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Niobium crystallizes in a body centred …

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Niobium crystallizes in a body centred cubic structure. If density is 8.55 gcm–3, The atomic radius of niobium, (given that its atomic mass is 93 u) is (A) 49.8 pm (B) 150.1 pm (C) 143.1 Å (D) 143.1 pm

Posted by Harsh Mishra 3 years, 11 months ago

CBSE > Class 12 > Chemistry

1 answers

Yogita Ingle 3 years, 11 months ago

Given density (d) = 8.55 g/cm³
Atomic mass (M) = 93u = 93 g/mol
We know, Avogadro number, N = 6.022 × 10²³
given lattice is body - centered cubic,
so, number of atoms per unit cell (z) = 2
we know,
=> 8.55 = (2 × 93)/(a³ × 6.023 × 10²³)
=> 8.55 × a³ × 6.023 × 10²³ = 186
=> a³ = 186/(8.55 × 6.023 × 10²³)
=> a³ = 36.124 × 10^-24
=> a = 3.3057 × 10^-8 cm
for BCC unit cell, radius = √3a/4
= (√3 × 3.3057 × 10^-8)/4
= (1.732 × 3.3057)/4 × 10^-8
= 1.431 × 10^-8 cm = 1.431 × 10^-10 m
= 1.431 A°
hence, atomic radius of Niobium is 1.431A°.

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