How many gold atoms would have to be lined up to span 6.5mm

In the tables you can find that the empirical radius of a gold atom is 135 pm.

That is 135*10^-12 m.

Then the diameter is two times that: 270*10^-12 m.

Now calculate how many times that is 6.5 mm = 6.5*10^-3 m

=> (6.5*10^-3 m) / (270*10^-12 m) = 24,074,074.

Answer: 24,074,074