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The Electromagnetic Spectrum: Question 10

Syllabus 3.3

Structured Extended 7 marks

A laser pointer emits green light of wavelength 532 nm532\text{ nm} in air, where electromagnetic waves travel at 3.0×108 m/s3.0\times10^{8}\text{ m/s}. A nearby radio transmitter broadcasts at a frequency of 1.5×106 Hz1.5\times10^{6}\text{ Hz}.

(a) Convert the wavelength of the green light into metres, giving your answer in standard form. [1]

(b) Calculate the frequency of the green light. Give your answer in standard form, to 3 significant figures. [2]

(c) Calculate how many times greater the frequency of the green light is than the frequency of the radio wave. Give your answer to 2 significant figures. [2]

(d) State which of the two waves, the green light or the radio wave, carries more energy, and explain your answer in terms of frequency. [2]

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Worked solution

Part (a): Converting the wavelength to metres

532 nm=532×10−9 m=5.32×10−7 m532\text{ nm} = 532\times10^{-9}\text{ m} = \boxed{5.32\times10^{-7}\text{ m}}

Part (b): Calculating the frequency of the green light

Rearrange v=fλv = f\lambda to make frequency the subject:

f=vλf = \frac{v}{\lambda}

Substitute v=3.0×108 m/sv = 3.0\times10^{8}\text{ m/s} and λ=5.32×10−7 m\lambda = 5.32\times10^{-7}\text{ m}:

f=3.0×1085.32×10−7f = \frac{3.0\times10^{8}}{5.32\times10^{-7}}

f=5.639…×1014 Hzf = 5.639\ldots\times10^{14}\text{ Hz}

Rounding to 3 significant figures:

f=5.64×1014 Hzf = \boxed{5.64\times10^{14}\text{ Hz}}

Part (c): Comparing the two frequencies

To find how many times greater the frequency of the green light is than the frequency of the radio wave, divide the two frequencies:

fgreenfradio=5.639×10141.5×106\frac{f_{\text{green}}}{f_{\text{radio}}} = \frac{5.639\times10^{14}}{1.5\times10^{6}}

fgreenfradio=3.759…×108\frac{f_{\text{green}}}{f_{\text{radio}}} = 3.759\ldots\times10^{8}

Rounding to 2 significant figures:

fgreenfradio≈3.8×108\frac{f_{\text{green}}}{f_{\text{radio}}} \approx \boxed{3.8\times10^{8}}

So the frequency of the green light is about 3.8×1083.8\times10^{8} times greater than the frequency of the radio wave.

Part (d): Comparing the energy carried by the two waves

Across the electromagnetic spectrum, waves of higher frequency carry more energy. The green light has a frequency of 5.64×1014 Hz5.64\times10^{14}\text{ Hz}, which is enormously higher than the radio wave’s frequency of 1.5×106 Hz1.5\times10^{6}\text{ Hz} (as shown by the ratio in part (c)).

Therefore, the green light carries more energy than the radio wave.

(This is the same general trend that makes the very highest-frequency regions of the spectrum (ultraviolet, X-rays and gamma rays) energetic enough to be ionising and damage living cells. Visible light itself sits well below that threshold, so it is not ionising, but the underlying trend of “higher frequency, more energy” still applies when comparing it with radio waves.)

Final answers

  • (a) Wavelength of the green light == 5.32×10−7 m5.32\times10^{-7}\text{ m}
  • (b) Frequency of the green light == 5.64×1014 Hz5.64\times10^{14}\text{ Hz}
  • (c) The green light’s frequency is about 3.8×1083.8\times10^{8} times greater than the radio wave’s
  • (d) The green light carries more energy, because it has a much higher frequency than the radio wave