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The distance between two consecutive crests of a wave, especially the points of an electromagnetic wave is known as its wavelength. In physics, wavelength and frequency are a closely associated phenomenon. The greater is the frequency, the lesser is the wavelength. When all the light waves progress through the vacuum at the equivalent speed, the total number of wave crests passing through a single point per second relies on the wavelength.Â

The wavelength equation is expressed by Î» The wavelength formula of a given wave is stated asÂ

Â Î» = v/fÂ

Where,Â

F = frequency

v= velocity of the wave

The unit of wavelength is m, frequency in Hz, and velocity is m/s.Â

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The dimensional formula of wavelength is expressed by the following formula:

[m0 l1 t0]

Where,Â

m= mass

l= length

t= time

Derivation

Wavelength= distance between similar points in adjacent cycles of a waveform

As the dimensional formula of distance is [m0 l1 t0], so, the wavelength formula is dimensionally represented as [m0 l1 t0].

Weinâ€™s law was named after German physicist Wilhelm Wien, who states that objects of different temperature emit spectra that peak at a different wavelength. It further explains that black body radiation has various peaks of temperature at wavelengths that are proportional inversely to temperature.Â

Î» max = b/T

Where,Â

b = Wienâ€™s displacement constant

T =temperature in kelvins

Photon is characterized by an equivalent energy E or by wavelength Î»

The photon energy is found to be inversely proportional to its wavelength.Â

The energy of photon equation:

E= hc/Î»

The wavelength concept is an important chapter of physics that helps us to understand a number of phenomena. Its main application is found in defining concepts of light.Â

FAQ (Frequently Asked Questions)

1. Explain the Wavelength and Frequency Formula?

In any sinusoidal wave, the wavelength is stated as the spatial period of the wave which is the distance over the shape of the wave that repeats itself. Frequency on the other hand defines the number of times a recurring event happens in a second. We are already familiar that sinusoidal waves move at a fixed speed, so the wavelength of the wave is inversely proportional to its frequency.Â Â

The wavelength and frequency formula is expressed asÂ

Speed = Frequency x Wavelength

Wavelength = (Wave Speed)/(Wave Frequency)

The representation of the formula given above can be seen as:

C = f Ă— Î»

In the aspect of wavelength to frequency, it is denoted as,Â

Î» = c/f

2. What is De Broglie Wavelength Equation?

De Broglie wavelength equation states that matter can act as a wave just like radiation and light. Similarly, it can behave as both waves and particles. It also explains concepts where electrons can be diffracted like a beam of light. It helps to shed light on the topic of wavelength.Â

De Broglie wavelength formula is derived from Plankâ€™s quantum theory and Einsteinâ€™s relativity theory.

E= hv = hcâ€¦â€¦â€¦.(i)

E= mc^{2}â€¦â€¦â€¦â€¦..(ii)

Equating both,Â

E= hc= mv^{2}, h= mv, or = hmv

De Broglie wavelength formula = = hmv

3. What is the Rydberg Formula?

The Rydberg formula is a mathematical expression that determines the wavelength of light radiated by an electron travelling between the energy level of two atoms. There is a change of energy when the electron shifts from one atomic orbital to another. When an electron shifts from a high energy orbital to a low energy one, a photon of light is produced. The photon of light is absorbed by the atom when an electron shifts from low energy to a high energy state.Â

The Rydberg formula is applicable to different elements and is expressed as follows:

V = 1/Î» = R( 1/(n_{1}^{2}-n_{2}^{2}) )