inter-atomic spacing

The image above represents angle of diffraction.

To compute for angle of diffraction, three essential parameters are needed and these parameters are Order of Reflection (n), Wavelength (λ) and Inter-atomic Spacing (d).

The formula for calculating angle of diffraction:

θ = sin^-1(^nλ/_2d)

Where:

θ = Angle of Diffraction
n = Order of Reflection
λ = Wavelength
d = Inter-atomic Spacing

Given an example;
Find the angle of diffraction when the order of reflection is 6, the wavelength is 3 and the inter-atomic spacing is 9.

This implies that;

n = Order of Reflection = 6
λ = Wavelength = 3
d = Inter-atomic Spacing = 9

θ = sin^-1(^nλ/_2d)
θ = sin^-1(⁽⁶⁾⁽³⁾/₂₍₉₎)
θ = sin^-1(⁽¹⁸⁾/₍₁₈₎)
θ = sin^-1(1)
θ = 90°

Therefore, the angle of diffraction is 90°.

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The image above represents wavelength.

To compute for wavelength, three essential parameters are needed and these parameters are Order of Reflection (n), Inter-atomic Spacing (d) and Angle of Diffraction (θ).

The formula for calculating wavelength:

λ = ^2dsinθ/_n

Where:

λ = Wavelength
n = Order of Reflection
d = Inter-atomic Spacing
θ = Angle of Diffraction

Given an example;
Find the wavelength when the order of reflection is 2, the inter-atomic spacing is 10 and the angle of diffraction is 12.

This implies that;

n = Order of Reflection = 2
d = Inter-atomic Spacing = 10
θ = Angle of Diffraction = 12

λ = ^2dsinθ/_n
λ = ^{2(10)sin(12°)}/₂
λ = ^20(0.207)/₂
λ = ^(4.158)/₂
λ = 2.079

Therefore, the wavelength is 2.079 m.

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The image above represents order of reflection.

To compute for order of reflection, three essential parameters are needed and these parameters are Wavelength (λ), Inter-atomic Spacing (d) and Angle of Diffraction (θ).

The formula for calculating order of reflection:

n = ^2dsinθ/_λ

Where:

n = Order of Reflection
d = Inter-atomic Spacing
λ = Wavelength
θ = Angle of Diffraction

Given an example;
Find the order of reflection when the inter-atomic spacing is 4, the wavelength is 12 and the angle of diffraction is 6.

This implies that;

d = Inter-atomic Spacing = 4
λ = Wavelength = 12
θ = Angle of Diffraction = 6

n = ^2dsinθ/_λ
n = ^2(4)sin(6°)/₁₂
n = ^8(0.104)/₁₂
n = ^(0.8362)/₁₂
n = 0.069

Therefore, the order of reflection is 0.069.

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