Answer to Question #170755 in Physical Chemistry for hAAHAN

Question

the smallest observed frequency for a transition between states of an electron n=2 is a one dimensional box is 3 * 10, what is length of box in nm

Answer 1

For a transition between states of an electron n=2 is a one dimensional box

Energy(E)=-13.6/2^2+13.6=10.2ev=10.2×1.602×10^9=1.63×10^-18j

For one dimensional box-

E=(n²h²)/8mL²

Where h=plank constant=6.626×10^-31m²kg/s

m=9.11×10^-31kg

L=length of the box

Now,

L²=(n²h²)/8mE

={2²×(6.626×10^-34)²m^2/kg/s}/{8×9.11×10^-31kg×1.63×10^-18 j }

=1.47×10^-19 m

L=3.84×10^-10 m=3.84×10^-1 nm

Hence the length of the box 3.84×10^-1 nm