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Compton Scattering Calculator

Calculate wavelength shift, energy transfer, and scattering parameters for Compton scattering

Parameters

nmⓘ
°ⓘ
kgⓘ
Show Trail

Controls

xⓘ

Calculated Values

Wavelength Shift:
2.43;pm2.43;pm
Scattered Wavelength:
0.10;nm0.10;nm
Energy Transfer:
0.00;J0.00;J
Compton Wavelength:
2.43;pm2.43;pm
Momentum Transfer:
0.00;kg⋅m/s0.00;kg·m/s

Examples

Example 1: X-ray Scattering

X-rays with wavelength 0.1 nm scattered at 90° by electrons.

  • Wavelength Shift: 2.432.43
  • Scattered Wavelength: 0.100.10
  • Energy Transfer: 0.000.00

Example 2: Backscattering

Same X-rays scattered at 180° (maximum energy transfer).

  • Wavelength Shift: 4.864.86
  • Scattered Wavelength: 0.100.10
  • Energy Transfer: 0.000.00

Example 3: Gamma Rays

Gamma rays with wavelength 0.01 nm scattered at 45°.

  • Wavelength Shift: 0.710.71
  • Scattered Wavelength: 0.010.01
  • Energy Transfer: 0.000.00

Visualization

Compton Scattering

Compton scattering is a fundamental quantum phenomenon where X-rays or gamma rays are scattered by electrons, resulting in a change in wavelength and energy. This effect provided crucial evidence for the particle nature of electromagnetic radiation and helped establish quantum mechanics.

The Compton wavelength shift is given by Δλ = λ' - λ = (h/mₑc)(1 - cos θ), where λ is the initial wavelength, λ' is the scattered wavelength, h is Planck's constant, mₑ is the electron rest mass, c is the speed of light, and θ is the scattering angle. The quantity h/mₑc is called the Compton wavelength of the electron.

The energy of the scattered photon is E' = E/(1 + (E/mₑc²)(1 - cos θ)), where E is the initial photon energy. The electron gains kinetic energy equal to the energy lost by the photon. The maximum energy transfer occurs at θ = 180° (backscattering).

Compton scattering is important in many areas of physics and technology, including medical imaging (CT scans), astrophysics (studying cosmic rays), and materials science (X-ray diffraction). It's also fundamental to understanding the interaction of high-energy radiation with matter.

The Compton effect demonstrates the wave-particle duality of light and the conservation of energy and momentum in quantum processes. It shows that photons behave as particles with momentum p = h/λ, while still exhibiting wave-like interference effects.

Key Concepts

  • Wavelength Shift: Δλ = (h/mₑc)(1 - cos θ)
  • Compton Wavelength: λ_c = h/mₑc ≈ 2.43 pm
  • Scattered Wavelength: λ' = λ + Δλ
  • Energy Transfer: ΔE = E - E'
  • Maximum Shift: Δλ_max = 2λ_c (at θ = 180°)
  • Momentum Conservation: p_photon = p_photon' + p_electron

Real-World Applications

  • Medical Imaging: CT scans and X-ray diagnostics
  • Astrophysics: Studying cosmic rays and gamma rays
  • Materials Science: X-ray diffraction analysis
  • Particle Physics: Understanding photon-electron interactions
  • Radiation Therapy: Cancer treatment planning

Explore Further

More modern physics tools

Physics Equations

Wavelength Shift:
Δλ=λ′−λ=hmec(1−cos⁡θ)\Delta\lambda = \lambda' - \lambda = \frac{h}{m_ec}(1 - \cos\theta)
Scattered Wavelength:
λ′=λ+hmec(1−cos⁡θ)\lambda' = \lambda + \frac{h}{m_ec}(1 - \cos\theta)
Energy Transfer:
ΔE=E−E′=hc(1λ−1λ′)\Delta E = E - E' = hc\left(\frac{1}{\lambda} - \frac{1}{\lambda'}\right)
Compton Wavelength:
λc=hmec\lambda_c = \frac{h}{m_ec}
Scattered Energy:
E′=E1+Emec2(1−cos⁡θ)E' = \frac{E}{1 + \frac{E}{m_ec^2}(1 - \cos\theta)}

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Calculate Compton Wavelength

First, we calculate the Compton wavelength of the electron:

Equation:

λc=hmec\lambda_c = \frac{h}{m_ec}

Calculation:

λc=6.63e−349.11e−31×3.00e+8=2.43 pm\lambda_c = \frac{6.63e-34}{9.11e-31 \times 3.00e+8} = 2.43 \text{ pm}

Explanation:

This is a fundamental constant related to the electron's mass.

2

Step 2: Calculate Wavelength Shift

The wavelength shift depends on the scattering angle:

Equation:

Δλ=λc(1−cos⁡θ)\Delta\lambda = \lambda_c(1 - \cos\theta)

Calculation:

Δλ=2.43×(1−cos⁡90°)=2.43 pm\Delta\lambda = 2.43 \times (1 - \cos90°) = 2.43 \text{ pm}

Explanation:

This gives the increase in wavelength due to the scattering.

3

Step 3: Calculate Scattered Wavelength

The scattered wavelength is the sum of initial and shift:

Equation:

λ′=λ+Δλ\lambda' = \lambda + \Delta\lambda

Calculation:

λ′=0.100+0.00243=0.10243 nm\lambda' = 0.100 + 0.00243 = 0.10243 \text{ nm}

Explanation:

The scattered photon has a longer wavelength than the incident photon.

4

Step 4: Calculate Energy Transfer

The energy lost by the photon equals the energy gained by the electron:

Equation:

ΔE=E−E′=hc(1λ−1λ′)\Delta E = E - E' = hc\left(\frac{1}{\lambda} - \frac{1}{\lambda'}\right)

Calculation:

ΔE=6.63e−34×3.00e+8×(11.00e−10−11.02e−10)=4.71e−17 J\Delta E = 6.63e-34 \times 3.00e+8 \times \left(\frac{1}{1.00e-10} - \frac{1}{1.02e-10}\right) = 4.71e-17 \text{ J}

Explanation:

This energy is transferred to the electron as kinetic energy.

Frequently Asked Questions (FAQ)

What is Compton scattering?

Compton scattering is the scattering of X-rays or gamma rays by electrons, resulting in a change in wavelength and energy. It demonstrates the particle nature of electromagnetic radiation.

What is the Compton wavelength?

The Compton wavelength is λ_c = h/mₑc ≈ 2.43 pm, which represents the wavelength shift when a photon is scattered at 180°. It's a fundamental constant related to the electron's mass.

Why does the wavelength increase during scattering?

The wavelength increases because the photon loses energy to the electron during the collision. Since E = hc/λ, a decrease in energy corresponds to an increase in wavelength.

What is the maximum wavelength shift?

The maximum wavelength shift occurs at θ = 180° (backscattering) and is equal to 2λ_c ≈ 4.86 pm. This represents the maximum energy transfer from photon to electron.

How does Compton scattering demonstrate wave-particle duality?

Compton scattering shows that photons behave as particles with momentum p = h/λ during collisions, while still exhibiting wave-like properties such as interference in other experiments.

Practice MCQs

  1. The Compton wavelength shift is maximum when the scattering angle is:
  2. The Compton wavelength of an electron is approximately:
  3. During Compton scattering, the scattered photon has:
  4. The wavelength shift in Compton scattering depends on:
  5. What is conserved in Compton scattering?

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