The wavelength of the light wave:
The given wavelength is 6×10-7 nm. To calculate the wave number and frequency of the light wave, we first need to convert the wavelength from nanometers (nm) to meters (m).

1 nm = 10-9 m

So, the wavelength in meters is:
6×10-7 nm × 10-9 m/nm = 6×10-16 m

The wave number:
The wave number (k) is defined as the number of wavelengths per unit distance. It is the reciprocal of the wavelength and is expressed in units of reciprocal meters (m-1).

Wave number (k) = 1 / wavelength (λ)

In this case, the wave number is:
k = 1 / (6×10-16 m) = 1.67×1015 m-1

The frequency:
The frequency (ν) of a light wave is the number of complete wavelengths that pass a point in one second. It is measured in units of hertz (Hz).

The speed of light (c) in a vacuum is approximately 3×108 m/s.

The frequency of a light wave is related to its wavelength and speed by the equation:
c = λν

Rearranging the equation to solve for frequency, we get:
ν = c / λ

Substituting the values, we have:
ν = (3×108 m/s) / (6×10-16 m) = 5×1014 Hz

Summary:
- The wave number of the light wave is 1.67×1015 m-1.
- The frequency of the light wave is 5×1014 Hz.

Visually appealing content:
Wavelength:
- Given wavelength: 6×10-7 nm
- Convert nm to m: 6×10-7 nm × 10-9 m/nm = 6×10-16 m

Wave number:
- Wave number (k) = 1 / wavelength (λ)
- k = 1 / (6×10-16 m) = 1.67×1015 m-1

Frequency:
- Speed of light (c) in a vacuum: 3×108 m/s
- Frequency (ν) = c / λ
- ν = (3×108 m/s) / (6×10-16 m) = 5×1014 Hz

Summary:
- Wave number: 1.67×1015 m-1
- Frequency: 5×1014 Hz