Ammonium chloride, crystalliazes in a body centered cubic latteice iwh edge length of unit cell equal to 387pm. If the size of `Cl^(-)` ion is 181pm, the size of `NH_(4)^(+)` ion would be:

Options

A. 116 pm
B. 154 pm
C. 174 pm
D. 206 pm

Answer

B

Explanation

In body centred cubic unit cell, ions touche each other along the body diagonal of the cube.
`2r_(c)+2r_(a)=sqrt(3)a`
`2(r_(c)+181 "pm")= sqrt(3) (387 "pm")`
`r_(c)=((sqrt(3))/(2))` (387 pm)-181 pm= 154.15 pm