Find the incorrect trend for alkaline earth metals

The correct option is: second ionization energy Be < Mg < Ca < Sr

Let us analyze the periodic trends for Group 2 elements (alkaline earth metals) to understand why this trend is incorrect:

1. Ionization Energy Trend (Incorrect Trend):
Ionization energy is the energy required to remove an electron from a gaseous atom or ion. As we move down Group 2 from Beryllium (Be) to Strontium (Sr), the atomic radius increases because new electronic shells are added. As a result, the outermost electrons are further away from the nucleus and experience a weaker electrostatic pull. Thus, it becomes easier to remove electrons, and both the first and second ionization energies decrease down the group.
Therefore, the correct trend for second ionization energy is:
$$\mathrm{Be}>\mathrm{Mg}>\mathrm{Ca}>\mathrm{Sr}$$
Since the option states the reverse order ($\mathrm{Be}<\mathrm{Mg}<\mathrm{Ca}<\mathrm{Sr}$), it is the incorrect trend and therefore the correct answer.

2. Verification of Other Options (Correct Trends):
• Atomic Size: As we go down the group, new shells are added, so atomic size increases: $\mathrm{Be}<\mathrm{Mg}<\mathrm{Ca}<\mathrm{Sr}$. This trend is correct.
• Hydration Enthalpy: Hydration enthalpy depends on the charge density of the cation. Since all Group 2 ions have a +2 charge, hydration enthalpy depends inversely on the ionic radius. Smaller ions have higher charge density and attract water molecules more strongly. Since ionic size increases down the group (${\mathrm{Be}}^{2+}<{\mathrm{Mg}}^{2+}<{\mathrm{Ca}}^{2+}<{\mathrm{Sr}}^{2+}$), the hydration enthalpy decreases down the group: $\mathrm{Sr}<\mathrm{Ca}<\mathrm{Mg}<\mathrm{Be}$. This trend is correct.
• Density: The density of alkaline earth metals does not show a regular trend. It first decreases from Be to Ca due to the rapid increase in atomic volume relative to atomic mass, and then increases from Ca to Sr. The actual order of density is: $\mathrm{Ca}<\mathrm{Mg}<\mathrm{Be}<\mathrm{Sr}$. This trend is correct.