Chapter 6.7, Problem 3.3ACP

### 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

# Sodium atoms are responsible for a closely spaced pair of lines in the yellow region of the Sun's visible spectrum at 589.00 nm and 589.59 nm. Determine the energy (in joules) of a photon at each of these wavelengths. Determine the difference in energy between the two photons.

Interpretation Introduction

Interpretation: The energy of a photon of line in the yellow region with wavelength 5.89×107m and 5.8959×107m has to be calculated and the energy difference between the two photons has to be determined.

Concept introduction:

• Planck’s equation,

E==hcλwhere, ν=frequencyλ=wavelength

The energy increases as the wavelength of the light decreases.

Explanation

The energy of a photon of line in the yellow region with wavelength 5.89â€‰Ã—â€‰10âˆ’7â€‰m and 5.8959â€‰Ã—â€‰10âˆ’7â€‰m is calculated and the energy difference between the two photons is also determined.

Given,

The wavelength of line in the yellow region is 589â€‰nmâ€‰â€‰=â€‰5.89â€‰Ã—â€‰10âˆ’7â€‰m

The wavelength of line in the yellow region is 589.59â€‰nmâ€‰â€‰=â€‰5.8959â€‰Ã—â€‰10âˆ’7â€‰m

• The energy of a photon of line in the yellow region with wavelength 5.89â€‰Ã—â€‰10âˆ’7â€‰m_ is calculated,

â€‚Â Eâ€‰=â€‰hcÎ»

Substituting the values

Â Â Eâ€‰=â€‰=â€‰6.626â€‰Ã—â€‰10â€‰âˆ’34â€‰J.s/photonâ€‰Ã—â€‰2.998â€‰Ã—â€‰10â€‰8â€‰m/s5.89â€‰Ã—â€‰10âˆ’7â€‰m=â€‰3.3726â€‰Ã—â€‰10â€‰âˆ’19â€‰J

The energy of a photon of line in the yellow region with wavelength 5.89â€‰Ã—â€‰10âˆ’7â€‰m is 3.3726â€‰Ã—â€‰10â€‰-19â€‰J

• The energy of a photon of line in the yellow region with wavelength 5.8959â€‰Ã—â€‰10âˆ’7â€‰m_ is calculated,

â€‚Â Eâ€‰=â€‰hcÎ»

Substituting the values

Â Â Â Â Eâ€‰=â€‰6.626â€‰Ã—â€‰10â€‰âˆ’34â€‰J

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