What Is the Wavelength of the Earth According to De Broglie's Equation?

[96hicksy]

So I was reading about De Broglie's theory of particle-wave duality the other day and I came across the equation: λ=h/p. I expect most of you are familiar with this equation but if you're not, it is: wavelength = Planck's length over momentum (mass x velocity).

So I thought i'd try and find the Earth's wavelength.

So first I found out what I would have to do to find p, which is (5.9742x10²⁴kg * (approx) 3x10⁴ m/s).

So... 6.626x10^-34/(5.9742x10²⁴kg * (approx) 3x10⁴ m/s)

This is equal to... 3.697×10^-63 meters.

When I first saw that, I was mind blown. Will someone explain why it's wavelength is that small?

Thanks, Ben - I'm unsure of this because well, I'm quite young (15).

 

[Rimantas B.]

The question should not be why the wavelength is small (the numbers simply make it so), the question should be what it means.
And such small a wavelength means that the Earth (if we consider it as a monolithic ball) is highly unlikely to exhibit any wave-like properties (to interfere, diffract, etc.) and is much more particle-like than wave-like.

By the way, it is nice to hear of someone who managed to find out about and become interested in De Broiglie's waves at the age of 15. Cheers!

Oh, and h is not Planck's length, it is Planck's constant. You got the number correct, though. Planck's length is a related but different thing.

 

[sophiecentaur]

No need to worry too much about this. The de Broglie wavelength only starts to show itself for small objects (particles), which really do tend to get bent round corners when they go through a narrow slot. You can spend a lot of time watching people walk through a doorway, waiting for them to be diffracted. It ain't going to happen to any measurable degree

 

[96hicksy]

Thanks guys! Slight confusion on Plancks constant, so sorry for that!

 

[pmacias]

Hi Ben,

Thank you for sharing your thoughts and calculations on finding the wavelength of the Earth using De Broglie's equation. It's great to see young scientists like yourself exploring and questioning scientific concepts.

First, I want to clarify that the equation you mentioned, λ=h/p, is actually the De Broglie wavelength of a particle, not the Earth. This equation is used to calculate the wavelength of any object with mass and momentum, including subatomic particles like electrons and protons. It is based on the idea that all particles, including matter, can exhibit wave-like behavior.

Now, to answer your question about why the Earth's calculated wavelength is so small, it is because the Earth has a very large mass and a relatively slow velocity (compared to subatomic particles). In the equation, momentum (p) is directly proportional to mass and velocity, so the larger the mass and slower the velocity, the smaller the momentum. This results in a very small wavelength, as you have calculated.

It's important to note that the De Broglie wavelength is a theoretical concept and it is not something that can be physically measured or observed for macroscopic objects like the Earth. It is mainly used in quantum mechanics to describe the wave-like behavior of particles at the atomic and subatomic level.

I hope this helps to clarify your question. Keep up your curiosity and enthusiasm for science!