What frequency corresponds to an absorption line at 460 nm?
A. $6.52 x 10^{14} Hz$
B. $4.32 x 10^{14} Hz$
C. $1.53 x 10^{14} Hz$
D. $6.88 x 10^{14} Hz
Answer (2)
The frequency corresponding to an absorption line at 460 nm is approximately 6.52 × 1 0 14 Hz . This was calculated using the formula f = λ c after converting the wavelength to meters. The selected answer is A. 6.52 × 1 0 14 Hz .
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Convert the wavelength from nm to meters: λ = 460 × 1 0 − 9 m = 4.6 × 1 0 − 7 m .
Use the formula f = λ c to find the frequency.
Substitute the values of c and λ : f = 4.6 × 1 0 − 7 m 3 × 1 0 8 m / s .
Calculate the frequency: f ≈ 6.52 × 1 0 14 Hz . The final answer is 6.52 × 1 0 14 Hz .
Explanation
Understanding the Problem We are given the wavelength of an absorption line, which is 460 nm, and we need to find the corresponding frequency. We know that the speed of light, c , relates frequency, f , and wavelength, λ , by the formula c = λ f . The speed of light is approximately 3 × 1 0 8 m/s.
Converting Wavelength to Meters First, we need to convert the wavelength from nanometers (nm) to meters (m). Since 1 nm = 1 0 − 9 m, we have: λ = 460 nm = 460 × 1 0 − 9 m = 4.6 × 1 0 − 7 m
Finding the Frequency Now, we can use the formula c = λ f to find the frequency f . We rearrange the formula to solve for f :
f = λ c
Substituting Values Substitute the values of c and λ into the formula: f = 4.6 × 1 0 − 7 m 3 × 1 0 8 m/s
Calculating the Frequency Calculate the frequency: f = 4.6 3 × 1 0 8 + 7 Hz = 4.6 3 × 1 0 15 Hz ≈ 0.65217 × 1 0 15 Hz = 6.5217 × 1 0 14 Hz
Selecting the Correct Answer Comparing the calculated frequency with the given options, we find that the closest answer is: A. 6.52 × 1 0 14 Hz
Examples
Understanding the relationship between wavelength and frequency is crucial in various fields. For example, in telecommunications, different frequencies of electromagnetic waves are used to transmit data. Similarly, in medical imaging, X-rays with specific wavelengths are used to visualize bones and tissues. The formula c = λ f helps engineers and scientists determine the appropriate frequencies or wavelengths for their applications, ensuring efficient and safe operation of devices and systems.
