How does an atom's size affect its ability to hold onto valence electrons?

Here, we are required to determine how an atom's size affect its ability to hold onto Valence electrons.

The bigger the size of an atom, the less is it's ability to hold onto Valence electron and vice versa.

First, we must establish the fact that according to Coulumb's law;

The force of attraction or repulsion between 2 charges is inversely proportional to the square of their distance apart.

On this premise;

For very big atoms with many energy levels, the atomic radius is longer and this consequently reduces the magnitude of the force of attraction between the nucleus and the Valence electrons.

The case is different for smaller atoms as the Valence electrons are closer to the nucleus and are therefore held strongly by the nucleus, so that they are not easily lost during chemical reactions.

Ultimately, the bigger the size of an atom, the less is it's ability to hold onto Valence electron.

P.S: This is evident in the reactivity of alkali metals and alkali earth metals which increases down the group as the atomic size increases.

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Vander waals forces are inter molecular bonds that exist within molecules of the same substance. a water molecule is made up of oxygen and hydrogen atoms which share electrons between each other. the vander waals forces are forces that exist between multitude of different  molecules of water. dipole dipole forces is the type of vander waals force that exist in water. the oxygen atom which is more electronegative pulls the shared electron closer to itself thus generating a partial negative charge while the hydrogen acquire a partial positive charge. these two different charges causes attraction to occur in water molecules.