One of the top$-$down approaches to create nano$-$particles is to deposit thin

layers of metals on foreign substrate and anneal it in order to obtain well$-$

defined nano$-$shapes.

Thin layer of Au was deposited on Si substrate and annealed to elevated T$.$

Owing to de$-$wetting procedure Au hemispheres of radius $3nm$ were created, as

shown in the Figure below:

Given that surface density of hemispheres is $4{10}^{12}c{m}^{-2},$ calculate the

thickness of the deposited Au layer $($in nm$).$