What is the wavelength (in nm) of the light emitted by a neon sign with a frequency of 4.26×10^14 Hz?
The wavelength (in nm) of the light emitted by a neon sign with a frequency of 4.26 × 10^14 Hz is 704 nm.The given frequency is 4.26 × 10^14 Hz. Speed of light = wavelength × frequencyThe speed of light is a constant, which is 3.0 × 10^8 m/s. We can use this value to calculate the wavelength. We can first convert the frequency to Hz to match the units used for the speed of light. 1 nm = 10^-9 m1 Hz = 1/s = s^-1Wavelength = Speed of light / frequencyWavelength = (3.0 × 10^8 m/s) / (4.26 × 10^14 Hz)Wavelength = 7.04 × 10^-7 mWavelength in nm = (7.04 × 10^-7 m) × (1 nm / 10^-9 m)Wavelength in nm = 704 nmTherefore, the wavelength (in nm) of the light emitted by a neon sign with a frequency of 4.26 × 10^14 Hz is 704 nm.
Understanding Wavelength Calculation
Wavelength Formula:
The wavelength of light can be calculated using the formula:
\[
\text{Wavelength} = \frac{\text{Speed of light}}{\text{Frequency}}
\]
Given Values:
- Frequency = 4.26 × 10^14 Hz
- Speed of light = 3.0 × 10^8 m/s
Calculations:
1. Convert frequency to Hz
\[
1 \, \text{nm} = 10^{-9} \, \text{m}
\]
\[
1 \, \text{Hz} = 1/s = s^{-1}
\]
2. Calculate wavelength in meters
\[
\text{Wavelength} = \frac{3.0 × 10^8 \, \text{m/s}}{4.26 × 10^14 \, \text{Hz}}
\]
\[
\text{Wavelength} = 7.04 × 10^{-7} \, \text{m}
\]
3. Convert wavelength to nanometers
\[
\text{Wavelength in nm} = 7.04 × 10^{-7} \, \text{m} \times \left(\frac{1 \, \text{nm}}{10^{-9} \, \text{m}}\right)
\]
\[
\text{Wavelength in nm} = 704 \, \text{nm}
\]
Conclusion:
Therefore, the wavelength of the light emitted by a neon sign with a frequency of 4.26 × 10^14 Hz is 704 nm. This calculation demonstrates the relationship between frequency, speed of light, and wavelength in determining the properties of light waves.