Chapter 36: Q70P (page 1113)

In Fig. 36-47, first-order reflection from the reflection planes shown occurs when an x-ray beam of wavelength $0.260 n m$ makes an angle $θ = 63.8 °$ with the top face of the crystal. What is the unit cell size $a_{0}$ ?

Short Answer

Expert verified

The unit cell distance is $0.570 nm$ .

Step by step solution

Bragg’s law

Diffraction is a phenomena in which the interference or the bending of waves occurs around the corners of the opening or obstacle through or on which it strikes.

The diffraction formula is following,

$nλ = 2 dsinθ λ = wavelength d = spacing θ = bragg angle n = order of diffraction$

Step 2: Identification of the given data

The wavelength is, $λ = 0.260 nm$ .

The angle is, $63.8 °$ .

The angle of incidence on the reflection planes is, $θ = 63.8 ° - 45 = 18 . 8^{0}$ .

The order of diffraction is, $n = 1$ .

Step 3: The unit cell size

From the given figure it is clear that the relation following will be formed,

$d = \frac{a_{0}}{\sqrt{2}} a_{0} = \sqrt{2} d$

Now from the bragg’s law,

$\sqrt{2} d = \frac{\sqrt{2} n λ}{2 \sin θ}$

Substitute all the value in the above equation.

$a_{0} = \frac{1 \times 0.260 nm}{\sqrt{2} \times \sin 18.8 °} a_{0} = 0.570 nm$

So the unit cell distance is $0.570 nm$ .

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In Fig. 36-47, first-order reflection from the reflection planes shown occurs when an x-ray beam of wavelength $0.260 n m$ makes an angle $θ = 63.8 °$ with the top face of the crystal. What is the unit cell size $a_{0}$ ?

Short Answer

Step by step solution

Bragg’s law

Step 2: Identification of the given data

Step 3: The unit cell size

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In Fig. 36-47, first-order reflection from the reflection planes shown occurs when an x-ray beam of wavelength0.260nmmakes an angleθ=63.8° with the top face of the crystal. What is the unit cell sizea0?

Short Answer

Step by step solution

Bragg’s law

Step 2: Identification of the given data

Step 3: The unit cell size

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Dynamics

Astrophysics

Electric Charge Field and Potential

Force

Particle Model of Matter

Translational Dynamics

Study anywhere. Anytime. Across all devices.

In Fig. 36-47, first-order reflection from the reflection planes shown occurs when an x-ray beam of wavelength $0.260 n m$ makes an angle $θ = 63.8 °$ with the top face of the crystal. What is the unit cell size $a_{0}$ ?