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Niobium crystallizes in a body centred c...

Niobium crystallizes in a body centred cubic stucture. If density is 8.55 `gcm^(-3)`. The atomic radius of niobium, (given that its atomic mass is 93 u) is

A

49.8pm

B

150.1pm

C

143.1 `overset(@)A`

D

143.1pm

Text Solution

Verified by Experts

`a^(3)=(MxxZ)/(rhoxxN_(0)xx10^(-30))=(93g"mol"^(-1)xx2)/(8.55gcm^(-3)xx6.02xx10^(23)"mol"^(-1)xx10^(-30))`
`=3.61xx10^(7)=36.1xx10^(6)`
`a=(36.1)^(1//3)xx10^(2)pm=3.304xx10^(2)"pm"=330.4"pm"`
`[x=(36.1)^(1//3)"log"x=(1)/(3)kg.36.1=(1)/(3)xx1.5575=0.519]`
or x=antilog 0.519=3.304]
For body-centred cubic,
`r=sqrt(3)/(4)a=0.433a=0.433=0.433xx330.4"pm"=143.1"pm"`.
Hence 'D' is correct choice.
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