Do you know why close packed planes are farther apart?

Close packed planes are the planes of low indices. If you have to take into account a fcc unit cell, the close packed planes are (111) planes. You can always calculate the distance between two planes using the formula

d= a/sqrt(h2+k2+l2)

which tells you that lower the indices, larger will be d.

This might be inadequate to explain the same question. Let us follow this way close packed planes are also farther apart because closer the packing of planes, higher will be the planar density of atoms. you might ask what if the planar density is going to be large, how does it affect the distance between the two planes... the answer is yes, in terms of geometry and interplanar spacing, close packed planes have high coordination and so the next planes should be kept larger apart in order that the interactions between the atomic positions make the atoms sit in the equilibrium positions.

Physically this could also be explained in terms of a simple diagram which is given in the second chapter of the book called X-ray diffraction by cullity where 2-d representation of planes in a lattice is drawn and it is shown that the interplanar spacings for closepacked planes are larger.

I don't really know whether it is a decent answer for this question. But I feel I need a physical basis still to explain the statement that close packed planes are farther apart. Though in terms of happening of slip one could explain that the close packed planes will have (t crss) minimum. This comes about from pieirls stress or the lattice frictional stress is minimum when w goes to maximum and b goes to minimum. The equation is t crss is proportional to exp (-w/b).

The above explanation might hold good to answer why slip gets activated in close packed planes and directions which inherently takes into account w to be larger or in other words d to be larger.

So please contribute to this question if you have anything further to be said. Let us discuss.