Compare the energies of following sets of quantum numbers for multielectron system.

(A) $\mathrm{n}=4,1=1$

(B) $\mathrm{n}=4,1=2$

(C) $\mathrm{n}=3, \mathrm{l}=1$

(D) $\mathrm{n}=3,1=2$

(E) $\mathrm{n}=4,1=0$

Choose the correct answer from the options given below :

<p>To compare the energies of electrons in a multielectron system, we must consider both the principal quantum number ($\mathrm{n}$) and the azimuthal quantum number ($\mathrm{l}$). In multielectron atoms, the energy levels are influenced by electron-electron repulsions, which modify the energy ordering compared to the hydrogen atom.</p> <p>The general rule, called the "n+l" rule or Madelung rule, states that the energy of an electron in a multielectron atom is primarily determined by the sum of the principal quantum number ($\mathrm{n}$) and the azimuthal quantum number ($\mathrm{l}$). An orbital with a lower $(\mathrm{n} + \mathrm{l})$ value has lower energy. If two orbitals have the same $(\mathrm{n} + \mathrm{l})$ value, the orbital with the lower $\mathrm{n}$ value has lower energy.</p> <p>Now, let's analyze each set of quantum numbers:</p> <p>(A) $\mathrm{n}=4, \mathrm{l}=1$<br> <p>$\mathrm{n} + \mathrm{l} = 4 + 1 = 5$</p></p> <p>(B) $\mathrm{n}=4, \mathrm{l}=2$<br> <p>$\mathrm{n} + \mathrm{l} = 4 + 2 = 6$</p></p> <p>(C) $\mathrm{n}=3, \mathrm{l}=1$<br> <p>$\mathrm{n} + \mathrm{l} = 3 + 1 = 4$</p></p> <p>(D) $\mathrm{n}=3, \mathrm{l}=2$<br> <p>$\mathrm{n} + \mathrm{l} = 3 + 2 = 5$</p></p> <p>(E) $\mathrm{n}=4, \mathrm{l}=0$<br> <p>$\mathrm{n} + \mathrm{l} = 4 + 0 = 4$</p></p> <p>Based on the $\mathrm{n} + \mathrm{l}$ values, the order of increasing energy is:</p> <p>(C) = (E) < (A) = (D) < (B)</p> <p>Among (C) and (E), (C) has lower $\mathrm{n}$ value, so it is lower in energy:</p> <p>(C) < (E) < (A) = (D) < (B)</p> <p>Among (A) and (D), (D) has lower $\mathrm{n}$ value, so it is lower in energy:</p> <p>Thus, the correct order is: (C) < (E) < (D) < (A) < (B)</p> <p>The correct answer is Option C:</p> <p>$(\mathrm{C}) < (\mathrm{E}) < (\mathrm{D}) < (\mathrm{A}) < (\mathrm{B})$</p></p>