The drawing shows sodium and chloride ions positioned at the corners of a cube that is part of the crystal structure of sodium chloride (common table salt). the edges of the cube are each 0.281 nm (1 nm = 1 nanometer = 10−9 m) in length. what is the value of the angle θ the in the drawing?

To solve for this problem, first we have to calculate for the diagonal or the hypotenuse on the bottom face of the cube. We can do this by using the hypotenuse formula. Since all sides are of equal lengths therefore:

c^2 = a^2 + b^2

a = b

c^2 = 2 a^2

where a = 0.281 nm therefore:

c^2 = 2 (0.281 nm)^2

c = 0.3974 nm

Now using the diagonal and the one vertical side of the cube which is still equivalent to a, we use the tan function to find for the angle θ.

tan θ = opposite side / adjacent side

tan θ = a / c

θ = tan^-1 (0.281 / 0.3974)

θ = 35.26°