Why Is My Calculated Debye Temperature for Sodium Higher Than Literature Values?

[MMS]

Homework Statement

Na has a bcc structure with molecular mass of 22.99 gr/mol, mass density of 0.971 gr/cm^3.
The average speed of sound in Na (at room temperature=300K) is 3200 m/s.
Calculate the Debye temperature for Na

Homework Equations

I worked out this equation to calculate the Debye temperature (If needed I can show how)

The Attempt at a Solution

I plugged in all the numbers in the above equation with the correct units and I get that the Debye temperature is 280.3K. However, in literature I found that it is approximately 150K.
Is there something wrong with my calculations? Am I missing out on something here?

Thank you!

 

[SteamKing]

Homework Statement

Na has a bcc structure with molecular mass of 22.99 gr/mol, mass density of 0.971 gr/cm^3.
The average speed of sound in Na (at room temperature=300K) is 3200 m/s.
Calculate the Debye temperature for Na

Homework Equations

I worked out this equation to calculate the Debye temperature (If needed I can show how)

The Attempt at a Solution

I plugged in all the numbers in the above equation with the correct units and I get that the Debye temperature is 280.3K. However, in literature I found that it is approximately 150K.
Is there something wrong with my calculations? Am I missing out on something here?

Thank you!

Please provide your calculations.

 

[MMS]

Please provide your calculations.

 

[SteamKing]

No, I meant your numbers.

 

[MMS]

No, I meant your numbers.

 

[MMS]

Anyone?

 

[SteamKing]

Anyone?

Your calculations are arithmetically correct, as far as I can see.

It's not clear that N_A ⋅ ρ / MW is an accurate substitute for the N / V which is used in other Debye Temperature derivations I have seen. Your expression doesn't seem to account for the fact that since sodium is bcc, there are two atoms per cell, rather than one. It makes a difference in calculating the edge length of the cell.

I think for calculating a reasonable approximation to the Debye Temp., this is the issue which must be resolved. In some articles I have seen, the authors try to use the properties of the material measured close to the Debye Temp., like the speed of sound and the density, to come up with a more accurate calculation.