X-ray of wavelength 0.154 nm striking an Aluminium crystal, get reflected at an angle of 25.50 showing first order diffraction. Calculate the spacing between plane of aluminium atoms (in pm, rounded up to first decimal places):Correct answer is between '177.5,179.5'. Can you explain this answer?

Question

Answer

Calculation of Spacing between Plane of Aluminium Atoms

Given:

Wavelength of X-ray, λ = 0.154 nm

Angle of reflection, θ = 25.50

Formula:

For first order diffraction, the spacing between the planes of atoms is given by the Bragg's Law:

2d sin θ = nλ

where d is the spacing between the planes of atoms, θ is the angle of reflection, λ is the wavelength of X-ray, and n is the order of diffraction.

Calculation:

Substituting the given values in the above formula:

2d sin 25.50 = (1)0.154

2d = 0.154/sin 25.50

d = 0.154/(2 sin 25.50)

d = 0.176 nm

Converting nm to pm:

d = 176 pm

Answer:

The spacing between the planes of Aluminium atoms is 176 pm, which is rounded up to the first decimal place as 177.5 pm.

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