Calculate the largest diameter a spherical silver nanoparticle

1.  Calculate the largest diameter a spherical silver nanoparticle can have for there to be no more than

10⁹ electron energy states over a 1 eV interval at an energy of 2 eV.

2.  Determine the temperature at which a perfect cube of gold (with a volume of 27 nm³) becomes quantum confined (via the metal‐to‐insulator transition).

3.  The wave function, (x), of an electron trapped in a potential well with a finite depth and width, L, is given by:

(x)   Ae^Cx

(x)   F sin(kx)  Gcos(kx)

(x)   Be^Cx

for x 0 for 0 x L

for x  L