Calculate the wavelength, in nanometers, for the colored line that appears in the spectrum of the hydrogen atom corresponding to an n=4 to n= 2 electronic transmission. The hydrogen atom emits visible light at the following wavelengths (given in nanometers with corresponding colors): 410 (violet), 434 (blue), 486 (green), and 656 (red). Part 2: Draw a simple energy level diagram for the hydrogen atom, and illustrate with arrows the transitions that give rise to VISIBLE light emissions.

Chemistry & Chemical Reactivity
9th Edition
ISBN:9781133949640
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Chapter6: The Structure Of Atoms
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Problem 19PS: The energy emitted when an electron moves from a higher energy state to a lower energy state in any...
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Part 1: Calculate the wavelength, in nanometers, for the colored line that appears in the spectrum of the hydrogen atom corresponding to an n=4 to n= 2 electronic transmission. The hydrogen atom emits visible light at the following wavelengths (given in nanometers with corresponding colors): 410 (violet), 434 (blue), 486 (green), and 656 (red). Part 2: Draw a simple energy level diagram for the hydrogen atom, and illustrate with arrows the transitions that give rise to VISIBLE light emissions.
Expert Solution
Step 1

Wavelength can be calculated using the equation:

                                           1λ =R(1n12 - 1n22)

                                             R = Rydberg constant = 109677 cm-1

                                           n1 = 4

                                           n2 = 2

                                          1λ =1.09 * 107 m-1(122 - 142)      = 1.09 * 107 m-1 ( 14-116)

                                                =  2043750 m-1

                                                = 2.04 * 106 m-1

                                            λ = 4.90 * 10-7 m

                                               = 490 * 10-9 m

                                               = 490 nm

                         Wavelength = 490 nm

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