Step 1: Analysis of Statement I.
Metallic character increases down a group and decreases from left to right across a period.
Potassium is the most metallic, followed by magnesium, aluminium and then boron.
Hence, the order $\mathrm{K>Mg>Al>B}$ is correct.
Statement I is true.
Step 2: Analysis of Statement II.
Atomic radius is not always greater than ionic radius.
For cations, ionic radius is smaller than atomic radius.
For anions, ionic radius is larger than atomic radius.
Hence, the statement is incorrect.
Statement II is false.
Step 3: Conclusion.
Statement I is true but Statement II is false.