Question

Determine the frequency of light whose wavelength is \(4.257 \times 10^{-7} {cm} .\)

Short answer

The frequency of light is approximately \(7.048 \times 10^{16} \text{ Hz}\).

Step-by-step solution

Convert Wavelength to Meters

The wavelength is given in centimeters. Convert it to meters by multiplying by the conversion factor, since 1 cm = 0.01 m.\[ 4.257 \times 10^{-7} \text{ cm} \times \frac{0.01 \text{ m}}{1 \text{ cm}} = 4.257 \times 10^{-9} \text{ m}\]

Use the Speed of Light Formula

The frequency of light can be found using the formula:\[ c = u \times \text{wavelength}\]where:- c is the speed of light (approximately \(3 \times 10^8 \text{ m/s}\))- \( u \) is the frequency- wavelength is the given wavelength in meters

Solve for Frequency

Rearrange the formula to solve for frequency \( u \):\[ u = \frac{c}{\text{wavelength}} \]Plug in the known values:\[ u = \frac{3 \times 10^8 \text{ m/s}}{4.257 \times 10^{-9} \text{ m}}\]Perform the division:\[ u \thickapprox 7.048 \times 10^{16} \text{ Hz}\]

Key concepts

Wavelength Conversion

To calculate the frequency of light, it's essential first to convert the wavelength into meters. This is because standard equations in physics involving speed and light use meters as the unit of distance. In the exercise, the wavelength is given as \(4.257 \times 10^{-7} \text{ cm}\). We need to convert it into meters. Remember that 1 centimeter equals 0.01 meters. Therefore, you multiply the given wavelength by 0.01:

Speed of Light Formula

The speed of light is a constant value that is used in many equations in physics. The standard value used is approximately \(3 \times 10^8 \text{ m/s}\). This speed is denoted by the symbol \( c \). The relationship between the speed of light, its frequency (\( u \)), and its wavelength (\( \text{wavelength} \)) is given by the following equation:
due to this, equations involving speed and light typically use meters as the unit of distance.
\[ c = u \times \text{wavelength} \]

• \( c \) is the speed of light (\(3 \times 10^8 \text{ m/s}\))
• \( u \) is the frequency
• \(\text{wavelength}\) is the final converted wavelength in meters

Frequency Calculation

After converting the wavelength into meters and knowing the speed of light, we can solve for the frequency of light using the formula:
\[ u = \frac{c}{\text{wavelength}} \]
By substituting the known values:
\[ u = \frac{3 \times 10^8 \text{ m/s}}{4.257 \times 10^{-9} \text{ m}} \]
Performing this division will yield the frequency:
\[ u \approx 7.048 \times 10^{16} \text{ Hz} \]
Hence, the frequency of light with a wavelength of \(4.257 \times 10^{-7} \text{ cm}\) is approximately \(7.048 \times 10^{16} \text{ Hz}\).
This calculation demonstrates how understanding the fundamental concepts of wavelength conversion, the speed of light formula, and frequency calculation can easily guide you to find the frequency of any given light.