Question

what is the frequency of light having a wavelength of 731 nm?
what is the wavelength (in nm) of radiation having a frequency of 1.97 × 10^9 hz? (this radiation is in the microwave region.)
round each of your answers to 3 significant digits.
part 1 of 2
frequency of light: 4.10 × 10^14 hz
part 2 of 2
wavelength of radiation: nm
try again
start over

Explanation:

Part 1 of 2: Calculate the frequency of light with wavelength \( \lambda = 731\space nm\)

Step 1: Convert wavelength to meters

The speed of light \( c = 3\times10^{8}\space m/s\). We know that \( 1\space nm=1\times 10^{-9}\space m\), so \( \lambda = 731\times10^{-9}\space m\)

Step 2: Use the formula \( c=\lambda

u\) (where \( c\) is the speed of light, \( \lambda\) is the wavelength and \(
u\) is the frequency)
Rearrange for \(
u\): \(
u=\frac{c}{\lambda}\)
Substitute \( c = 3\times 10^{8}\space m/s\) and \( \lambda=731\times 10^{-9}\space m\)
\(
u=\frac{3\times 10^{8}}{731\times 10^{-9}}=\frac{3}{731}\times10^{17}\)
\(
u\approx4.10\times 10^{14}\space Hz\)

Part 2 of 2: Calculate the wavelength of radiation with frequency \(

u = 1.97\times 10^{9}\space Hz\)

Step 1: Use the formula \( c = \lambda

u\)
Rearrange for \( \lambda\): \( \lambda=\frac{c}{
u}\)

Step 2: Substitute \( c = 3\times 10^{8}\space m/s\) and \(

u=1.97\times 10^{9}\space Hz\)
\( \lambda=\frac{3\times 10^{8}}{1.97\times 10^{9}}=\frac{3}{1.97}\times10^{-1}\)
\( \lambda\approx0.152\space m\)
Convert to \( nm\): \( 0.152\space m = 0.152\times10^{9}\space nm=1.52\times 10^{8}\space nm\)

Answer:

• Part 1: The frequency of light with wavelength \(731\space nm\) is \(4.10\times 10^{14}\space Hz\)
• Part 2: The wavelength of radiation with frequency \(1.97\times 10^{9}\space Hz\) is \(1.52\times 10^{8}\space nm\)