Wavelength - differences in equations

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In summary, the Rydberg formula is used to calculate the wavelength of UV light coming out from a hydrogen atom. The Rydberg formula is different than the lambda formula because it takes into account the mass of the electron.
  • #1
The_ArtofScience
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Hi

If I wanted to find a wavelength of electrons having an average speed of 1.7e+8, would use lamdba = h/ mv or lamdba = hc/ E? I noticed that the 2nd eq is used mostly for transition states when an electron either falls or jumps from its n shell. What's the major difference?

Thanks in advance
 
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  • #2
In the beginning of 20th century the interplay of special relativity of Einstein and the photon quantization hypothesis of Planck (that light is emitted or absorbed in parcels of energy E = h nu, called photons) lead to the formula

lambda = h / p

applicable to photons. Around 1922 de Broglie guessed that material particles like electrons may also have a wave associated with them so he postulated the same exact formula applies to electrons and other material particles.

The moment of the mass zero relativistic photons is p = E/c which leads to lamdba = hc/ E.
The moment of non-relativistic electrons is p = mv, leading to lamdba = h/mv.

Your two formulas are just two particular cases of the same master formula.
 
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  • #3
The_ArtofScience said:
If I wanted to find a wavelength of electrons having an average speed of 1.7e+8,

I assume the speed is in m/sec.

would use lamdba = h/ mv or lamdba = hc/ E?

Neither one. The correct starting point for the wavelength is [itex]\lambda = h / p[/itex] where p is the momentum of the particle.

[itex]\lambda = h/mv[/itex] uses the non-relativistic momentum [itex]p=mv[/itex] instead of the relativistic momentum [itex]p = mv / \sqrt {1 - v^2/c^2}[/itex]. Your speed is more than half the speed of light, so it makes a significant difference.

[tex]\lambda = hc/E[/itex] applies only to massless particles like photons, for which [itex]E = pc[/itex], that is, [itex]p = E/c[/itex].
 
  • #4
Thanks guys

I'm also wondering about what electron transitions correspond to a UV light coming out from a hydrogen atom. How do I calculate that? And how do I differentiate that from the visible light?
 

Related to Wavelength - differences in equations

1. What is the equation for calculating wavelength?

The equation for calculating wavelength is λ = c/f, where λ represents wavelength, c represents the speed of light, and f represents frequency.

2. How does wavelength differ from frequency?

Wavelength and frequency are inversely proportional - as wavelength increases, frequency decreases, and vice versa. Wavelength is a measure of the distance between two consecutive points on a wave, whereas frequency is a measure of the number of waves that pass a given point in a second.

3. Can the wavelength of a wave change?

Yes, the wavelength of a wave can change when it moves from one medium to another. This phenomenon is known as refraction. Additionally, the wavelength of a wave can also change if the source of the wave is moving relative to the observer.

4. What is the relationship between wavelength and energy?

The energy of a wave is directly proportional to its frequency. This means that as wavelength increases, energy decreases, and vice versa. This relationship is expressed by the equation E = hf, where E represents energy, h represents Planck's constant, and f represents frequency.

5. How is wavelength measured?

Wavelength is typically measured in meters (m) or nanometers (nm). Nanometers are often used to measure the wavelength of electromagnetic waves, such as light, while meters are used for larger waves, such as sound waves.

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