Question

Part A

Compute the energy separation between the ground and first excited states for an electron in a one-dimensional box that is 5.10 angstroms in length. Express the energy difference in kJ⋅mol−1.

Express your answer to three significant figures and include the appropriate units.

E=

Part B

Compute the wavelength of light (in nm) corresponding to this energy.

Express your answer to three significant figures and include the appropriate units.

λ=

Answer 1

Solution knery of electron inside a 18 box is given by : En = n²h² where n=1,2,3... & me 2 m= mass of electron &- vength off t h = Plank's Constant for ground state, n=1 E = nha - (1² h 2 = h. 8 ml 8 ml Sail 2 For 1st excited state, n=2 T hrillsness than²n2 = (20 h = 4h² &neda 8ml 8ml 2 Therefore the curpy sepration between the ground and Ist excited state is given by DE = E₂-6 4 h = ☆ *(4-) - 342 aml 8ml 8ml ² 8me2

DE 3x (6.626X163453)? ** 9.1x10-3! * (51x10 -"om) d=5.14 = 5.18100 h = 6.626x1034 Js 72.0 X 10-1" ng X 26.01 X10-20m2 me 9. 1x10 kg -68 22 3x43.900 10 Is -68 + 51 0.06x 10 DE = 0.06% 1017 J the fenoo, DE= hx - Planck's constant () velocity of right da warelength of light etxel 6640" Is 10.06x1017 = 6.626x10 "Is x 3.0x10 m/s dis 6.626 X1024 Js X3.0 x10' mis 0.06x10-17] = 3.313 x107m = 331.3*00-9m