Question

A metal crystallizes with cubic close packed structure. The sin2
θ values of Bragg reflections
of Miller planes (200) and (111) are 0.18 and 0.14 respectively. What will be value for the unit
cell length?

Answer 1

Answer:

Explanation:

The sin2 value of the brag reflection of Miler planes (200) and (111) is provided as 0.18 and 0.14, respectively. Metal crystallises with a cubic close-packed structure. The goal is to establish the metal's unit length.

The sin2 value of brag reflection is given by the formula:

sin2θ = λ$^2/(4a^2)$

Where sin2θ is the sin2 value of brag reflection, λ is the wavelength of X-rays used, and a is the unit length of the crystal.

Using the given sin2 values and assuming the same wavelength of X-rays used for both Miler planes, we can express the equation as:

0.18 = λ$^2/(4a^2)$for (200) Miler plane

0.14 = λ$^2/(4a^2)$for (111) Miler plane

Solving for a in both equations, we get:

a = λ/√(4sin2θ)

Substituting the values for sin2θ and assuming a common wavelength of X-rays used, we get:

a = λ/√(4(0.18)) for (200) Miler plane

a = λ/√(4(0.14)) for (111) Miler plane

Simplifying the equations, we get:

a = 0.290λ for (200) Miler plane

a = 0.335λ for (111) Miler plane

Therefore, the unit length of the metal is dependent on the wavelength of the X-rays used. The specific value of the unit length cannot be determined without knowing the wavelength of the X-rays used.

Metal crystallizes with cubic close packed structure. The sin2 value of brag reflection of Miler planes (200) and (111) are given as 0.18 and 0.14, respectively. The unit length of the metal is dependent on the wavelength of the X-rays used, and cannot be determined without knowing the wavelength of the X-rays used.

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