Chapter 6, Problem 7PS

### 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

# The most prominent line in the emission spectrum of aluminum is at 396.15nm. What is the frequency of this line? What is the energy of one photon with this wavelength? Of 1.00 mol of these photons?

Interpretation Introduction

Interpretation: The frequency, the energy per photon and the energy of one mole of photons of prominent line in emission spectrum of aluminium have 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 frequency, the energy per photon and the energy per mole of photons of prominent line in emission spectrum of aluminium is calculated below.

Given,

The wavelength of prominent line in emission spectrum of aluminum is,

â€‚Â 396.15nmâ€‰=â€‰396.15Â Ã—â€‰10â€‰âˆ’9m

• The frequency of prominent line in emission spectrum of aluminium is calculated by using the equation,

Â Â Î½â€‰=â€‰cÎ»

Substituting the values to the above equation,

â€‚Â Î½â€‰=â€‰2.998â€‰Ã—â€‰10â€‰8â€‰m/sâ€‰396.15Â Ã—â€‰10â€‰âˆ’9mâ€‰=â€‰7.5676â€‰Ã—â€‰10â€‰14â€‰sâˆ’1

The frequency of prominent line in emission spectrum of aluminum is 7.5676â€‰Ã—â€‰10â€‰14â€‰s-1

• The energy per photon of prominent line in emission spectrum of aluminium is calculated,

â€‚Â Eâ€‰=â€‰hÎ½

Substituting the values to the above equation,

â€‚Â Eâ€‰=â€‰hÎ½=â€‰6

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