Units of the Thermal de Broglie wavelength?

In summary, the Thermal de Broglie wavelength is a concept in quantum mechanics that describes the wavelength of a particle at a given temperature, based on the de Broglie hypothesis. It can be calculated using the formula λ = h/√(2πmkT), with units typically in meters or nanometers. Its significance lies in understanding the wave-particle duality of matter and its role in quantum mechanics, including calculating the probability of finding a particle at a specific location. The Thermal de Broglie wavelength is also inversely proportional to the speed of particles, known as the de Broglie relation.
  • #1
rwooduk
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1. Units of the Thermal de Broglie wavelength?
2. λ = h / (2*pi*mkT)^(.5)
3. through dimensional analysis i get S (J / kg)^.5

can you even have .5 of a unit?
 
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  • #2
Yes, you can have a quantity that has a dimension with a fractional exponent.

However, here, you want to end up with just a unit of length.

Try expressing a Joule in terms of kg, m, and s.
 
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  • #3
Thank you will try that!

and yes its a wavelength so should simply be in meters, what was i thinking, lol

will do the dimensional to confirm anyway, thanks!
 

1. What is the Thermal de Broglie wavelength?

The Thermal de Broglie wavelength is a concept in quantum mechanics that describes the wavelength of a particle at a given temperature. It is based on the de Broglie hypothesis, which states that particles can exhibit wave-like behavior.

2. How is the Thermal de Broglie wavelength calculated?

The Thermal de Broglie wavelength can be calculated using the formula λ = h/√(2πmkT), where h is Planck's constant, m is the mass of the particle, k is the Boltzmann constant, and T is the temperature in Kelvin.

3. What units are used for the Thermal de Broglie wavelength?

The units for the Thermal de Broglie wavelength are typically meters (m) or nanometers (nm), as it represents a physical length. However, it can also be expressed in other units such as Angstroms (Å) or picometers (pm).

4. What is the significance of the Thermal de Broglie wavelength?

The Thermal de Broglie wavelength is significant because it helps us understand the wave-particle duality of matter. It also plays a crucial role in quantum mechanics and can be used to calculate the probability of finding a particle at a particular location.

5. How does the Thermal de Broglie wavelength relate to the speed of particles?

The Thermal de Broglie wavelength is inversely proportional to the speed of particles. This means that as the speed of a particle increases, its wavelength decreases. This relationship is known as the de Broglie relation and is an important concept in quantum mechanics.

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