What Is the Correct Debye Temperature Calculation for Gold?

[Spring lady]

Homework Statement

Calculate the Debye temperature for gold

Homework Equations

$$Θ_D = \hbar \frac{v_s}{k_b} \sqrt[3]{6π^2 \frac{N}{V}}$$
Speed of sound in gold: $$v_s=3240 m/s$$

The Attempt at a Solution

I used the equation for Θ_D and for the concentration I used the value for atom density that I calculated for gold 5.9*10^28m^-3. I also checked this atom density for gold on the internet and I found the same value. However, I got that the Debye temperature for gold is 375.52 K and a tabular value for gold is 165 K.

Can someone please tell me where I made the mistake in my calculation and these formulas?

 

[SteamKing]

Homework Statement

Calculate the Debye temperature for gold

Homework Equations

$$Θ_D = \hbar \frac{v_s}{k_b} \sqrt[3]{6π^2 \frac{N}{V}}$$
Speed of sound in gold: $$v_s=3240 m/s$$

The Attempt at a Solution

I used the equation for Θ_D and for the concentration I used the value for atom density that I calculated for gold 5.9*10^28m^-3. I also checked this atom density for gold on the internet and I found the same value. However, I got that the Debye temperature for gold is 375.52 K and a tabular value for gold is 165 K.

Can someone please tell me where I made the mistake in my calculation and these formulas?

We can't tell you where you made a mistake in your calculations unless you post them.

 

[Spring lady]

I posted all relevant values and constants. The calculation is very simple, I just typed all these constants in a calculator. I checked everything and I repeated this many times, but I got the same value. I thought that maybe I used the wrong formula or the wrong values for the speed of sound and N/V. Can someone please tell me if these parameters and formula are correct at all?