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The hydrogen atom can absorb light of wavelength 1094 nm. Find the initial and final values of n associated with this absorption.


**I know this has something to do with rydberg's equation, however I'm not exactly sure how to go about this.

Verified Answer :

MissPhiladelphia

Rydberg equation is

\(\frac{1}{wavelength}= R( \frac{1}{ n_{1}^{2} }-\frac{1}{ n_{2}^{2} })\)

R is the Rydberg constant which is equal to 1.096776 x 10^7 m^-1. Wavelength is 1.094 x 10^-6 m.

So the equation becomes,

\(\frac{1}{1.094 \ x \ 10^{-6} }=1.096776 \ x \ 10^{7}( \frac{1}{ n_{1}^{2} }-\frac{1}{ n_{2}^{2} })\)

This is trial and error. Our basis should be: n2>n1 and both are whole numbers. According to quantum theory, electrons jump in discrete energies, so there is no in-between. Energy levels must be in a specific quantum number. Then, in order to absorb light, the photon must be able to go to a higher energy level.

If n1 = 1, n2 = 1.04
   n1 = 2, n2 = 2.45
   n1 = 3, n2 = 6

Hence, n1 = 3 and n2 = 6.

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