9702 · 7.4

Electromagnetic spectrum — practice questions

Practice and worked examples for 9702 Electromagnetic spectrum. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

A certain radio wave has a frequency of 1.5 x 10⁷ Hz. Calculate its wavelength in a vacuum.

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Recall the wave equation for EM waves in a vacuum: $c = f\lambda$
Identify known values: $c = 3.00 x 10⁸ m s^{-1}$ (speed of light), $f = 1.5 x 10⁷ Hz$ (frequency).
Rearrange the formula to solve for wavelength: $\lambda = \frac{c}{f}$
Substitute the values: $\lambda = \frac{3.00 \times 10^8 \text{ m s}^{-1}}{1.5 \times 10^7 \text{ Hz}}$
Calculate the wavelength: $\lambda = 20 \text{ m}$
State the answer with units: The wavelength of the radio wave is 20 m.

Worked example 2

Green light has a typical wavelength of 550 nm. Calculate its frequency.

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Start with the wave equation for electromagnetic waves: $c = f\lambda$ .
Identify the known values. The speed of light in a vacuum is $c = 3.00 \times 10^8 \text{ m s}^{-1}$ . The wavelength is given as $\lambda = 550 \text{ nm}$ .
Convert the wavelength to the SI unit of metres. Since 1 nm = $10^{-9}$ m, we have: $\lambda = 550 \times 10^{-9} \text{ m} $.$
Rearrange the wave equation to solve for frequency, $f$ : $f = \frac{c}{\lambda}$ .
Substitute the known values into the rearranged formula: $f = \frac{3.00 \times 10^8 \text{ m s}^{-1}}{550 \times 10^{-9} \text{ m}}$ .
Calculate the result: $f = 5.4545... \times 10^{14} \text{ Hz}$ .
State the final answer to an appropriate number of significant figures (3 s.f. to match the data) and with the correct unit: The frequency of the green light is $5.45 \times 10^{14} \text{ Hz} $.$

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