Q. 50

The longest wavelength doublet absorption transition is observed at 589 and 589.6 nm. Calculate the frequency of each transition and energy difference between two excited states.

Answer :

Given:

Wavelength, λ1 = 589 nm


Wavelength, λ2 = 589.6 nm


To find frequency:


Speed of Light = [Frequency] × [Wavelength]


We know speed of light = 3×108 m/s


Frequency, v1 = [3×108] / [589 × 10-9]


v1 = 5.093×1014 Hz


Frequency, v2 = [3×108] / [589.6 × 10-9]


V2 = 5.088×1014 Hz


Change in Energy, ∆E = E2-E1 = h[v2-v1]


= [6.626× 10-34] {[5.093 - 5.088] × 1014}


= [6.626× 10-34] {[5× 10-3] × 1014}


= 3.313× 10-22J


Therefore, the energy difference between two excited states is 3.31× 10-22J.


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