Find the Block on the Extended Periodic Table Using the Diagonal Rule
Charcoal, 59 bytes
Ｎθ⊞υ²Ｗ›θ⊗Συ«≧⁻⊗Συθ⊞υ⁺⁴⌈υ»§”&gt;-◧βYTＢ↷p{ï⭆Σ]¬∕↷›”ＬΦυ‹﹪⊖θΣυΣ✂υκ

Try it online! Link is to verbose version of code. Explanation:
Ｎθ

Input the atomic number.
⊞υ²

Start with just an s-shell.
Ｗ›θ⊗Συ«

Repeat while the number of electrons left will fill all the shells twice...
≧⁻⊗Συθ

... remove those electrons, and...
⊞υ⁺⁴⌈υ

... add another shell which can hold 4 more electrons than the previous.
»§”&gt;-◧βYTＢ↷p{ï⭆Σ]¬∕↷›”ＬΦυ‹﹪⊖θΣυΣ✂υκ

Count how many of the remaining shells have no electrons and look that up in the compressed string of block letters. (Because of the way Sum works in Charcoal, the calculation is adjusted slightly to avoid a sum of no elements, which ends up offsetting the result by 1, which is compensated by moving the z to the beginning of the string where it can be cyclically indexed.)