Chapter 6.7, Problem 3.4ACP

### 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

# Hydrogen has an absorption line at 434.1 nm. What is the energy (in kilojoules per mole) of photons with this wavelength?

Interpretation Introduction

Interpretation: The energy per mole of photons of the absorption line of hydrogen at 434.1nm has to be calculated.

Concept introduction:

• Planck’s equation,

E=where, 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

The energy per mole of photons of the absorption line of hydrogen at 434.1â€‰nm is calculated below.

Given,

The wavelength of absorption line of hydrogen is 434.1Â nmâ€‰=â€‰4.341Â Ã—â€‰10â€‰âˆ’7m.

The energy per photon is,

Â Â Â Â Eâ€‰=â€‰hÎ½â€‰Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (a)

The frequency per mole of photons is,

Â Â Â Â Î½â€‰=â€‰cÎ»Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b)

Combining equation (a) and (b),

The energy per photon is,

â€‚Â Eâ€‰=â€‰hcÎ»â€‰

Substituting the values to the above equation,

â€‚Â Eâ€‰=hcÎ»â€‰=â€‰6

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