Calculate the radius of an atom of an element in pm if it forms bcc unit cell structure having edge length 4.3 10⁻⁸ ~cm .

Step-by-step solution

Body-centered cubic structure atoms contact along the body diagonal, whose length equals 4r . The body diagonal relates to edge length a through spatial geometry: a 3 = 4r . Isolating the radius yields r = a 3 4 . Given edge length a = 4.3 10⁻⁸ cm converts to a = 430 pm using 1 cm = 10¹⁰ pm. Substitution gives r = 430 3 4 . With 3 1.732 , the calculation proceeds: r = 430 1.732 4 = 744.76 4 = 186.19 pm. The approximate radius of 186.2 pm corresponds to option A .