Question

For light with a wavelength of 3.30 μm, calculate the corresponding wavenumber value.

Answer 1

To calculate the wavenumber for a 3.30 μm wavelength of light, first convert the wavelength to meters and then use the formula Wavenumber = 1 / Wavelength to get
`3.03 x 10^5 \ m^-^1`.

Step-by-step explanation:

To calculate the corresponding wavenumber value for light with a wavelength of 3.30 μm, you can use the formula for wavenumber:

Wavenumber
`(\( \\u \))` =
`1 / Wavelength (\( \lambda \))`

The wavelength needs to be in meters for standard units, so first convert 3.30 μm (micrometers) to meters:

3.30 μm =
`3.30 x 10^-^6 m`

Now use the formula to find the wavenumber:

`\( \\u \) = 1 / (3.30 x 10^-^6 m)`

=
`3.03 x 10^5 \ m^-^1`

The wavenumber of light with a wavelength of 3.30 μm is
`3.03 x 10^5 \ m^-^1` (meters inverse).