Step 1: Analyzing statement 1.
The ionization energy generally increases across a period and decreases down a group. In the case of the second ionization energy for boron family elements, the order should be \( \text{B}>\text{Ga}>\text{Al} \). This is because boron has a smaller atomic size compared to aluminum and gallium, so the second ionization energy is higher for boron. The given order \( \text{B}>\text{Al}>\text{Ga} \) is incorrect.
Step 2: Analyzing statement 2.
For the first ionization energy of the carbon family elements, we know that the ionization energy decreases as we move down the group due to increasing atomic size. Therefore, the correct order should be \( \text{Si}>\text{Ge}>\text{Sn}>\text{Pb} \). The order given in statement 2, \( \text{Si}>\text{Ge}<\text{Pb}<\text{Sn} \), is incorrect.
Step 3: Conclusion.
Both statement 1 and statement 2 are incorrect. Therefore, the correct answer is option (D).
Final Answer: (D) Both statement 1 and statement 2 are incorrect