Given information:
- Ionic radii of A and B-ions are 0.98 x 10^-10 m and 1.81 x 10^-10 m, respectively.
- Compound AB is formed by A and B-ions.
- We need to determine the coordination number of each ion in AB.

Definition of coordination number:
- The coordination number of an ion is the number of ions or molecules surrounding it in a crystal lattice.

Explanation:
- In a crystal lattice, each ion is surrounded by a certain number of oppositely charged ions to maintain electrostatic neutrality.
- The coordination number of an ion depends on its size, charge, and the size and charge of the surrounding ions.
- Smaller ions can accommodate more ions around them, whereas larger ions have fewer ions around them.
- Similarly, ions with higher charge can attract more oppositely charged ions, resulting in higher coordination numbers.

Calculation of coordination number:
- In the compound AB, A and B-ions are oppositely charged and attract each other.
- The ionic radii of A and B-ions are 0.98 x 10^-10 m and 1.81 x 10^-10 m, respectively.
- Since the size of B-ion is larger than A-ion, it is likely that A-ion will be surrounded by more B-ions than vice versa.
- Therefore, we need to find the maximum number of B-ions that can be accommodated around A-ion, which will give us the coordination number of A-ion in AB.
- To do this, we can calculate the distance between the centers of A and B-ions, which should be equal to the sum of their radii.
- Assuming that the ions are spherical, the distance between their centers (d) can be calculated as:
d = rA + rB
where rA and rB are the radii of A and B-ions, respectively.
- Substituting the given values, we get:
d = 0.98 x 10^-10 m + 1.81 x 10^-10 m
d = 2.79 x 10^-10 m
- Now, we can calculate the maximum number of B-ions that can be arranged around A-ion by assuming that they touch each other.
- Since the distance between the centers of two adjacent B-ions is equal to their diameter (2rB), the number of B-ions that can be arranged around A-ion can be calculated as:
n = (d / 2rB) - 1
where n is the coordination number of A-ion and rB is the radius of B-ion.
- Substituting the given values, we get:
n = (2.79 x 10^-10 m / (2 x 1.81 x 10^-10 m)) - 1
n = 2.44
- Since the coordination number of an ion must be a whole number, we can round off 2.44 to the nearest whole number, which is 2.
- Therefore, the coordination number of A-ion in AB is 2.
- Similarly, we can calculate the coordination number of B-ion in AB by assuming that it is surrounded by A-ions. However, this information is not required to answer the given question.

Conclusion:
- The correct answer is option B, which states that the coordination number of each ion in