How do you find the de Broglie Wavelength if you only have Temperature and Density?

[MonkeySage]

For a given element, I'm given the temperature of the sample, it's melting point, and the density of the element. I need to determine whether the element can be treated using classical statistics.

I was going to do this by calculating the de Broglie wavelength but I don't have a distance between particles, I don't have mass, and I don't have momentum.

kT= 0.329 eV

Density= 2g/cm3

[gomipile]

Maybe you're supposed to use the information to identify the element? The only two metals that are around that density are Beryllium and Cesium. You didn't provide the melting point, though, even though you said that it was provided to you.

[MonkeySage]

Amorphous carbon, with the melting point at around 3823K.

[gomipile]

Amorphous carbon, with the melting point at around 3823K.

Wait, you were given the element's name, too?

That makes it a lot easier. From that and the other givens, you can look up or derive everything you said you didn't have in the top post.

[MonkeySage]

There's no mass to look up, though... and I don't know of any way to determine the de Broglie Wavelength without mass, let alone determine whether I treat the substance using classical statistics or quantum statistics.

[gomipile]

There's no mass to look up, though...

Well, the average mass is on every periodic table. It comes in 11au, 12au, 13au, and 14au masses, with 12au being the most common by far.

Read literally, your post sounds like you think carbon's mass doesn't exist or isn't recorded anywhere. I'm sure that's not what you meant, though.

[MonkeySage]

I don't mean the mass of carbon. I mean the mass of the material.... like the actual amount of stuff I'm supposed to be working with. How much amorphous carbon. That is not given.

[tyckspoon]

I don't mean the mass of carbon. I mean the mass of the material.... like the actual amount of stuff I'm supposed to be working with. How much amorphous carbon. That is not given.

That would probably spoil the question, if I understand correctly - if you knew you had 2g (or however much) worth of carbon, you'd almost immediately assume you should handle it as a classical material because you have classical quantities of it at classical energies.

(Speaking of energy, I think you're over-thinking the question with the de Broglie thing - you have two values, both of which are related to temperature, and the internet suggests one of them can be converted to the other relatively easily. Maybe take the temperature of the sample, convert it to Kelvin, and see if that suggests anything about your answer? Keeping in mind I don't actually know what the answer is, and the tendency of particle physics to measure friggin' everything in eV hurts my brain.)