Compton Scattering Calculator With Temperature

Compton Scattering Equation:

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

Compton Shift (Δλ):

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1. What is Compton Scattering?

Compton scattering is the quantum mechanical phenomenon where X-ray or gamma ray photons scatter off electrons, resulting in a wavelength shift (Compton shift) that depends on the scattering angle.

2. How Does the Calculator Work?

The calculator uses the Compton scattering equation:

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

Where:

\( \Delta\lambda \) — Compton 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 shift occurs because photons transfer some energy to electrons during scattering. The effect is fundamental evidence of light's particle nature.

3. Importance of Compton Shift Calculation

Details: Calculating the Compton shift is essential in X-ray spectroscopy, radiation therapy planning, and understanding quantum mechanical interactions between matter and radiation.

4. Using the Calculator

Tips: Enter the scattering angle (0-180°). Optionally include an initial wavelength to calculate the final wavelength after scattering. Temperature effects are negligible for standard calculations.

5. Frequently Asked Questions (FAQ)

Q1: Why is temperature negligible in standard calculations?
A: The Compton shift depends primarily on the scattering angle and fundamental constants. Thermal motion effects become significant only at extremely high temperatures (>10⁶ K).

Q2: What is the Compton wavelength?
A: The characteristic length scale \( h/(m_e c) \) ≈ 2.43 pm that appears in the scattering formula.

Q3: When does Compton scattering dominate?
A: For X-rays and gamma rays (wavelengths ~0.01-10 nm) interacting with loosely bound or free electrons.

Q4: How does this relate to the photoelectric effect?
A: Compton scattering and the photoelectric effect are complementary phenomena showing light's particle nature at different energy ranges.

Q5: What's the maximum possible Compton shift?
A: At 180° backscattering, Δλ ≈ 4.86 pm (twice the Compton wavelength).