Question

If the $Z_{eff}$ of cubes a, b and c is x, y and z respectively, find xyz. (For instance if x = 2, y = 3, z = 5, xyz = 235)

a)

b)

c)

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Answer 1

Let's try to get a 3-D understanding of the crystal structure by looking at a different view. You must already have an idea from the videos.

Can you see that the portions depicted here are ${\frac{1}{8}}^{th}$ of a sphere?

Since we have 8 such portions in total, we get

$\frac{1}{8}\ast 8=1$

Similarly for the other 2.

Here we have one full sphere in the middle.

And the remaining is a similar structure to the previous one

So, 1 + $\frac{1}{8}\ast 8=2$

Here, the spheres portions on the faces will contribute 1/2.

And those at the corners will contribute 1/8 again.

So, $\frac{1}{2}\ast 6=3$

And $\frac{1}{8}\ast 8=1$

So total 3 + 1 = 4