# 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?

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#### Solution Preview

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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.