The element 'X' forms a chloride with a formula \[XC{l_3}\] which is solid with a high melting point The element 'X' would most likely be in the same group of the periodic table as :
A.$Na$
B.$Mg$
C.$Al$
D.$Si$

Hint: To answer this question, recall the trends in the periodic table. The modern periodic law developed by Moseley states that the physical and chemical properties of elements are the periodic function of their atomic number. The element which can lose three electrons will form a trihalide.

Complete step by step answer:
The unknown element 'X' generates a chloride with the formula \[XC{l_3}\] which is solid with a high melting point.
Also, one atom of X reacts with 3 $Cl$ atoms that indicate that the valency of the element is 3. Where the valency is indicative of the combining capacity of the element. Taking a look at the options:
$Na$: The valency of sodium is 1. Hence, this option is wrong and can be eliminated
$Mg$: The valency of magnesium is 2. Hence, this option is wrong and can be eliminated
$Al$: The valency of aluminium is 3. Hence, this option is correct.
$Si$: The valency of silicon is 4. Hence, this option is wrong and can be eliminated

Thus, X is Aluminium and the correct option is C.

Note:
Let us summarize the trends of fundamental properties of an element: Atomic Radii and Ionic radii: The atomic radii and ionic radii of elements decrease while moving from left to right in a period. Ionization Enthalpy: Across a period in the periodic table, ionization energy generally increases. While the trend of ionization enthalpy in the groups, it decreases from top to bottom in a group. Electron gain enthalpy: Electron gain enthalpy becomes more negative as we move from left to right in a period. Electron gain enthalpy is negative when energy is released while accepting an electron. While it is positive when energy is supplied to an atom while adding an electron.