1. x-rays of wavelength 0.138nm fall on a crystal whose atoms, lying in planes, are spaced 0.285 nm apart. At what angle with the surface must the x-rays be directed if the a. first diffraction maximum is observed? b. second diffraction maximum is observed? c. third diffraction maximum is observed? g

a.) 25.8 degree

b.) 44.1 degree

c.) 55.5 degree.

Explanation:

Given that the

Wavelength (λ) = 0.138 nm

Spacing d = 0.285 nm

Using the formula dtan Ø = n(λ)

Where n = number of diffraction maximum observed

1.) For the first diffraction maximum,

Substitute the values into the formula where n = 1

0.285 × 10^-9 × tanØ = 1 × 0.138 × 10^-9

Tan Ø = 0.138/0.285

Tan Ø = 0.4842

Ø = tan^-1(0.4842)

Ø = 25.84 degree

2.) For the second diffraction maximum

Where n = 2

0.285 × 10^-9 × tanØ = 2× 0.138 × 10^-9

Tan Ø = 0.276/0.285

Tan Ø = 0.9684

Ø = tan^-1(0.9684)

Ø = 44.1 degree

3.) For the third diffraction maximum

Where n = 3

0.285 × 10^-9 × tanØ = 3 × 0.138 × 10^-9

Tan Ø = 0.414/0.285

Tan Ø = 1.4526

Ø = tan^-1(1.4526)

Ø = 55.5 degree