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Difficulty: EasyElectromagnetic Waves and Electromagnetic Spectrum

An optical communication sensor operates using an electromagnetic wave with a frequency of 1.5×1014 Hz1.5 \times 10^{14}\text{ Hz} in a vacuum. Given that the speed of light in vacuum is 3.0×108 m/s3.0 \times 10^8\text{ m/s}, what is the wavelength of this electromagnetic radiation?

  1. 2.0×10−6 m2.0 \times 10^{-6}\text{ m}Answer
  2. B
    5.0×105 m5.0 \times 10^5\text{ m}
  3. C
    4.5×1022 m4.5 \times 10^{22}\text{ m}
  4. D
    2.0×10−7 m2.0 \times 10^{-7}\text{ m}

Answer

The wavelength of the electromagnetic wave is 2.0×10−6 m2.0 \times 10^{-6}\text{ m}.
Using the electromagnetic wave relation c=fλc = f\lambda, dividing the speed of light (3.0×108 m/s3.0 \times 10^8\text{ m/s}) by the given frequency (1.5×1014 Hz1.5 \times 10^{14}\text{ Hz}) correctly gives 2.0×10−6 m2.0 \times 10^{-6}\text{ m}.

Step-by-Step Solution

1
Identify given quantities and formula
Speed of light c=3.0×108 m/sc = 3.0 \times 10^8\text{ m/s}, frequency f=1.5×1014 Hzf = 1.5 \times 10^{14}\text{ Hz}, wave equation c=fλc = f \lambda
The fundamental wave equation relates wave speed, frequency, and wavelength for all electromagnetic waves.
2
Rearrange formula to solve for wavelength λ\lambda
\(\lambda = \frac{c}{f}\)
Isolating the target unknown variable allows direct calculation.
3
Substitute values and compute
\(\lambda = \frac{3.0 \times 10^8}{1.5 \times 10^{14}} = 2.0 \times 10^{-6}\text{ m}\)
Dividing the coefficients (3.0/1.5=2.03.0 / 1.5 = 2.0) and subtracting the powers of ten (8−14=−68 - 14 = -6) yields the accurate wavelength.

Key Concept

Wave Equation for Electromagnetic Waves
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Topics

Electromagnetic Waves and Electromagnetic Spectrum

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