Niobium Crystalizes $(g 3)$ BCl lattice and has density of $8.55$ kg $/ d m^{3}$ . Calculate the atomic radius of Niobium.

Open in App

Solution

Atomic mass of $N b = 93 u$
Given density is $8.55 k g / d m^{3}$
no. of atoms in unit cell of $B C C$ lattice, $Z = 2$
We have,
$ρ = \frac{Z M}{a^{3} N_{A}} = \frac{2 \times 93}{a^{3} \times 6.022 \times 10^{23}}$
$a^{3} = \frac{186}{8.55 \times 6.022 \times 10^{23}} = \frac{186}{5.14881} \times 10^{- 24}$
$a^{3} = 36.124 \times 10^{- 24}$
$a = 3.3 \times 10^{- 8} d m$
For BCC,
$r = \frac{a \sqrt{3}}{4} = \frac{3.3 \times 10^{- 8} \times 1.732}{4} d m$
$r = 1.4289 \times 10^{- 8} d m$
$r = 1.43 \times 10^{- 8} d m$

Suggest Corrections

Similar questions

Q. Niobium crystallises as body centered cube (BCC) and has density of

8.55 k g / d m^{3}

. Calculate the atomic radius of niobium. (Given: Atomic mass of niobium

= 93

Niobium crystallises in body - centred cubic structure. If density is $8.55 g c m^{- 3}$ . Calculate atomic radius of niobium using its atomic mass 93 u.

Q. Niobium is found to crystallize with bcc structure and found to have the density of

8.55

g cm

^{- 3}

Determine the atomic radius of niobium if its atomic mass is

93

Q. Niobium is found to crystalline with bcc structure and found to have a density of

8.55 g

{c m}^{- 3}

. Determine the atomic radius of niobium if its atomic mass is

93 u

Q. Chromium metal crystallizes with a body-centered cubic lattice. The length of the unit cell edge is found to be

287 p m

. Calculate the atomic radius. What would be the density of chromium in

g / c m^{3}

Join BYJU'S Learning Program

Niobium Crystalizes (g3) BCl lattice and has density of 8.55 kg/dm3. Calculate the atomic radius of Niobium.

Atomic mass of Nb=93uGiven density is 8.55kg/dm3no. of atoms in unit cell of BCC lattice, Z=2We have, ρ=ZMa3NA=2×93a3×6.022×1023a3=1868.55×6.022×1023=1865.14881×10−24a3=36.124×10−24a=3.3×10−8dmFor BCC,r=a√34=3.3×10−8×1.7324dmr=1.4289×10−8dmr=1.43×10−8dm

Niobium Crystalizes $(g 3)$ BCl lattice and has density of $8.55$ kg $/ d m^{3}$ . Calculate the atomic radius of Niobium.