Each Rubidium halide crystallizing in the NaCl type lattice has a unit...
Ionic radii can be determined by comparing the unit cell lengths of different ionic compounds. In this case, we are comparing the unit cell lengths of rubidium halides (RbX) and potassium halides (KX), where X represents the halogen.
Given:
Unit cell length of RK = 133 pm
Unit cell length of RbX = 30 pm greater than RK
To find the ionic radius of Rb, we need to calculate the unit cell length of RbX.
Let's assume the unit cell length of RbX is L.
Key point 1: Relationship between unit cell length and ionic radii
The unit cell length (L) can be expressed as the sum of the ionic radii (rRb and rX) plus the distance between the centers of the Rb and X ions (d):
L = rRb + rX + d
Key point 2: Relationship between unit cell lengths of different compounds
Since the unit cell length of RbX is 30 pm greater than RK, we can write:
L = LK + 30 pm
L = rK + rX + d + 30 pm
Key point 3: Relationship between ionic radii and unit cell lengths
Since the ionic radii of potassium (rK) and halogen (rX) are constant for a given halogen, we can write:
L = rK + rX + d + 30 pm
L - 30 pm = rK + rX + d
Key point 4: Relationship between unit cell lengths and ionic radii
Since the unit cell length of RK is given as 133 pm, we can substitute the values:
133 pm - 30 pm = rK + rX + d
Key point 5: Simplification
133 pm - 30 pm = rK + rX + d
103 pm = rK + rX + d
Key point 6: Relationship between ionic radii and unit cell lengths
Using the same logic, we can write the equation for RbX:
L = rRb + rX + d
L = 103 pm + rX + d
Key point 7: Relationship between unit cell lengths of different compounds
Since the unit cell length of RbX is given as L (30 pm greater than RK), we can substitute the values:
L = LK + 30 pm
L = 133 pm + 30 pm
L = 163 pm
Key point 8: Relationship between ionic radii and unit cell lengths
Substituting the values in the equation for RbX:
163 pm = 103 pm + rX + d
Key point 9: Simplification
163 pm = 103 pm + rX + d
60 pm = rX + d
Key point 10: Relationship between unit cell lengths and ionic radii
Using the equation for RK:
133 pm - 30 pm = rK + rX + d
Key point 11: Simplification
103 pm = rK + rX + d
Key point 12: Relationship between ionic radii and unit cell lengths
Substituting the values in the equation for RK:
103 pm = rK + rX + d
Key point 13: Simplification
103 pm = r