At $100^{\circ} \mathrm{C}$, copper(Cu) has FCC unit cell structure with cell edge length $x \stackrel{\circ}{\mathrm{A}}$. What is the approximate density of $\mathrm{Cu}$ (in $\mathrm{g~cm}^{-3}$) at this temperature? [Atomic mass of $\mathrm{Cu}=63.55 \mathrm{~u}$]

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Solid State

10 0^{\circ} C

, copper(Cu) has FCC unit cell structure with cell edge length

x A \circ

. What is the approximate density of

Cu

(in

g cm^{- 3}

) at this temperature?
[Atomic mass of

Cu = 63.55 u

]

Answer: (D)

An FCC cell contains

Z = 4

atoms, and the density is

d = \frac{Z M}{N _{A} a ^{3}}

. With

M = 63.55

N_{A} = 6.022 \times 1 0^{23}

and the edge

a = x \times 1 0^{- 8} cm

(since

1 \overset{˚}{A} = 1 0^{- 8} cm

d = \frac{4 \times 63.55}{6.022 \times 1 0 ^{23} \times ( x \times 1 0 ^{- 8} ) ^{3}} = \frac{254.2}{6.022 \times 1 0 ^{23} \times x ^{3} \times 1 0 ^{- 24}} = \frac{2542}{6.022 x ^{3}} \approx \frac{422}{x ^{3}} g cm^{- 3}

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Single correct option