Among the following alkaline earth metal halides, one which is covalent and soluble in organic solvents is :

The correct answer is Beryllium chloride.

Let us understand the step-by-step reasoning behind this answer:

1. Fajan's Rules for Covalency:
According to Fajan's rules, the covalent character of an ionic bond increases with:
- Smaller size of the cation
- Larger size of the anion
- Higher charge on either the cation or the anion

A smaller cation has a high charge density, which gives it a high polarizing power. This polarizing power allows it to distort the electron cloud of the anion, leading to sharing of electrons (covalent character) rather than complete transfer (ionic character).

2. Comparing the Alkaline Earth Metal Cations:
The given options represent halides of group 2 elements (alkaline earth metals):
- Beryllium (${\mathrm{Be}}^{2+}$)
- Magnesium (${\mathrm{Mg}}^{2+}$)
- Calcium (${\mathrm{Ca}}^{2+}$)
- Strontium (${\mathrm{Sr}}^{2+}$)

As we move down Group 2 of the periodic table, the ionic radius of the cations increases in the following order:
${\mathrm{Be}}^{2+}<{\mathrm{Mg}}^{2+}<{\mathrm{Ca}}^{2+}<{\mathrm{Sr}}^{2+}$

3. Polarizing Power and Bond Character:
Since Beryllium (${\mathrm{Be}}^{2+}$) is the smallest cation in this group, it has the highest charge density and polarizing power. Consequently, Beryllium chloride (${\mathrm{BeCl}}_2$) exhibits significant covalent character, whereas the chlorides of the larger alkaline earth metals (like ${\mathrm{MgCl}}_2$, ${\mathrm{CaCl}}_2$, and ${\mathrm{SrCl}}_2$) are predominantly ionic.

4. Solubility in Organic Solvents:
According to the "like dissolves like" principle:
- Ionic compounds tend to be soluble in polar solvents (like water).
- Covalent compounds tend to be soluble in non-polar organic solvents (like ethanol, ether, or benzene).

Due to its strong covalent nature, Beryllium chloride is highly soluble in organic solvents, whereas the other chlorides, being ionic, prefer polar solvents like water.