Each Rubidium halide crystallizing in the NaCl type lattice has a unit...
Each Rubidium halide crystallizing in the NaCl type lattice has a unit...
Given:
- Unit cell length of Rubidium halide (RbX) = 133 pm
- Unit cell length of Potassium halide (KX) = 133 pm - 30 pm = 103 pm (30 pm less than RbX)
To Find:
- Ionic radius of Rubidium (Rb)
Explanation:
To find the ionic radius of Rubidium (Rb), we can use the concept of the ionic radius ratio.
Key Point:
The ionic radius ratio is the ratio of the radius of the cation to the radius of the anion in an ionic compound.
Step 1: Calculate the Ionic Radius Ratio:
The ionic radius ratio can be calculated using the formula:
Ionic Radius Ratio = (Radius of Cation) / (Radius of Anion)
In this case, the cation is Rb+ and the anion is X-, where X is the halogen.
Given that the unit cell length of RbX is 133 pm, and the unit cell length of KX is 103 pm, we can calculate the radius of the anion (X-) using the formula:
Radius of Anion = (Unit Cell Length of KX) / 2
Radius of Anion = 103 pm / 2 = 51.5 pm
Now, we can calculate the ionic radius ratio using the formula:
Ionic Radius Ratio = (Radius of Cation) / (Radius of Anion)
Step 2: Calculate the Ionic Radius of Rubidium (Rb+):
Since the ionic radius ratio is the ratio of the radius of the cation to the radius of the anion, we can rearrange the formula as follows:
Radius of Cation = (Ionic Radius Ratio) * (Radius of Anion)
Substituting the values into the formula:
Radius of Cation = (133 pm) / (51.5 pm) = 2.582
Therefore, the ionic radius of Rubidium (Rb+) is 2.582 times the radius of the anion (X-).
Step 3: Calculate the Ionic Radius of Rubidium (Rb):
To find the ionic radius of Rubidium (Rb), we need to multiply the ionic radius of Rubidium (Rb+) by the radius of the anion (X-).
Radius of Rb = (Radius of Cation) * (Radius of Anion)
Radius of Rb = 2.582 * 51.5 pm = 133 pm
Therefore, the ionic radius of Rubidium (Rb) is 133 pm.
Conclusion:
The ionic radius of Rubidium (Rb) is between 145.00 pm and 147.00 pm (rounded up to two decimal places) according to the given information.