Chapter 6, Problem 54GQ

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# Excited H atoms have many emission lines. One series of lines, called the Pfund series, occurs in the infrared region. It results when an electron changes from higher energy levels to a level with n = 5. Calculate the wavelength and frequency of the lowest energy line of this series.

Interpretation Introduction

Interpretation: The wavelength and frequency of the least energetic in Pfund series of the excited H atom is to be calculated.

Concept introduction:

• Electronic transitions that take place in excited H atom is,
1. 1. Lyman series: electronic transitions take place to the n=1 level and it is in ultraviolet region.
1. 2. Balmer series: electronic transitions take place from n>2 to the n=2 level and it is in visible region.
2. 3. Ritz-Paschen series: electronic transitions take place from n>3 to the n=3 level and it is in infrared region.
3. 4. Brackett series: electronic transitions take place from n>4 to the n=4 level.
4. 5. Pfund series: electronic transitions take place from n>5 to the n=5 level

EnergybetweenthestatesΔE=EfinalEinitial=Rhc(1nfinal21ninitial2)where,R=Rydbergconstanth=Planck'sconstantc=speedoflightn=Principalquantumnumber

As the energy gap between two transition states increases the wavelength of the radiation emitted decreases

• Planck’s equation,

E==hcλwhere, E=energyh=Planck'sconstantν=frequency

The energy increases as the wavelength of the light decrease. Also the energy increases as the frequency of the light increases.

• The frequency of the light is inversely proportional to its wavelength.

ν=cλwhere, c=speedoflightν=frequencyλ=wavelength

Explanation

As the energy gap between two transition states decreases the wavelength of the radiation emitted increases

Hence the line with highest wavelength is produced in Pfund series of H atom when the electronic transitions that take place from the nâ€‰=â€‰6 to the nâ€‰=â€‰5.

Since Eâ€‰=â€‰hcÎ» ,the energy decreases as the wavelength of the light increases. The electronic transitions that taking place from the nâ€‰=â€‰6 to the nâ€‰=â€‰5 has the least energy

The lowest energy line in Pfund series of the excited H atom forms if the transition of electron is from nâ€‰=â€‰6 to the nâ€‰=â€‰5

Â Â Râ€‰=â€‰1.097â€‰Ã—â€‰107â€‰mâ€‰âˆ’1hâ€‰=â€‰6.626â€‰Ã—â€‰10â€‰-34â€‰J.scâ€‰=â€‰2.998â€‰Ã—â€‰10â€‰8â€‰m/sninitialâ€‰=â€‰6nfinalâ€‰=â€‰5

Energy is determined,

Energyâ€‰betweenâ€‰theâ€‰statesâ€‰â€‰Î”Eâ€‰=â€‰Efinalâ€‰âˆ’â€‰Einitial=â€‰âˆ’Rhc(1nfinal2â€‰âˆ’â€‰1ninitial2)â€‰=â€‰âˆ’â€‰1.097â€‰Ã—â€‰107â€‰mâ€‰âˆ’1â€‰Ã—â€‰6.626â€‰Ã—â€‰10â€‰âˆ’34â€‰J.sâ€‰Ã—â€‰2.998â€‰Ã—â€‰10â€‰8â€‰m/sâ€‰(152â€‰âˆ’â€‰162)=â€‰âˆ’2.6634â€‰Ã—â€‰10â€‰âˆ’20â€‰J/photon

The energy emitted by the photon does not have any sign and absolute value is taken

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