The volume of simple unit cell is x 10⁻²³ ~cm ^3 . Calculate the value of x if volume occupied by a particle in it is 2.1 10⁻²³ ~cm ^3 .

Step-by-step solution

Volume of Simple Cubic Unit Cell from Atomic Volume Given the volume of a single atom as V_ atom = 4 3 r^3 = 2.1 10⁻²³ cm³, solve for r^3 : r^3 = 3 V_ atom 4 = 3(2.1 10⁻²³) 4 = 6.3 10⁻²³ 4 For a simple cubic unit cell, atoms touch along edges, so the edge length is a = 2r and the cell volume is V_ cell = a^3 = (2r)^3 = 8r^3 . Substituting the expression for r^3 : V_ cell = 8 ( 6.3 10⁻²³ 4 ) = 50.4 10⁻²³ 4 = 12.6 10⁻²³ Using 3.14159 , the volume is V_ cell 4.0107 10⁻²³ cm³. Expressed as x 10⁻²³ cm³, x 4.0 when round