   Chapter 6.7, Problem 3.4ACP

Chapter
Section
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 434.1nm is calculated below.

Given,

The wavelength of absorption line of hydrogen is 434.1 nm=4.341 ×107m.

The energy per photon is,

E=                                (a)

The frequency per mole of photons is,

ν=cλ                                    (b)

Combining equation (a) and (b),

The energy per photon is,

E=hcλ

Substituting the values to the above equation,

E=hcλ=6

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