Light having a wavelength of [tex]450 nm(4.50 \times 10^{-7} m)[/tex] moves through space at [tex]3.0 \times 10^8 m / s[/tex]. What is the frequency of the light?
A. [tex]6.67 \times 10^{14} Hz[/tex]
B. [tex]1.50 \times 10^{-15} Hz[/tex]
C. [tex]7.41 \times 10^{-3} Hz[/tex]
Answer (1)
The problem provides the wavelength and speed of light and asks for the frequency.
The relationship between speed, wavelength, and frequency is c = λ f .
Solving for frequency gives f = λ c .
Substituting the given values, the frequency is 6.67 × 1 0 14 Hz .
Explanation
Understanding the Problem We are given the wavelength of light, λ = 450 nm = 4.50 × 1 0 − 7 m , and the speed of light, c = 3.0 × 1 0 8 m/s . We need to find the frequency of the light.
Stating the Formula The relationship between the speed of light, wavelength, and frequency is given by the formula: c = λ f where:
c is the speed of light,
λ is the wavelength,
f is the frequency.
Solving for Frequency We need to solve for the frequency f . Rearranging the formula, we get: f = λ c
Calculating the Frequency Now, we substitute the given values into the formula: f = 4.50 × 1 0 − 7 m 3.0 × 1 0 8 m/s f = 4.50 3.0 × 1 0 8 + 7 Hz f = 3 2 × 1 0 15 Hz f ≈ 0.6667 × 1 0 15 Hz f ≈ 6.67 × 1 0 14 Hz
Final Answer The frequency of the light is approximately 6.67 × 1 0 14 Hz . Therefore, the correct answer is A.
Examples
Understanding the frequency of light is crucial in various applications, such as telecommunications, medical imaging, and astronomy. For instance, in telecommunications, different frequencies of light are used to transmit data wirelessly. In medical imaging, X-rays, which are high-frequency electromagnetic waves, are used to create images of the inside of the human body. In astronomy, analyzing the frequency of light emitted by stars and galaxies helps us understand their composition, distance, and motion. Knowing how to calculate frequency from wavelength and speed is a fundamental skill in these fields.
