Question

An element crystallises in bcc structure. The edge length of its unit cell is 288 pm. If the density of the crystal is 7.2 g ${cm}^{-3}$. What is the atomic mass of the element?
(1) 51.8 (2) 103.6
(30 25.9 (4) 207.2

Answer 1

The correct option is 1.

we have given that

density, d=7.2 g$c{m}^3$

edge=$288\times {10}^{-10}$ cm

$N_A$=$6.02\times {10}^{23}$

for BCC structure Z=2

Atomic mass=?

d=$\frac{ZM}{a^3{N}_A}$

M=$\frac{d\times a^3\times N_A}{Z}$

M=$\frac{7.25\times (2.88\times {10}^{-10})\times 6.02\times {10}^{23}}{2}$

M=51.77 g/mol(approx)