The correct order of thermal stability of hydroxides is

The thermal stability of hydroxides of Group 2 elements depends on the stability of the hydroxide lattice and the ease with which they decompose upon heating. The decomposition reaction for these hydroxides is:

where M represents the metal (Mg, Ca, Sr, or Ba). The stability is influenced by the size of the cation. As we move down the group from Mg to Ba, the atomic number increases, and the size of the cation increases due to the addition of electron shells.

The polarizing power of the cation plays a key role. Smaller cations have higher charge density and greater polarizing power. This distorts the electron cloud of the hydroxide ion (OH⁻), weakening the O-H bond and making it easier to lose a water molecule upon heating. Therefore, hydroxides with smaller cations decompose at lower temperatures and are less stable.

Conversely, larger cations have lower charge density and less polarizing power. This results in less distortion of the OH⁻ ion, leading to stronger bonds and higher decomposition temperatures. Hence, hydroxides with larger cations are more stable.

Ordering the cations by increasing size:

Thus, the thermal stability of their hydroxides increases in the same order:

Now, comparing the options:

• Option A: $$ Mg(OH)_2 < Sr(OH)_2 < Ca(OH)_2 < Ba(OH)_2 $$ is incorrect because Sr(OH)₂ should be more stable than Ca(OH)₂.
• Option B: $$ Mg(OH)_2 < Ca(OH)_2 < Sr(OH)_2 < Ba(OH)_2 $$ matches the correct order.
• Option C: $$ Ba(OH)_2 < Sr(OH)_2 < Ca(OH)_2 < Mg(OH)_2 $$ is incorrect because Ba(OH)₂ is the most stable, not the least.
• Option D: $$ Ba(OH)_2 < Ca(OH)_2 < Sr(OH)_2 < Mg(OH)_2 $$ is incorrect for the same reason and also misorders Ca and Sr.

Hence, the correct answer is Option B.