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Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

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BuyFindarrow_forward

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 434.1nm is calculated below.

Given,

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

h=6.626×1034J.sc=2.998×108m/sAvogadro's number,NA=6.022×1023photons/mol

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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