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Colours and energies of electromagnetic radiation

We saw in the explanation for why the sky is blue that different wavelengths or frequencies of light correspond to different colours of light. The table below gives the wavelengths and colours of light in the visible spectrum:

Colours and wavelengths of light in the visible spectrum.
Colour Wavelength range (nm)
violet 390 - 455
blue 455 - 492
green 492 - 577
yellow 577 - 597
orange 597 - 622
red 622 - 780

We also know that the energy of a photon of light can be found from:

E = h f = h c λ

Therefore if we know the frequency or wavelength of light, we can calculate the photon's energy and vice versa.

Investigation : frequency, wavelength and energy relation

Refer to [link] : Copy the table into your workbook and add two additional columns.

  1. In the first new column write down the lower and upper frequencies for each colour of light.
  2. In the second column write down the energy range (in Joules) for each colour of light.

Questions

  1. Which colour of visible light has the highest energy photons?
  2. Which colour of visible light has the lowest energy photons?

Discharge lamps (sometimes incorrectly called neon lights) use the spectra of various elements to produce lights of many colours.

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A photon of wavelength 500 nm is emitted by a traffic light.

  1. What is the energy of the photon?
  2. What is the frequency of the photon?
  3. Use [link] to determine the colour of the light.
  1. We are given λ = 500 × 10 - 9 m and we need to find the photon's energy , frequency and colour .

  2. E = h c λ = ( 6 , 63 × 10 - 34 ) × ( 3 × 10 8 ) 500 × 10 - 9 = 3 , 98 × 10 - 19 J

    The energy of the photon is 3 , 98 × 10 - 19 J.

  3. E = h f f = E h = 3 . 98 × 10 - 19 6 , 63 × 10 - 34 = 6 × 10 14 Hz

    The frequency of the photon is 6 × 10 14 Hz .

  4. The wavelength given in the question is 500 nm. We can see in the table that green light has wavelengths between 492 - 577 nm. Therefore 500 nm is in this range so the colour of the light is green .

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I have some sources which emit light of the following wavelengths:

  1. 400 nm,
  2. 580 nm,
  3. 650 nm,
  4. 300 nm.

What are the colours of light emitted by the sources (see [link] )? Which source emits photons with the highest energy and which with the lowest energy?

  1. Four wavelengths of light are given and we need to find their colours .

    We also need to find which colour photon has the highest energy and which one has the lowest energy.

    1. 400 nm falls into the range for violet light (390 - 455 nm).
    2. 580 nm falls into the range for yellow light (577 - 597 nm).
    3. 650 nm falls into the range for red light (622 - 780 nm).
    4. 300 nm is not shown in the table. However, this wavelength is just a little shorter than the shortest wavelength in the violet range. Therefore 300 nm is ultraviolet .
  2. We know E = h c λ

    For 400 nm:

    E = h c λ = ( 6 , 63 × 10 - 34 ) × ( 3 × 10 8 ) 400 × 10 - 9 = 4 , 97 × 10 - 19 J

    For 580 nm:

    E = h c λ = ( 6 , 63 × 10 - 34 ) × ( 3 × 10 8 ) 580 × 10 - 9 = 3 , 43 × 10 - 19 J

    For 650 nm:

    E = h c λ = ( 6 , 63 × 10 - 34 ) × ( 3 × 10 8 ) 650 × 10 - 9 = 3 , 06 × 10 - 19 J

    For 300 nm:

    E = h c λ = ( 6 , 63 × 10 - 34 ) × ( 3 × 10 8 ) 300 × 10 - 9 = 6 , 63 × 10 - 19 J

    Therefore, the photons with the highest energy are the ultraviolet photons.

    The photons with the lowest energy are from light which is red .

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Source:  OpenStax, Siyavula textbooks: grade 12 physical science. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11244/1.2
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