Question

An element crystallises in bcc lattice with cell edge of 400pm. Calculate its density if 500 g of this element contains 2.5 × 10²⁴ atoms. 

Answer 1

Given: a = 400pm = 400 × 10¹⁰ cm

Z = 2(for bcc) M = ? d = ?

Using formula d = \(\frac{Z\times M}{a^3 \times N_A}\)

∴ 2.5 × 10²⁴ atoms of an element have mass = 500 g

∴ 6.022 × 20²³ atoms of an element have mass

\(= \frac{500 \times 6.022 \times 10^{23}}{2.5 \times 10 ^{24}}\)

∴ M = 120.44 g

Substituting all values in the formula: