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# Hydrogen Spectrum

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1. For each of the following transitions in he 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

2. One of the emission lines of the hydrogen atom spectrum has a wavelength of 93.8 nm.

a. Determine the region of the electromagnetic spectrum this emission is found.
b. Determine the initial and final values of n associated with the emission.

3. What is the difference between an emission spectrum and an absorption spectrum?

https://brainmass.com/physics/energy/transitions-hydrogen-atom-emission-lines-absorption-376572

#### Solution Preview

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 ...

#### Solution Summary

The transition in the hydrogen atom, emission lines and absorption spectrums are given. Step by step solution provided for questions involving hydrogen.

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