Each rubidium halide crystallizing in the NaCl type lattice has a unit cell length 30 pm greater than for corresponding potassium salt (`r_(k)=133`pm) of the same halogen. What is the ionic radius of `Rb^(+)`?

Options

A. 1265 pm
B. 1056 pm
C. 985 pm
D. 148 pm

Answer

D

Explanation

For NaCl structure, edge length = `2(r_("cation")+r_("anion"))`
Edge length of rubidium halide unit cell, x = `2(r_(Rb^(+))+r_(X^(-)))`
Edge length of potassium halide unit cell, y = `2(r_(K^(+))+r_(X^(-)))`
but x - y = 30 pm
`2(r_(Rb^(+))+r_(X^(-)))-2(r_(K^(+))+r_(X^(-)))=30`
`r_(Rb^(+))-r_(K^(+))=15"pm"," "r_(Rb^(+))=r_(K^(+))+15"pm"=133+15=148"pm"`