Let us assume that we are considering Germanium.

How can I find the lattice constant?

I have seen that there are different formulas for space lattice depending on the case FCC (face-centred cubic), BCC (body-centred cubic) and SC (simple cubic) ... but I don't know how to proceed.

 

Using an online search would be my first choice. There does not appear to be universal agreement on a precise value. Something in the range of 3-6 Angstroms appears to be common.

 

Every source I found said 5.66.

 

Every source I found said 5.66.

I'm not surprised. Here was the low value

https://www.bartleby.com/questions-...oms-per-/bfd9ce51-6a66-4a64-aaab-3fdb9df82aed

 

I suspect that question purposely misstated it stymie those who looked up the answer.

 

I suspect that question purposely misstated it stymie those who looked up the answer.

I did consult more than one source, but I did not take a deeper dive. In the days before the internet, we had the CRC handbook to refer to. I lost mine in one of my moves.

 

I'm not surprised. Here was the low value

https://www.bartleby.com/questions-...oms-per-/bfd9ce51-6a66-4a64-aaab-3fdb9df82aed

The assigned exercise asks you to find the lattice constant and the distribution of electrons in the orbital of the assigned element.
On the second point there is no problem, but on the first there is still some doubt.

Perhaps the two data are related and one is used to find the other?