Character table of point group D₈ is given below Value of (a+b+c+d+e+f+g+h+i+j+k) is equal to ____ · ABC26OR0699

Subject: Organic Chemistry · Chapter: Reagents, Reaction Mechanisms & Named Reactions · Topic: Reagents, Reaction Mechanisms & Named Reactions – General · Exam: GATE 2000-2022 · Marks: 2 · Difficulty: Medium

Character table of point group $\mathrm{D}_{8}$ is given below
$\mathrm{D}_{8}$E$2 \mathrm{C}_{8}$$2 \mathrm{C}_{4}$$2 \mathrm{C}_{8}^{3}$$\mathrm{C}_{2}$$4 \mathrm{C}_{2}^{\prime}$$4 \mathrm{C}_{2}^{\prime \prime}$
$\mathrm{A}_{1}$a111111
$\mathrm{A}_{2}$b1111hi
B ${ }_{1}$c-11-111j
B ${ }_{2}$d-11-11-11
$\mathrm{E}_{1}$e$\sqrt{2}$0$-\sqrt{2}$-200
$\mathrm{E}_{2}$f0-20k00
$\mathrm{E}_{3}$g$-\sqrt{2}$0$\sqrt{2}$-200
Value of $(a+b+c+d+e+f+g+h+i+j+k)$ is equal to ____
Answer
Answer (as printed): 9

The options are missing from the source scan for this question, so there is nothing here for this letter to point at. The letter is what the book printed.

Explanation
Answer: 9 — a = b = c = d = 1 and e = f = g = 2, which sums to 10. Orthogonality gives h = i = −1 (A₂ under C₂′, C₂″), j = −1 (B₁ under C₂″) and k = 2 (E₂ under C₂). 10 − 1 − 1 − 1 + 2 = 9.

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