Quantom dot...please help me?

Question

Quantum dot contains 10,000 atoms of silicon. Calculate mass (g), volume (cm^3), and if dot is acute, length (mass & mm).

Thanks alot!

Answer 1

the molar mass of silicon is 28.05g
this is the mass of 6.022*10^23 atoms
so the mass of 1 atom is 28.05/6.02*10^23
and mass of 10^4 is 28.05*10^4/6.022*10^23 =4.658*10^-19g
The density of silicon is 2.329
so the volume is 4.658*10^-19/2.329 =2*10^-19cm^3
If we assume a spheric atom then V=4/3*pi*r^3
so r^3= 3V/(4*pi)=4.77*10^-20cm^3
taking the cubic root r=3.628*10^-7cm= 3.628*10^-6mm
the diameter is the double 7.656*10^-6 mm