1.37 Niobium crystallises in body-centred cubic structure. If density is 8.55 g cm^–3, calculate atomic radius of niobium using its atomic mass 93 u.

<p><strong>1.37 </strong>Calculation of edge length of unit cell(a)</p><p>Atomic mass of the element (M)= 93g mol⁻¹</p><p>Number of particles in bcc type unit cell (Z) = 2</p><p>Mass of the unit cell = Z × MNA = 2 × (93 g mol⁻¹) (6.022×10²³mol⁻¹)</p><p>=30.89×10⁻²³g</p><p>Density of unit cell (d) =8.55 g cm⁻³</p><p>Volume of unit cell (a³)=Mass of unit cell</p><p>Density of unit cell=(30.89×10⁻²³g)(8.55 g cm⁻³)</p><p>=36.16×10⁻²⁴cm³</p><p>Edge length of unit cell (a) = (36.13×10⁻²⁴cm³)¹³</p><p>=3.31 × 10⁻⁸cm</p><p><strong>Step II: </strong>Calculation of radius of unit cell (r)</p><p>For bcc structure, r=√3a4</p><p>=√3×(3.31×10⁻⁸cm)4</p><p>=1.43×10⁻⁸cm</p>

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