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The melting point of $ Al{F_3} $ is $ 1291^\circ C $ and that $ Si{F_4} $ is $ 77^\circ C $ (it sublimes) because:
(a) There is a very large difference in the ionic character of the $ Al - F $ and $ Si - F $ bonds.
(b) In $ Al{F_3} $ , $ A{l^{3 + }} $ interacts very strongly with the neighbouring $ {F^ - } $ ions to give a three dimensional structure but in $ Si{F_4} $ , no such interaction is possible.
(c) The silicon ion in the tetrahedral $ Si{F_4} $ is not shielded effectively from the fluoride ions whereas in $ Al{F_3} $ ,the $ A{l^{3 + }} $ ion is shielded on all sides.
(d) The attractive forces between the $ Si{F_4} $ molecules are strong whereas those between the $ Al{F_3} $ molecules are weak.

Answer
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Hint: In these questions, first we have to know about the factors on which the melting point of any compound depends and then the comparison, why the melting point is $ Al{F_3} $ higher than that of $ Si{F_4} $ We will start with the factors on which melting point depends:
The factors on which the melting point of a compound effects:
(a) Size of the molecule
(b) Force of attraction between the molecules

Complete step-by-step answer
Now, exploring about the factors:
(a) Size of the molecule: The compounds have different structural arrangements and have different melting points.
(b) Force of attraction between the molecules: The higher the force of attraction between the molecules higher the melting points. The ionic compounds are having higher high melting points, due to their electrostatic forces between the ions which are very high and also in the organic compounds, the compounds having hydrogen bonding results in higher melting points.
As we know, the $ Al{F_3} $ is having ionic bonds and $ Si{F_4} $ is having covalent bonds.
So, from the above discussions, the compounds having ionic bonds are having high melting points because of their very strong attraction.
Hence, the correct option is (b) In $ Al{F_3} $ , $ A{l^{3 + }} $ interacts very strongly with the neighbouring $ {F^ - } $ ions to give a three dimensional structure but in $ Si{F_4} $ , no such interaction is possible.

So, option b is correct.

Note
The ionic bond having compounds has a higher melting point than that of the covalent bonds having compounds due to their ion-ion interaction having a very high electrostatic force of attraction. The covalent bonds have lower force of attraction that of the ionic bonds.