What is the correct method for finding the lattice constant of NaCl?

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Homework Statement

NaCl is a simple cubic lattice, with the Na and Cl atoms alternating positions. Assuming that the atoms are hard spheres with nearest neighbors touching, what is the lattice constant of NaCl? (The effective radius of Na is 1.0 angstroms, and the effective radius of Cl is 1.8 angstroms.)

Homework Equations

lattice constant = 2 * radius

=> a = 2r

The Attempt at a Solution

I did a = 2 (r₁ + r₂) = 2(1.0 + 1.8) = 5.6 angstroms. I've googled the lattice constant of NaCl to be 5.65 angstroms.

However, my solutions manual says that a = r₁ + r₂ = 1.0 + 1.8 = 2.8 angstroms is the correct answer.

I thought that the lattice constant is equal to the complete distance of the two atoms, from one end to the other, so that means 2r.

I'm wondering which answer is correct and why?

 

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Please help, I actually lost a little sleep last night trying to figure this out.

I asked my professor and he didn't give me a straight answer on whether my method of thinking is correct or not. However, my impression from his response was my method was correct but on second thought, I'm having doubts.