* MCl₂: The formula tells us that element M forms a +2 ion (M²⁺). This is because chlorine (Cl) has a -1 charge, and two chlorine atoms are needed to balance the +2 charge of M.

* More reactive than magnesium: This means M is located higher up in the same group (column) of the periodic table as magnesium (Mg). Elements higher up in a group are more reactive because their outer electrons are easier to remove.

* Smaller radius than barium: This tells us that M is located higher up in the same period (row) of the periodic table as barium (Ba). Elements higher up in a period have smaller atomic radii because their electrons are held closer to the nucleus.

Putting it all together:

* M is more reactive than magnesium, meaning it's in the same group as magnesium.

* M is smaller than barium, meaning it's in the same period as barium.

The only element that fits both of these criteria is Calcium (Ca).

Therefore, element M is Calcium (Ca).