Isomerism:
Isomerism is a phenomenon in which two or more compounds have the same molecular formula but different structural arrangements or connectivity of atoms. In isoelectronic and isostructural compounds, the number of electrons and the arrangement of atoms are the same. Let's analyze the given pairs of compounds to determine which one satisfies these conditions.

Pairs of Compounds:
1) BeCl2 and XeF2
2) TeI2 and XeF2
3) IBr2- and XeF2
4) IF3 and XeF2

Analysis:
1) BeCl2 and XeF2:
- BeCl2 has a linear structure with two Cl atoms bonded to the central Be atom.
- XeF2 has a linear structure with two F atoms bonded to the central Xe atom.
- Both compounds have the same number of valence electrons, 16, making them isoelectronic.
- However, their structures are different. BeCl2 is a linear molecule, while XeF2 is bent.
- Therefore, BeCl2 and XeF2 are not isostructural.

2) TeI2 and XeF2:
- TeI2 has a linear structure with two I atoms bonded to the central Te atom.
- XeF2 has a linear structure with two F atoms bonded to the central Xe atom.
- Both compounds have the same number of valence electrons, 16, making them isoelectronic.
- Their structures are also the same, with a linear arrangement of atoms.
- Therefore, TeI2 and XeF2 are both isoelectronic and isostructural.

3) IBr2- and XeF2:
- IBr2- has a linear structure with two Br atoms bonded to the central I atom and an additional lone pair of electrons on I.
- XeF2 has a linear structure with two F atoms bonded to the central Xe atom.
- Both compounds have the same number of valence electrons, 16, making them isoelectronic.
- Their structures are different. IBr2- has a linear shape with an additional lone pair, while XeF2 is bent.
- Therefore, IBr2- and XeF2 are not isostructural.

4) IF3 and XeF2:
- IF3 has a T-shaped structure with three F atoms bonded to the central I atom.
- XeF2 has a linear structure with two F atoms bonded to the central Xe atom.
- Both compounds have the same number of valence electrons, 16, making them isoelectronic.
- Their structures are different. IF3 has a T-shaped arrangement, while XeF2 is bent.
- Therefore, IF3 and XeF2 are not isostructural.

Conclusion:
Among the given pairs of compounds, only TeI2 and XeF2 are both isoelectronic and isostructural. The other pairs do not satisfy both conditions simultaneously.

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