Calculate the volume of bcc unit cell if radius of an atom present in it is 1.86 10⁻⁸ ~cm .

Step-by-step solution

Body-centered cubic unit cell volume calculation In a BCC structure, atoms contact along the body diagonal, which spans 4r as it connects opposite corners through the center. For a cube with edge length a , the body diagonal equals 3 a , yielding the fundamental relationship: 4r = 3 a Solving for a : a = 4r 3 Substituting r = 1.86 10⁻⁸ cm: a = 4 1.86 10⁻⁸ 1.73205 4.295586 10⁻⁸ cm The cubic unit cell volume is then: V = a^3 = (4.295586 10⁻⁸)^3 7.925 10⁻²³ cm³ Among the options, 7.925 10⁻²³ cm³ most closely matches o