The correct answer is 35
\(\frac{hc}{λ} - Ø = KE = eV_0 \)
\(⇒ \frac{6.63 × 10^{-34} × 3 × 10^8}{6630 × 10^{-10}} - 6.63 × 10^{-34}\)
\(= ƒ_{th} = 1.6 × 10^{-19} × 0.4\)
\(⇒ ƒ_{th} ≃35.11 × 10^{13} H\)
Let $ f: \mathbb{R} \to \mathbb{R} $ be a twice differentiable function such that $$ f''(x)\sin\left(\frac{x}{2}\right) + f'(2x - 2y) = (\cos x)\sin(y + 2x) + f(2x - 2y) $$ for all $ x, y \in \mathbb{R} $. If $ f(0) = 1 $, then the value of $ 24f^{(4)}\left(\frac{5\pi}{3}\right) $ is: