Multiple Choice
Which type of electromagnetic radiation has the shortest wavelengths?
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9. Quantum Mechanics
Wavelength and Frequency
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A wave has a frequency of 6.0 × 10^{14} Hz and travels at the speed of light (3.0 × 10^{8} m/s). What is the wavelength λ of this wave?
A
1.8 × 10^{-8} m
B
2.0 × 10^{-6} m
C
3.0 × 10^{6} m
D
5.0 × 10^{-7} m
Verified step by step guidance1
Identify the given quantities: frequency \(f = 6.0 \times 10^{14}\) Hz and speed of light \(v = 3.0 \times 10^{8}\) m/s.
Recall the relationship between the speed of a wave, its frequency, and its wavelength: \(v = f \times \lambda\), where \(\lambda\) is the wavelength.
Rearrange the formula to solve for the wavelength: \(\lambda = \frac{v}{f}\).
Substitute the known values into the equation: \(\lambda = \frac{3.0 \times 10^{8} \text{ m/s}}{6.0 \times 10^{14} \text{ Hz}}\).
Perform the division of the coefficients and subtract the exponents in the powers of ten to find the wavelength \(\lambda\).
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