
= ℎ𝑓− ℎ𝑐  ′
= Eincident photon – hf’
= 𝐸 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝑝ℎ𝑜𝑡𝑜𝑛 − ℎ𝑐  ′
= ℎ𝑐  − 𝐸 scattered photon
= ℎ𝑐  − ℎ𝑓′
= ℎ𝑐  − ℎ𝑐  ′
where: f = frequency of incident photon
f’ = frequency of scattered photon
 = wavelength of incident photon
’ = wavelength of scattered photon

5. The kinetic energy of the scattered electron can also be calculated using the following equation:
𝑲= 𝟏 𝟐 𝒎 𝒗 𝟐

6. For an electron C = 2.426 pm = 2.426 x 10-12 m
The change in wavelength (Compton shift) expected for a photon scattered through the angle  by a particle of rest mass m0 is independent of the wavelength  of the incident photon.
𝝀 ′ −𝝀= 𝒉 𝒎 𝟎 𝒄 (𝟏− 𝒄𝒐𝒔 𝝓) Compton effect
  𝝀 ′ −𝝀= 𝝀 𝑪 𝟏−𝒄𝒐𝒔𝝓
where
𝜆 𝐶 = ℎ 𝑚 0 𝑐 Compton wavelength
𝝀 ′ −𝝀= 𝒄 𝒇 ′ −  = 𝒄 𝒇 ′ − 𝒄 𝒇 =  ′ − 𝒄 𝒇 Compton shift
 For an electron C = pm = x m
c = 3.0 x 108 m/s
m0= 9.11 x kg

7. Key points
The frequency and consequently the energy of the photon is higher before the collision.
After the collision, some energy has been transferred to the electron. This leaves the photon having a lower frequency after the collision.
Since wavelength is inversely related to frequency, the wave has a lower frequency after the collision.
Energy is conserved before and after this collision.
Momentum is conserved before and after this collision.