Answer

Verified

456k+ views

**Hint:**Inter planar spacing between two planes is given by the formula:

${ d\ =\ \frac { a }{ \sqrt { { h }^{ 2 }+{ k }^{ 2 }+{ l }^{ 2 } } } }$

Here h, k, l usually occurs as (h k l) and these are the miller indices. ‘a’ in the equation is the edge length. By substituting the values given in the question, we will get the interplanar distance. Interplanar distance is the perpendicular distance between two successive planes.

**Complete step by step answer:**

The inter planar spacing between two planes is given by the formula:

${ d\ =\ \frac { a }{ \sqrt { { h }^{ 2 }+{ k }^{ 2 }+{ l }^{ 2 } } } }$

Where, h, k, l are Miller indices; a is the lattice parameter and d is the interplanar distance.

Here in this question, it has been given that a = 450 pm.

The interplanar spacing or interplanar distance is the perpendicular distance between two successive planes in a family (h k l). It is commonly indicated as d

_{hkl}and corresponds to the reciprocal of the length of the corresponding vector in reciprocal space.

Here, in the question, it has been provided that (2 2 1) plane. So, here value of h = 2, k = 2 and l = 1

Substitute these values in the formula:

${ d\ =\ \frac { a }{ \sqrt { { h }^{ 2 }+{ k }^{ 2 }+{ l }^{ 2 } } } }$

${ \ =\ \frac { 450 }{ \sqrt { { 2 }^{ 2 }+{ 2 }^{ 2 }+{ 1 }^{ 2 } } } }={ \frac { 450 }{ \sqrt { 9 } } =150\ pm }$

**Hence, the answer is option (B) 150 pm.**

**Additional Information:**

Miller indices: Miller indices form a notation system in crystallography for planes in crystal (Bravais) lattices. In particular, a family of lattice planes is determined by three integers h, k, and l, the Miller indices.

Lattice constants: The lattice constant, or lattice parameter, refers to the physical dimension of unit cells in a crystal lattice. Lattices in three dimensions generally have three lattice constants, referred to as a, b, and c. For example, The lattice constant for diamond is a = 3.57 angstrom units at 300 K.

**Note:**The interplanar distance will remain the same for all the combinations for particular value of h,k,l. i.e, for eg: (2 2 1), (1 2 2),(1 2 1) all have the same interplanar distances here.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

What percentage of the solar systems mass is found class 8 physics CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you graph the function fx 4x class 9 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

Why is there a time difference of about 5 hours between class 10 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE