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## Which of the following transitions would emit the shortest wavelength? select one; (a) n=2 to 1 (b) n=1 to 3 (c) n=1 to…

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Which of the following transitions would emit the shortest wavelength? select one; (a) n=2 to 1 (b) n=1 to 3 (c) n=1 to 2 (d) n=3 to 1

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2023-04-07T05:49:11+00:00
2023-04-07T05:49:11+00:00 1 Answer
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## Answer ( 1 )

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The energy of a photon emitted during a transition between two energy levels is given by the Rydberg formula:

1/? = R [1/n?� – 1/n?�]

where ? is the wavelength of the emitted photon, R is the Rydberg constant, and n? and n? are the initial and final energy levels, respectively.

To determine which transition would emit the shortest wavelength, we need to find the transition with the largest value of (1/n?� – 1/n?�).

(a) n=2 to 1: (1/n?� – 1/n?�) = (1/1� – 1/2�) = 0.75

(b) n=1 to 3: (1/n?� – 1/n?�) = (1/3� – 1/1�) = 8/9

(c) n=1 to 2: (1/n?� – 1/n?�) = (1/2� – 1/1�) = 3/4

(d) n=3 to 1: (1/n?� – 1/n?�) = (1/1� – 1/3�) = 8/9

Therefore, the transition that would emit the shortest wavelength is option (b) n=1 to 3, since it has the largest value of (1/n?� – 1/n?�) and thus the smallest denominator in the Rydberg formula, resulting in the shortest wavelength.