Question

Consider a transition from the ground state : nx=1, ny=1, nz=1 to the excited state nx=2, ny=2, nz=1. What are the dimensions of a cubic QD if the wavelength of light absorbed is 570 nm?

Answer 1

For particle in 3d box

E = ( h^2/8ml^2) ( nx^2 + ny^2 +nz^2)   where l = box length

when ground state E = ( h^2/8ml^2) ( 1+1+1) = 3h^2 / ( 8ml^2)

in exited state E = ( h^2/8ml^2) ( 2^2 + 2^2 + 1^2) = 9 h^2 / ( 8ml^2)

difference in energy = ( h^2/8ml^2) ( 9-3) = 6h^2 / 8ml^2

differnece in energy = energy of tranion = E = hc /lamda = ( 6.625x10^-34 x 3x10^8) / ( 570x10^-9)

         = 3.487 x 10^-19

now mass oe electron = 9.1 x 10^-31

we equate ad find L

6 x ( 6.625x10^-34)^2 / ( 8 x 9.1x10^-31 x l^2) = 3.487 x 10^-19

l = 1 x 10^-9 m = 1 nm

hence box length QD is 1nm