Calculate the wavelength of the yellow light emitted by a sodium lamp if the frequency of the radiation is 5.09 × 1014 Hz (5.09 × 10141/s).

Taking into account the definition of wavelength, frecuency and propagation speed, the wavelength of the yellow light is 5.89×10⁻⁷ m.

Wavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length (m).

Frequency is the number of vibrations that occur in a unit of time. Its unit is s⁻¹ or hertz (Hz).

The propagation speed is the speed with which the wave propagates in the medium, that is, it is the magnitude that measures the speed at which the wave disturbance propagates along its displacement.

The propagation speed relate the wavelength (λ) and the frequency (f) inversely proportional using the following equation:

v = f * λ

All electromagnetic waves propagate in a vacuum at a constant speed of  3x10⁸ m/s, the speed of light.

In this case, you know:

Replacing:

3x10⁸ m / s= 5.09×10¹⁴ Hz× λ

Solving:

λ= 3×10⁸ m/s ÷ 5.09×10¹⁴ Hz

λ=5.89×10⁻⁷ m

In summary, the wavelength of the yellow light is 5.89×10⁻⁷ m.

Learn more:  

λ = 0.58×10⁻⁶ m

Explanation:

Given data:

Wavelength of yellow light = ?

Frequency of yellow light = 5.09 ×10¹⁴ s⁻¹

Solution:

Formula:

Speed of light = frequency  ×   wavelength

Speed of light = 3×10⁸ m/s

by putting values,

3×10⁸ m/s = 5.09 ×10¹⁴ s⁻¹  × λ

λ = 3×10⁸ m/s / 5.09 ×10¹⁴ s⁻¹

λ = 0.58×10⁻⁶ m