An electron in a hydrogen atom could undergo any of thetransitions listed below,

Question

An electron in a hydrogen atom could undergo any of thetransitions listed below, by emitting light. Which transition wouldgive light of the shortest wavekenght? How do you explain theresult if you were to choose from 1. n=4 to n=2 2. n=4 to n=3 3. n=3 to n=1 4. n=2 to n-1 and 5. n=4 to n=1 Thanks An electron in a hydrogen atom could undergo any of thetransitions listed below, by emitting light. Which transition wouldgive light of the shortest wavekenght? How do you explain theresult if you were to choose from 1. n=4 to n=2 2. n=4 to n=3 3. n=3 to n=1 4. n=2 to n-1 and 5. n=4 to n=1 Thanks

Explanation / Answer

The anwser is 5. n=4 to n=1 explain: Energy of a photon in a hydrogen transition in a fancy formulagiven by f= 3.29*10^15 (1/(ni)^2 - 1/(nf)^2) f is the frequency of the light emitted. ni= initial energystate nf= final energy state. since photons are light c=f (c=speed of light wavelength of light) so in the above equation c/(3.29*10^15 (1/(ni)^2 - 1/(nf)^2))= using the numbers given 5.) gives the shortestwavelength without using a big formula E_hydrogen_ =Constant/(n^2)   (n is the quantum number the constant isnegative) so n=1 has the losest energy and it goes up like 1/n^2 You want to produce the largest frequency of light (same assmallest wavelength) but the energy space gets smaller as nincreases 1/100 ~ 1/121 In short you want the smallest quantum numbers with thelargest distance between them ( in general plug and chug with thelarge formula will provide the anwser.

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