Question

An element (atomic mass M g/mol) having bcc structure has unit cell edge 400 pm. The density of the element is ____________ g/cm³.

[N_A = 6.0 × 10²³ atom mol⁻¹)

पर्याय

• ${\displaystyle \frac{\text{M}}{6.4}}$

• ${\displaystyle \frac{\text{M}}{19.2}}$

• ${\displaystyle \frac{\text{M}}{9.6}}$

• ${\displaystyle \frac{\text{M}}{38.4}}$

Answer 1

An element (atomic mass M g/mol) having bcc structure has unit cell edge 400 pm. The density of the element is ${\displaystyle \underline{\frac{\text{M}}{19.2}}}$ g/cm³.

Explanation:

For bcc unit cell, n = 2

400 pm = 400 × 10⁻¹⁰ cm

ρ = ${\displaystyle \frac{\text{n M}}{{\text{a}}^3{\text{N}}_{\text{A}}}}$

= ${\displaystyle \frac{2\times \text{M}}{{\left(400\right)}^3\times {10}^{-30}\times (6.0\times {10}^{23})}}$

= ${\displaystyle \frac{\text{M}}{19.2}}$ g/cm³