= Solution
\b[The 020 reflection is extinguished by the diamond basis, even though it satisfies the face-centered lattice parity rule.] Write the diamond structure as an FCC lattice with identical atoms at basis positions $(0,0,0)$ and $(1/4,1/4,1/4)$.
The <structure factor> separates into lattice and basis terms:
$$
F_{hkl}=f\left[1+(-1)^{h+k}+(-1)^{h+l}+(-1)^{k+l}\right]
\left[1+e^{i\pi(h+k+l)/2}\right].
$$
At $(h,k,l)=(0,2,0)$, all indices are even, so the first bracket is $4$. The second bracket is $1+e^{i\pi}=0$. The two identical sublattices scatter with opposite phases and cancel:
$$
\boxed{F_{020}=0,\qquad I_{020}\propto|F_{020}|^2=0.}
$$
For all-even reflections of diamond, the additional allowed condition is $h+k+l$ divisible by four. This is a <systematic absence>, not an absence of the corresponding family of geometrical planes.
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