   Chapter 6.7, Problem 3.3ACP

Chapter
Section
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 5.89×107m and 5.8959×107m is calculated and the energy difference between the two photons is also determined.

Given,

The wavelength of line in the yellow region is 589nm=5.89×107m

The wavelength of line in the yellow region is 589.59nm=5.8959×107m

• The energy of a photon of line in the yellow region with wavelength 5.89×107m_ is calculated,

E=hcλ

Substituting the values

E==6.626×1034J.s/photon×2.998×108m/s5.89×107m=3.3726×1019J

The energy of a photon of line in the yellow region with wavelength 5.89×107m is 3.3726×10-19J

• The energy of a photon of line in the yellow region with wavelength 5.8959×107m_ is calculated,

E=hcλ

Substituting the values

E=6.626×1034J

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