Hydrogen Spectrum

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Please refer to the attachment.

1. For each of the following transitions in the hydrogen atom, calculate the energy, frequency, and wavelength of the associated radiation, and determine whether the radiation is emitted or absorbed.
a. n=5 to n=1
b. n=4 to n=6
Solution: Electron energy in the nth levels in a hydrogen atom is given by:
En = - 13.6/n2 eV ........(1)
a) Energy in the level n = 5 = E5 = - 13.6/52 = - 0.544 eV
Energy in the level n = 1 (Ground state) = E1 = - 13.6/12 = - 13.6 eV
Change in the energy of the electron in transition = Initial energy - Final energy
= - 0.544 - (- 13.6) = 13.6 - 0.544 = 13.056 eV = 13.056 x 1.6 x 10-19 = 20.89 x 10-19 J
Applying the equation: E = hυ ........(2) where υ = Frequency of the radiation emitted, h = Planck's constant = 6.62 x 10-34 Js
20.89 x 10-19 = 6.62 x 10-34 υ
υ = 20.89 x 10-19/6.62 x 10-34 = 3.16 x 1015 Hz
Wave length λ = c/υ = 3 x 108/3.16 x 1015 = 9.49 x 10-8 m
As the transition is from a higher energy level to a lower energy level, the radiation equal to the energy level difference is emitted.
Energy of the radiation = 20.89 x 10-19 J
Frequency of the ...