If spheres of radius 'r' are arranged in ccp fashion (ABC ABC…) the vertical distance between any two consecutive A layers is

Options

A. `4rsqrt(2/3)`
B. `4r sqrt(3/2)`
C. 6 r
D. `rsqrt6`

Explanation

To find the vertical distance between any two consecutive A layers in a cubic close-packed (CCP) arrangement, we can follow these steps:

### Step 1: Understand the Arrangement
In a cubic close-packed (CCP) structure, the spheres are arranged in layers. The arrangement follows an ABCABC pattern, meaning that every third layer is identical.

### Step 2: Identify the Relationship Between Radius and Edge Length
In a CCP structure, the spheres touch each other along the face diagonal. The relationship between the radius (r) of the spheres and the edge length (A) of the cube can be established. The face diagonal of the cube can be expressed as:
\[ \text{Face diagonal} = \sqrt{2}A \]
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