What is the frequency of green light
that has a wavelength of 531 nm? (c
= 3.00 x 108 m/s)

We are given:

Wavelength of Green light (λ) = 531 nm  OR   531 * 10⁻⁹ m

Speed of light (c) = 3* 10⁸ m/s

Solving for the Frequency of the wave:

We know the relation:

c = νλ    

(where ν is the frequency, c is the speed of light and λ is the wavelength)

3*10⁸ = ν*(531*10⁻⁹)

ν = 3*10⁸ / 531*10⁻⁹                  [dividing both sides by the wavelength]

ν = 3*10⁸*10⁹ / 531                   [ since a⁻¹ = 1/a]

ν = 3*10¹⁷ / 531                         [ since mᵃ * mᵇ = mᵃ⁺ᵇ]

ν = 10¹⁷ / 177

ν = 1000 * 10¹⁴ / 177                 [we split the numerator to simplify]

ν = 5.65 * 10¹⁴

Hence, the frequency of Green light is 5.65 * 10¹⁴ Hz

f = 5.6×10¹⁴ Hz  

Explanation:

Given data:

Wavelength of green light = 531 nm (531×10⁻⁹ m)

Frequency of green light = ?

Solution:

Formula;

Speed of wave = wavelength × frequency

Speed of wave = 3.00×10⁸ m/s

by putting vales,

3.00×10⁸ m/s = 531×10⁻⁹ m × f

f = 3.00×10⁸ m/s / 531×10⁻⁹ m

f  = 0.0056×10¹⁷ s⁻¹

f = 5.6×10¹⁴ Hz    (Hz = s⁻¹)