Which of the following statements does not follow from the fact that the alkali metals have relatively weak metal-metal bonding? $$ \begin{array}{l}{\text { (a) The alkali metals are less dense than other metals. }} \\ {\text { (b) The alkali metals are soft enough to be cut with a knife. }} \\ {\text { (c) The alkali metals are more reactive than other metals. }} \\ {\text { (d) The alkali metals have higher melting points than }} \\ {\text { other metals. }} \\ {\text { (e) The alkali metals have lowization energies. }}\end{array} $$

Since alkali metals have weak metal-metal bonding, it means that these bonds are easily broken. This will allow alkali metals to possess certain properties. Now, let's analyze each statement to see if they are directly related to weak metal-metal bonding: (a) The alkali metals are less dense than other metals: Alkali metals, particularly those in Group 1 of the periodic table, are known to be less dense than transition metals. This is partially due to having less packed atomic arrangements, which in turn, is affected by their weaker metal-metal bonding. (b) The alkali metals are soft enough to be cut with a knife: The weakness of metal-metal bonding translates to the metal's ability to be deformed and cut easily. Therefore, this statement is related to the weak bonding nature of alkali metals. (c) The alkali metals are more reactive than other metals: The reactivity of alkali metals increases as their metal-metal bonds weakens. This means they have a greater tendency to lose an electron and form a positive ion, also explaining their low ionization energies. (d) The alkali metals have higher melting points than other metals: Melting points depend on the strength of the interaction between atoms. As alkali metals have weak metal-metal bonding, they are expected to have lower melting points compared to other metals. (e) The alkali metals have low ionization energies: Ionization energies depend on how easily an atom can lose an electron. Since alkali metals have weak metal-metal bonding, their atoms can lose an electron more easily, resulting in a low ionization energy.

From the analysis above, the statement that does not follow from the fact that alkali metals have relatively weak metal-metal bonding is: \( \text{(d) The alkali metals have higher melting points than other metals.} \) This statement contradicts the expected properties of alkali metals, which are known to have lower melting points due to their weak metal-metal bonding.