What is the wavelength of a beam of X-rays (in mathringA ) which is diffracted by a crystal in a direction making an angle of 60° with the incident beam and corresponding to first order reflection from crystal lattice planes separated by 3 × 10-10 m ?

Question

What is the wavelength of a beam of X-rays (in mathringA ) which is diffracted by a crystal in a direction making an angle of 60° with the incident beam and corresponding to first order reflection from crystal lattice planes separated by 3 × 10-10 m ? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

The Bragg's angle is half the angle through which the beam is deviated. Thus, in this case, the Bragg's angle is

θ = 1/2 \times 6 0^{\circ} = 3 0^{\circ}

Bragg's equation is given as:

2 d sin θ = nλ

Here,

d = 3 \times 1 0^{- 10} m, θ = 3 0^{\circ}; n = 1, λ =

?

λ = \frac{2 d s i n θ}{n} = \frac{2 \times ( 3 \times 1 0 ^{- 10} ) s i n 3 0 ^{\circ}}{1} m

= 3 \times 1 0^{- 10} m = 3 \overset{˚}{A}

Q. What is the wavelength of a beam of X-rays (in A˚ ) which is diffracted by a crystal in a direction making an angle of 60∘ with the incident beam and corresponding to first order reflection from crystal lattice planes separated by 3×10−10m ?

The Bragg's angle is half the angle through which the beam is deviated. Thus, in this case, the Bragg's angle is θ=1/2×60∘=30∘ Bragg's equation is given as: 2dsinθ=nλ Here, d=3×10−10m,θ=30∘;n=1,λ= ? λ=n2dsinθ​=12×(3×10−10)sin30∘​m =3×10−10m=3A˚

Q. What is the wavelength of a beam of X-rays (in $\overset{˚}{A}$ ) which is diffracted by a crystal in a direction making an angle of $6 0^{\circ}$ with the incident beam and corresponding to first order reflection from crystal lattice planes separated by $3 \times 1 0^{- 10} m$ ?