\( Mg>Al>C>O \)
\( Al>B>N>F \)
\( Be>Mg>Al>Si \)
\( Si>P>Cl>F \)
The atomic radius generally decreases across a period (from left to right) and increases down a group.
(1) Mg > Al > C > O:
Mg and Al are in Period 3 (Mg is in Group 2, Al is in Group 13). Mg has a larger atomic radius than Al due to the general trend of decreasing radius across a period.
C and O are in Period 2 (C is in Group 14, O is in Group 16). C has a larger atomic radius than O for the same reason.
However, comparing elements from different periods (e.g., Mg/Al with C/O) violates periodic trends because atomic size increases down a group. Hence, this order is not entirely correct.
(2) Al > B > N > F:
Boron (B) and Aluminum (Al) are in Group 13, with B in Period 2 and Al in Period 3. Al has a larger radius than B due to being in a lower period.
Nitrogen (N) and Fluorine (F) are in Period 2. Radius decreases from B to N to F across the period. So this sequence follows the trend correctly within their groups and periods.
This sequence is correct.
(3) Be > Mg > Al > Si:
Beryllium (Be) is in Period 2, Group 2.
Magnesium (Mg) is in Period 3, Group 2 — so Mg > Be (down a group, size increases).
Aluminum (Al) is in Period 3, Group 13 — so Mg > Al (across period, size decreases).
Silicon (Si) is in Period 3, Group 14 — so Al > Si (again, across period, size decreases).
This sequence follows the periodic trend correctly.
Conclusion:
Among the given options, the correct order of atomic radii based on periodic trends is Be > Mg > Al > Si.
Final Answer:
The final answer is $ Be > Mg > Al > Si $.
The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant $k$ and natural length $\frac{2L}{5}$. In thermodynamic equilibrium, the piston is at a distance $\frac{L}{2}$ from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is $P = \frac{kL}{A} \alpha$, then the value of $\alpha$ is ____
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is:
The term independent of $ x $ in the expansion of $$ \left( \frac{x + 1}{x^{3/2} + 1 - \sqrt{x}} \cdot \frac{x + 1}{x - \sqrt{x}} \right)^{10} $$ for $ x>1 $ is: