Compton Scattering Calculator

Compton Wavelength Shift Equation:

\[ \Delta\lambda = \frac{h}{m_e c} (1 - \cos\theta) \]

Wavelength Shift (Δλ):

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1. What is Compton Scattering?

Compton scattering is the inelastic scattering of a photon by a charged particle, usually an electron. It results in a decrease in energy (increase in wavelength) of the photon, known as the Compton effect. The wavelength shift depends on the angle of scattering.

2. How Does the Calculator Work?

The calculator uses the Compton wavelength shift equation:

\[ \Delta\lambda = \frac{h}{m_e c} (1 - \cos\theta) \]

Where:

\( \Delta\lambda \) — Wavelength shift (m)
\( h \) — Planck's constant (6.626 × 10^-34 J·s)
\( m_e \) — Electron rest mass (9.11 × 10^-31 kg)
\( c \) — Speed of light (3 × 10⁸ m/s)
\( \theta \) — Scattering angle (degrees)

Explanation: The equation shows that the wavelength shift depends only on the scattering angle and fundamental constants. The term h/m_ec is called the Compton wavelength of the electron (≈2.426 pm).

3. Importance of Compton Shift

Details: The Compton effect provided crucial evidence for the particle nature of light (photons) and helped establish quantum mechanics. It's important in X-ray physics, radiation therapy, and materials science.

4. Using the Calculator

Tips: Enter the scattering angle between 0° and 180°. The calculator will show the resulting wavelength shift in picometers (pm). The Compton wavelength (h/m_ec) is shown for reference.

5. Frequently Asked Questions (FAQ)

Q1: What is the maximum possible Compton shift?
A: The maximum shift occurs at 180° (backscattering) and is twice the Compton wavelength (≈4.852 pm).

Q2: Why doesn't the initial wavelength appear in the equation?
A: The shift Δλ is independent of the initial wavelength, though the percentage change in wavelength depends on it.

Q3: What are typical applications of Compton scattering?
A: Used in Compton telescopes, material analysis, and understanding X-ray interactions with matter.

Q4: Does this work for scattering by particles other than electrons?
A: Yes, but the shift would be much smaller for protons or nuclei due to their larger mass.

Q5: How was this effect discovered?
A: Arthur Compton observed it in 1923 with X-rays scattering off electrons in graphite, earning him the 1927 Nobel Prize.