Step 1: Count atoms from structure
Carbon (C) = 15 atoms
Hydrogen (H) = 11 atoms
Oxygen (O) = 4 atoms
Nitrogen (N) = 1 atom
Iodine (I) = 4 atoms
Step 2: Compute mass contribution
\[ \begin{aligned} \text{Mass of C} &= 15 \times 12 = 180 \, \text{g/mol} \\ \text{Mass of H} &= 11 \times 1 = 11 \, \text{g/mol} \\ \text{Mass of O} &= 4 \times 16 = 64 \, \text{g/mol} \\ \text{Mass of N} &= 1 \times 14 = 14 \, \text{g/mol} \\ \text{Mass of I} &= 4 \times 127 = 508 \, \text{g/mol} \end{aligned} \]
Step 3: Total molar mass of thyroxine
\[ \text{Molar mass} = 180 + 11 + 64 + 14 + 508 = 777 \, \text{g/mol} \]
Step 4: Percentage of Iodine
\[ \text{Percentage of Iodine} = \frac{508}{777} \times 100 \approx 65.37\% \]
Correct Answer: 65%
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: