De Broglie Wavelength: Homework Question Solution

In summary, the conversation discusses solving a mathematical equation and finding the correct answer by understanding the proper steps and units to use. The individual initially struggles with finding the correct answer but eventually realizes their mistake and is able to solve the problem correctly.
  • #1
robertjford80
388
0

Homework Statement



Screenshot2012-06-10at84946PM.png




The Attempt at a Solution



I don't see how they got sqrt(1.5/E) I tried it like this

Screenshot2012-06-10at84925PM.png


Not the right answer.
 
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  • #2
robertjford80 said:

Homework Statement



Screenshot2012-06-10at84946PM.png

The Attempt at a Solution



I don't see how they got sqrt(1.5/E) I tried it like this

Screenshot2012-06-10at84925PM.png


Not the right answer.

It looks like you took the square root of h/(√2m) when you should have done the exact opposite: you should have squared it. Here's the reason. If:$$\sqrt{1.5} = \frac{h}{\sqrt{2m}}$$then$$1.5 = \frac{h^2}{2m}$$

I computed h^2/(2mE), and I plugged in a value of E = 1 so that I would get the same numerical answer as they did. I also had Google express it in nm^2 instead of m^2, so that the answer would be the same as theirs:

Google Calculator link
 
  • #3
cool, i got it now.
 

What is the De Broglie wavelength?

The De Broglie wavelength is a concept in quantum mechanics that describes the wavelength of a particle, such as an electron, based on its momentum. It is named after French physicist Louis de Broglie.

How is the De Broglie wavelength calculated?

The De Broglie wavelength is calculated using the formula λ = h / p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle.

What is the significance of the De Broglie wavelength?

The De Broglie wavelength is significant because it shows that particles, such as electrons, have both wave-like and particle-like properties. This helped to shape our understanding of quantum mechanics and the behavior of subatomic particles.

What factors affect the De Broglie wavelength?

The De Broglie wavelength is affected by the mass and velocity of the particle. As the mass increases, the wavelength decreases, and as the velocity increases, the wavelength also decreases.

How is the De Broglie wavelength related to the uncertainty principle?

The De Broglie wavelength is related to the uncertainty principle, which states that the more precisely we know the momentum of a particle, the less precisely we can know its position. This is because measuring the momentum of a particle requires interacting with it, which can change its position. The De Broglie wavelength is a manifestation of this principle.

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