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The Electromagnetic Spectrum: Question 6

Syllabus 3.3

Multiple choice Core 1 mark

A wave travels through a vacuum with a wavelength of 5.0×10−7 m5.0\times10^{-7}\text{ m} (500 nm). Which region of the electromagnetic spectrum does this wave belong to?

Choose an answer to check it, then compare with the worked solution below.
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Worked solution

Step 1: Recall the approximate wavelength of each region

Moving across the electromagnetic spectrum, typical wavelengths shrink dramatically:

  • radio waves: from a few millimetres up to hundreds or thousands of metres, vastly longer than 5.0×10−7 m5.0\times10^{-7}\text{ m}.
  • visible light: roughly 4×10−7 m4\times10^{-7}\text{ m} (violet) to 7×10−7 m7\times10^{-7}\text{ m} (red).
  • X-rays: very much shorter, typically of the order of 10−10 m10^{-10}\text{ m} or less.
  • gamma rays: shorter still, at the extreme high-frequency end of the spectrum.

Step 2: Compare the given wavelength

The wave in the question has wavelength 5.0×10−7 m5.0\times10^{-7}\text{ m}. This falls squarely inside the visible-light range of roughly 4×10−74\times10^{-7} to 7×10−7 m7\times10^{-7}\text{ m}. It is far too long to be an X-ray or gamma ray, and far too short to be a radio wave.

Step 3: Match to the correct option

A wavelength of 5.0×10−7 m5.0\times10^{-7}\text{ m} belongs to visible light, matching option B.

Why the other options are wrong

OptionRegionError
Aradio wavesRadio wavelengths are many orders of magnitude longer than 5.0×10−7 m5.0\times10^{-7}\text{ m} (millimetres to kilometres, not hundreds of nanometres)
CX-raysX-ray wavelengths are far shorter than 5.0×10−7 m5.0\times10^{-7}\text{ m}, of the order of 10−10 m10^{-10}\text{ m}
Dgamma raysGamma-ray wavelengths are even shorter than X-rays, nowhere near 5.0×10−7 m5.0\times10^{-7}\text{ m}

Final answers

  • A wavelength of 5.0×10−7 m5.0\times10^{-7}\text{ m} (500 nm) lies within the visible-light range, option B.