Atomic Structure

Step 1: Understanding Electron Gain Enthalpy
Electron gain enthalpy ( ) is the energy change when an atom gains an electron. It can be:
Negative (exothermic): When energy is released, meaning the atom strongly attracts electrons (e.g., halogens).
Positive (endothermic): When energy must be supplied to add an electron, meaning the atom resists gaining electrons (e.g., noble gases).
Step 2: Identifying Elements with Positive Electron Gain Enthalpy
- Option (1): S, Se, Te Incorrect. These elements belong to group 16 (oxygen family) and generally have negative electron gain enthalpy.
- Option (2): Kr, Xe, Rn Correct. These noble gases have completely filled electronic configurations, making electron addition unfavorable, resulting in a positive electron gain enthalpy.
- Option (3): Cl, Br, I Incorrect. These are halogens with high electron affinity and negative electron gain enthalpy.
- Option (4): K, Rb, Cs Incorrect. These alkali metals have low electron affinity but still have negative electron gain enthalpy.

Step 3: Verify the Correct Answer
Since noble gases resist electron gain due to their stable configuration, the set with positive electron gain enthalpy is Kr, Xe, Rn (Option 2).

Step 1: Energy Levels in a Hydrogen Atom
For a hydrogen atom ( ), the energy of orbitals depends only on the principal quantum number ( ) and not on the azimuthal quantum number ( ). This means: Thus, in a hydrogen atom, the energy of the 2s and 2p orbitals is the same, making Statement I correct.

Step 2: Energy Levels in a Helium Atom
For a helium atom ( ), there is electron-electron interaction in addition to the nuclear attraction. Due to this, the energy of orbitals with the same principal quantum number ( ) but different azimuthal quantum numbers ( ) differs: Thus, in a helium atom, the energy of the 2s and 2p orbitals is not the same, making Statement II incorrect.

Step 3: Verify the Correct Answer
Since Statement I is correct and Statement II is incorrect, the correct answer is Option (3).

Step 1: Energy Level Formula for Hydrogen-Like Atoms The energy of an electron in a hydrogen-like atom is given by: where: - J (constant), - is the atomic number (for Lithium ion ), - is the principal quantum number.

Step 2: Calculate Energy for and For : For :

Step 3: Calculate Energy Difference The energy required to excite the electron from to is:

Step 1: Understanding Isoelectronic Species
Isoelectronic species have the same number of electrons but different nuclear charges. Both (11 protons, 10 electrons) and (9 protons, 10 electrons) are isoelectronic. Thus, Reason (R) is correct.

Step 2: Comparing Ionic Radii of and
- is a cation formed by losing one electron, reducing electron-electron repulsion and making it smaller than its parent atom.
- is an anion formed by gaining one electron, increasing electron-electron repulsion and making it larger than its parent atom.
Since has a smaller radius than , the assertion that their radii are the same is incorrect.
Step 3: Verify the Correct Answer
Since (A) is incorrect but (R) is correct, the correct answer is Option (4).