What is the frequency of an orange light with a wavelength of [tex]$6.3 \times 10^{-7} m$[/tex]? Give your answer in proper scientific notation. [tex]
\begin{array}{c}
{[?] \times 10^{[?]} Hz} \\
c=3.0 \times 10^8 m / s
\end{array}
[/tex] Enter the coefficient in the green box and the exponent in the yellow box.
Answer (1)
Use the formula c = λ f to relate the speed of light, wavelength, and frequency.
Solve for the frequency: f = λ c .
Substitute the given values: f = 6.3 × 1 0 − 7 m 3.0 × 1 0 8 m / s .
Calculate the frequency and express it in scientific notation: f = 4.76190476 × 1 0 14 Hz . The final answer is 4.8 × 1 0 14 Hz .
Explanation
Problem Analysis We are given the wavelength of orange light, λ = 6.3 × 1 0 − 7 m , and the speed of light, c = 3.0 × 1 0 8 m / s . We need to find the frequency, f , of the orange light.
Relating Speed, Wavelength, and Frequency The relationship between the speed of light, wavelength, and frequency is given by the formula: c = λ f
Solving for Frequency We can solve for the frequency by rearranging the formula: f = λ c
Substituting Values Now, we substitute the given values into the formula: f = 6.3 × 1 0 − 7 m 3.0 × 1 0 8 m / s
Calculating Frequency Calculating the frequency: f = 6.3 3.0 × 1 0 − 7 1 0 8 Hz f = 0.476190476 × 1 0 8 + 7 Hz f = 0.476190476 × 1 0 15 Hz
Expressing in Scientific Notation To express the frequency in proper scientific notation, we need to have the coefficient between 1 and 10. So, we rewrite the frequency as: f = 4.76190476 × 1 0 14 Hz
Final Answer Therefore, the frequency of the orange light is approximately 4.8 × 1 0 14 Hz .
Examples
Understanding the frequency of light is crucial in many real-world applications. For example, in telecommunications, different frequencies of light are used to transmit data through fiber optic cables. Also, in medical imaging, the frequency of light is used in various diagnostic techniques such as fluorescence microscopy. The relationship between frequency and wavelength is also fundamental in understanding the electromagnetic spectrum, which includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
