The incorrect decreasing order of atomic radii is

The atomic radius decreases across a period (from left to right) and increases down a group. We need to evaluate each option to find the incorrect decreasing order.

Option A: Si > P > Cl > F
Si, P, and Cl are in period 3. Atomic radius decreases across the period: Si (143 pm) > P (110 pm) > Cl (99 pm). F is in period 2 and has a smaller radius (72 pm) than Cl. Thus, Cl > F holds. The order Si > P > Cl > F is correct.

Option B: Be > Mg > Al > Si
Be (period 2, group 2) has an atomic radius of 112 pm. Mg (period 3, group 2) has a larger radius (160 pm) due to increasing principal quantum number down the group. Thus, Mg > Be, so Be > Mg is false. For Mg > Al > Si: Mg (160 pm) > Al (143 pm) > Si (118 pm) is correct across period 3, but the initial Be > Mg is incorrect. Hence, the entire order Be > Mg > Al > Si is incorrect.

Option C: Al > B > N > F
Al (period 3, group 13) has a radius of 143 pm. B (period 2, group 13) has a radius of 85 pm. Since atomic radius increases down the group, Al > B holds. In period 2, radius decreases: B (85 pm) > N (75 pm) > F (72 pm). Thus, Al > B > N > F is correct.

Option D: Mg > Al > C > O
Mg (160 pm) > Al (143 pm) in period 3 is correct. Al (143 pm) > C (77 pm, period 2) holds as period 3 elements have larger radii than period 2. In period 2, C (77 pm) > O (73 pm) is correct. Thus, Mg > Al > C > O is correct.

Option B is the incorrect decreasing order.

Final Answer: B