Question

Two lines, A and B, of an X-ray beam, give second-order reflection maximum at a glancing angle of 60° and third-order reflection maximum at an angle of 30° respectively from the face of the same crystal. If the wavelength of line B is 0.25 nm, then the wavelength of line A will be:
1. 0.65 nm
2. 0.35 nm
3. 0.95 nm
4. 0.15 nm

Answer 1

Correct Answer - Option 1 : 0.65 nm

Concept:

In X-ray scattering

nλ = 2d sin θ

\(d=\frac{nλ}{2sin \theta}\)  ---(1)

where d = distance between atomic planes, θ = glancing angle, λ = wavelength

Calculation:

Given:

For line A:

n1 = 2, θ1 = 60o, λ1 = ?

For line B;

n2 = 3, θ2 = 30o, λ2 = 0.25 nm

Distance between atomic planes d1 and d2 is equal for same crystal i.e.;

d1 = d2 = d

From equation (1);

\(\frac{n_1λ_1}{2sin \ \theta_1}=\frac{n_2λ_2}{2sin \ \theta_2}\)

\({λ_1}=\frac{3 \times0.25 \ nm}{2\times sin \ 30}.sin \ 60\)

On solving we'll get;

λ1 = 0.649 nm ≈ 0.65 nm