\( Mg>Al>C>O \)
\( Al>B>N>F \)
\( Be>Mg>Al>Si \)
\( Si>P>Cl>F \)
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 $.
A piston of mass M is hung from a massless spring whose restoring force law goes as F = -kx, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with 'n' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height $ L_0 $ to $ L_1 $, the total energy delivered by the filament is (Assume spring to be in its natural length before heating) 
Given below are two statements:
Statement (I):
are isomeric compounds.
Statement (II):
are functional group isomers.
In the light of the above statements, choose the correct answer from the options given below:
Among the following cations, the number of cations which will give characteristic precipitate in their identification tests with
\(K_4\)[Fe(CN)\(_6\)] is : \[ {Cu}^{2+}, \, {Fe}^{3+}, \, {Ba}^{2+}, \, {Ca}^{2+}, \, {NH}_4^+, \, {Mg}^{2+}, \, {Zn}^{2+} \]