Given light with frequencies of: 5.5 x 1014 Hz, 7 x 1014 Hz and 8 x 1014 Hz, calculate the wavelengths in free space. What color are these waves?

The relation between frequency and wavelength is shown below as:

c = frequency * Wavelength

Where, c is the speed of light having value = 3*10⁸ m/s

So, Wavelength is:

Wavelength = c / Frequency

Given:

Frequency = 5.5 * 10¹⁴ Hz

So,

Wavelength = 3*10⁸ m/s / 5.5 * 10¹⁴ Hz = 545 * 10⁻⁹ m = 545 nm (1 nm = 10⁻⁹ m)

This wavelength corresponds to green color.

Frequency = 7 * 10¹⁴ Hz

So,

Wavelength = 3*10⁸ m/s / 7 * 10¹⁴ Hz = 428 * 10⁻⁹ m = 428 nm (1 nm = 10⁻⁹ m)

This wavelength corresponds to Violet color.

Frequency = 8 * 10¹⁴ Hz

So,

Wavelength = 3*10⁸ m/s / 8 * 10¹⁴ Hz = 375 * 10⁻⁹ m = 375 nm (1 nm = 10⁻⁹ m)

It does not fall in visible region. So no color. It is in UV region.