The spacing between the principal planes of a crystal is 4 mathringA. It is found that first order brag reflection of a beam of monochromatic X-rays occurs at an angle of 30°. The wavelength of X-rays is

Question

The spacing between the principal planes of a crystal is 4 mathringA. It is found that first order brag reflection of a beam of monochromatic X-rays occurs at an angle of 30°. The wavelength of X-rays is (A) 4 mathringA (B) 2 mathringA (C) 1 mathringA (D) 1.5 mathringA

Tardigrade Admin · Accepted Answer

Using the Braggs formula 2 d sin θ=n λ where d = distance between diffracting planes. We can determine the wavelength of these waves, 2 × 4 × 10-10 sin 30° =λ 8 × 10-10 × (1/2) =λ 4 × 10-10=λ λ = 4 mathringA

Q. The spacing between the principal planes of a crystal is $4 \overset{˚}{A}$ . It is found that first order brag reflection of a beam of monochromatic $X$ -rays occurs at an angle of $3 0^{\circ}$ . The wavelength of $X$ -rays is

$4 \overset{˚}{A}$

$2 \overset{˚}{A}$

$1 \overset{˚}{A}$

$1.5 \overset{˚}{A}$

Using the Braggs formula $2 d sin θ = nλ$
where $d =$ distance between diffracting planes.
We can determine the wavelength of these waves,
$2 \times 4 \times 1 0^{- 10} sin 3 0^{\circ}$
$= λ 8 \times 1 0^{- 10} \times \frac{1}{2}$
$= λ 4 \times 1 0^{- 10} = λλ$
$= 4 \overset{˚}{A}$

Q. The spacing between the principal planes of a crystal is 4A˚. It is found that first order brag reflection of a beam of monochromatic X-rays occurs at an angle of 30∘. The wavelength of X-rays is

4A˚

2A˚

1A˚

1.5A˚