Bragg's Law Diffraction Calculator

X-ray Diffraction, Angle, Wavelength & Crystal Spacing

Calculate any parameter in Bragg's Law: wavelength (λ), angle (θ), crystal plane spacing (d), or diffraction order (n). Enter three values to solve for the fourth.

Practical Examples

See how Bragg's Law is used in real scenarios.

Find the X-ray Wavelength

Wavelength

Given d = 0.203 nm, θ = 22.5°, n = 1, find λ.

d: 0.203 nm, θ: 22.5°, n: 1

Find the Crystal Plane Spacing

Crystal Plane Spacing

Given λ = 0.154 nm, θ = 30°, n = 1, find d.

λ: 0.154 nm, θ: 30°, n: 1

Find the Bragg Angle

Bragg Angle

Given λ = 0.154 nm, d = 0.203 nm, n = 1, find θ.

λ: 0.154 nm, d: 0.203 nm, n: 1

Find the Diffraction Order

Diffraction Order

Given λ = 0.154 nm, d = 0.203 nm, θ = 22.5°, find n.

λ: 0.154 nm, d: 0.203 nm, θ: 22.5°

Other Titles
Understanding Bragg's Law Diffraction Calculator: A Comprehensive Guide
Master X-ray diffraction and Bragg's Law with this interactive tool.

What is Bragg's Law?

  • Fundamental Principle
  • Historical Background
  • Importance in Science
Bragg's Law describes the condition for constructive interference of X-rays scattered by crystal planes. It is fundamental in crystallography and material science.
Bragg's Law Formula
The law is mathematically expressed as nλ = 2d sinθ, where n is the order, λ is the wavelength, d is the spacing, and θ is the angle.

Bragg's Law in Action

  • X-ray diffraction in NaCl crystals.
  • Determining unknown wavelengths using known d and θ.

Step-by-Step Guide to Using the Calculator

  • Input Selection
  • Unit Handling
  • Result Interpretation
Select which parameter you want to solve for, enter the other three, and choose appropriate units. The calculator will compute the missing value and show the formula used.
Flexible Input and Output
You can solve for wavelength, angle, spacing, or order. The tool automatically handles unit conversions between nm and Å.

Calculator Usage Examples

  • Solving for θ when λ, d, and n are known.
  • Finding d when λ, θ, and n are given.

Real-World Applications of Bragg's Law

  • Material Science
  • Chemistry and Biology
  • Industrial Uses
Bragg's Law is used to determine crystal structures, analyze materials, and identify unknown substances in chemistry and biology.
From Lab to Industry
Industries use X-ray diffraction for quality control, mineral analysis, and research and development.

Applications in Science and Industry

  • Identifying minerals in geology.
  • Analyzing protein structures in biology.

Common Misconceptions and Correct Methods

  • Angle Measurement
  • Order Selection
  • Unit Consistency
A common mistake is using the wrong angle (should be the angle between incident ray and crystal plane, not the surface). Always use degrees unless specified otherwise.
Avoiding Calculation Errors
Ensure all units are consistent and the order n is a positive integer. The angle θ must be between 0 and 90 degrees (exclusive).

Misconceptions in Practice

  • Entering θ as 45° instead of 22.5°.
  • Using nm for λ and Å for d without conversion.

Mathematical Derivation and Examples

  • Derivation of Bragg's Law
  • Worked Examples
  • Advanced Calculations
Bragg's Law is derived from the condition for constructive interference of X-rays reflected from parallel crystal planes.
Worked Example
Given d = 0.203 nm, θ = 22.5°, n = 1, λ = 2d sinθ / n = 20.203sin(22.5°)/1 ≈ 0.155 nm.

Mathematical Examples

  • Calculate λ for d = 0.203 nm, θ = 22.5°, n = 1.
  • Find θ for λ = 0.154 nm, d = 0.203 nm, n = 1.