Hi, I appear to have lost some mass/density.(adsbygoogle = window.adsbygoogle || []).push({});

Q: Calculate the atom density, n, of aluminium at 600k.

Data given (some of it not relevant to this part of the ? but i'll post it all).

The debye temperature [tex]T_D = 428 K[/tex] . The velocity of sound at room temp, [tex] v = 5100m s^{-1}[/tex]. The interatomic spacing a = 405pm, and its relative atomic mass is 27.

I found the atom density n to be:

[tex] n = (KT_D / \hbar v )^3.(1 / 6\pi^2)[/tex]

I used [tex]{\omega_m}^3 = 6\pi^2 v^3 n[/tex], and the fact [tex]{\omega_m} = K T_D / \hbar[/tex] to get my equations for n.

I assumed the atom density was the same at 600k as at room temperature (the way the question was worded I couldn't see any other method). Plugging the numbers in I found [tex]n = 2.24x10^{28} m^{-3}[/tex].

Then I'm asked to compare the density found with aluminiums true density of [tex]2700 kg m^{-3}[/tex] and explain any difference.

My density is just the atom density multiplied by the atomic mass (assuming the mass is just contained within the aluminium).

Therefore

[tex]/rho = n m(amu) = n = 2.24x10^{28} * (27 / 6.022x10^{26})) = 1000 kg m^{-3}[/tex].

There in lies my problem. I'd expect my approximations to overestimate the density if anything.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Help - Where am I going wrong!

**Physics Forums | Science Articles, Homework Help, Discussion**