객관식
Which of the following types of electromagnetic radiation has the shortest wavelength?
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9. Quantum Mechanics
Wavelength and Frequency
객관식
Which of the following best describes the relationship between the frequency (ν) and wavelength (λ) of electromagnetic radiation?
A
They are directly proportional; as frequency increases, wavelength also increases.
B
They are inversely proportional; as frequency increases, wavelength decreases.
C
They are both constant for all types of electromagnetic radiation.
D
They are unrelated; frequency and wavelength change independently.
검증된 단계별 안내1
Recall the fundamental relationship between the speed of light (c), frequency (\(\nu\)), and wavelength (\(\lambda\)) of electromagnetic radiation, which is given by the equation:
\[ c = \nu \times \lambda \]
Understand that the speed of light (c) is a constant in a vacuum, approximately \(3.00 \times 10^{8} \text{ m/s} \), meaning it does not change for different types of electromagnetic waves.
Since \( c \) is constant, if the frequency (\(\nu\)) increases, the wavelength (\(\lambda\)) must decrease to keep the product \( \nu \times \lambda \) equal to \( c \). This shows an inverse relationship between frequency and wavelength.
Express the inverse proportionality explicitly by rearranging the equation:
\[ \lambda = \frac{c}{\nu} \]
This formula shows that wavelength is inversely proportional to frequency.
Conclude that as frequency increases, wavelength decreases, and vice versa, which means frequency and wavelength are inversely proportional.
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