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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

The most prominent line in the emission spectrum of magnesium is 285.2 nm. Other lines are found at 383.8 and 518.4 nm. In what region of the electromagnetic spectrum are these lines? What is the energy of 1.00 mol of photons with the wavelength of the most energetic line?

Interpretation Introduction

Interpretation:

The region of line in emission spectrum of magnesium and the most energetic line among them has to be identified. The energy of 1.0mol photons of most energetic line in the emission spectrum of magnesium has to be calculated.

Concept introduction:

  • Electromagnetic radiations are a type of energy surrounding us. They are of different types like radio waves, IR, UV, X-ray etc.
  • Ultraviolet radiation lies in the wavelength of 100nm to 400nm whereas the visible light lies in the wavelength of 400nm to 700nm.
  • 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 region of line in emission spectrum of magnesium is identified

Emission spectrum of magnesium has three lines in 285.2nm, 383.8nm and 518.4nm where 285.2nm is prominent.

Ultraviolet radiation lies in the wavelength of 100nm to 400nm whereas the visible light lies in the wavelength of 400nm to 700nm.

Therefore, 285.2nm and 383.8nm lies in the ultraviolet region. The line which is found in 518.4nm is in visible light region.

  • The most energetic line among the lines in emission spectrum of magnesium is identified

E=hcλ so the energy increases as the wavelength of the light decrease. So the radiation having lower wavelength has higher energy per photon.

Here the prominent line which found in 285.2nm has the lowest wavelength comparing to other lines.

Therefore,

The prominent line which found in 285.2nm has the highest energy.

  • The energy of one mole of photons of most energetic line in the emission spectrum of magnesium is calculated below.

Given information,

The wavelength of most energetic line is 285.2nm=2.852 ×107m.

Planck'sconstant,h=6.626×1034J.sspeedoflight,c=2.998×108m/sAvogadro's number,NA=6

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