Analyze Statement (I)

Statement (I): The first ionisation enthalpy of group 14 elements is higher than the corresponding elements of group 13.

Compare elements in the same period:

• Group 13: $ns^2 np^1$
• Group 14: $ns^2 np^2$

Group 14 elements have one extra electron in the $p$-subshell, giving a more stable electronic configuration than group 13. Hence, removing an electron from group 14 generally requires more energy than from the corresponding group 13 element.

Example:

• $\mathrm{B} < \mathrm{C}$
• $\mathrm{Al} < \mathrm{Si}$
• $\mathrm{Ga} < \mathrm{Ge}$

Therefore, Statement (I) is correct.

Analyze Statement (II)

Statement (II): Melting points and boiling points of group 13 elements are in general much higher than those of corresponding elements of group 14.

This is not true.

In general, group 14 elements have stronger covalent/network structures or stronger bonding tendencies than corresponding group 13 elements.

For example:

• Carbon and silicon have very high melting points due to giant covalent structures.
• Group 13 elements like boron, aluminium, gallium, etc. do not generally have melting/boiling points much higher than the corresponding group 14 elements.

In fact, often the reverse trend is seen for corresponding elements.

Therefore, Statement (II) is incorrect.

Choose the correct option

• Statement I: Correct
• Statement II: Incorrect

So, the correct option is: $\boxed{\text{A}}$