Questions: Calculate the frequency of the red light emitted by a neon sign with a wavelength of 710 nm. 4.10 x 10^14 s^-1 5.05 x 10^14 s^-1 4.26 x 10^14 s^-1 2.30 x 10^14 s^-1 3.40 x 10^14 s^-1

Calculate the frequency of the red light emitted by a neon sign with a wavelength of 710 nm.
4.10 x 10^14 s^-1
5.05 x 10^14 s^-1
4.26 x 10^14 s^-1
2.30 x 10^14 s^-1
3.40 x 10^14 s^-1

Transcript text: Calculate the frequency of the red light emitted by a neon sign with a wavelength of 710 nm. $4.10 \times 10^{14} \mathrm{~s}^{-1}$ $5.05 \times 10^{14} \mathrm{~s}^{-1}$ $4.26 \times 10^{14} \mathrm{~s}^{-1}$ $2.30 \times 10^{14} \mathrm{~s}^{-1}$ $3.40 \times 10^{14} \mathrm{~s}^{-1}$

Solution

Solution Steps

Step 1: Understand the Relationship Between Wavelength and Frequency

The frequency ($ f $) of light is related to its wavelength ($ \lambda $) and the speed of light ($ c $) by the equation: \[ f = \frac{c}{\lambda} \] where $ c = 3.00 \times 10^8 \, \text{m/s} $.

Step 2: Convert Wavelength to Meters

The given wavelength is 710 nm. Convert this to meters: \[ 710 \, \text{nm} = 710 \times 10^{-9} \, \text{m} \]

Step 3: Calculate the Frequency

Substitute the values into the frequency equation: \[ f = \frac{3.00 \times 10^8 \, \text{m/s}}{710 \times 10^{-9} \, \text{m}} \] \[ f = \frac{3.00 \times 10^8}{710 \times 10^{-9}} \] \[ f \approx 4.2254 \times 10^{14} \, \text{s}^{-1} \]

Step 4: Match the Calculated Frequency to the Given Options

The calculated frequency $ 4.2254 \times 10^{14} \, \text{s}^{-1} $ is closest to the option $ 4.26 \times 10^{14} \, \text{s}^{-1} $.