A silicon crystal is doped with phosphorous to a concentration of phosphorous atoms per cubic meter. We have to find, on an average, the distance between these atoms.

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The concentration of phosphorous atoms per cubic meter is . We assume that on an average the distance between two neighbouring phosphorous atoms be a m. That is phosphorous atoms are distributed in a cubic lattice of lattice length a m.

We have

The average distance between phosphorous atoms is therefore 46.4 nm.