# Calculate the largest diameter a spherical silver nanoparticle

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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)   AeCx

(x)   F sin(kxGcos(kx)

(x)   BeCx

for x 0 for 0 x L

for x  L

(a)  Given that F = G = 5, k = 1, and C= 2 plot (using MatLab or another plotting program) the wave function over the range ‐2 ≤ x ≤ L + 2.

(b)Given that (L) = (0), determine the values of L and B if the wave function corresponds to the third lowest energy state.

• 5 years ago
Calculate the largest diameter a spherical silver nanoparticle
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