An emission ray has a frequency of 5.10 * 10¹Ê Hz. Given that the speed of light is 2.998 * 10§ m/s, what is the wavelength of the ray?

The answer is 5.88 · 10⁻⁷ m.

To calculate this we will use the light equation:

v = λ · f,

where:

v - the speed of light (units: m/s)

λ - the wavelength of the ray (units: m)

f - the frequency of the ray (units: Hz = 1/s since Hz means cycles per second (f=1/T))

It is given:

f = 5.10 · 10¹⁴ Hz = 5.10 · 10¹⁴ 1/s

v = 2.998 · 10⁸ m/s

λ = ?

If v = λ · f, then λ = v : f:

λ = 2.998 · 10⁸ m/s : 5.10 · 10¹⁴ 1/s

= 0.588 · 10⁸⁻¹⁴ · m

= 0.588 · 10⁻⁶ m

= 5.88 · 10⁻⁷ m