Five ionization energy values in KJ mol-1 are \(E_1 = 870,\, \ E_2 = 830,\, \ E_3 = 1010,\, \ E_4 = 1290\) and \(E_5 = 376\). These are

The first \(I.E.\) of successive elements in group 15, 16, 17, 18 and I, respectively.

The correct answer is option 2. The first \(I.E.\) of successive elements in group 15, 16, 17, 18 and I, respectively.

The five ionization energy \((I.E.)\) values \((E_1\, \ to\, \ E_5)\) most likely represent the first ionization energies for elements across different groups in the periodic table, specifically:

Group \(15\) (Nitrogen family) - \(E_1\)

Group \(16\) (Oxygen family) - \(E_2\)

Group \(17\) (Halogens) - \(E_3\)

Group \(18\) (Noble gases) - \(E_4\)

Group \(1\) (Alkali metals) - \(E_5\)

Here is a breakdown of why this is the most likely scenario:

Trends in Ionization Energy:

Across a period (left to right): IE generally increases due to increasing nuclear charge (protons) attracting electrons more tightly.

Down a group (top to bottom): IE generally decreases as the distance between the nucleus and outermost electrons increases (larger atomic radius).

Electron configuration: Removing an electron from a filled or half-filled subshell requires more energy compared to partially filled ones.

Analysis of Values:

\(E_1\) & \(E_2\): These values are relatively close, suggesting removing electrons from similar orbitals (likely valence electrons) within Group 15 (Nitrogen family) and Group 16 (Oxygen family).

\(E_3\): This value shows a moderate increase, possibly corresponding to removing an electron from a different orbital (perhaps a d-orbital in Group 17 - Halogens).

\(E_4\): This significant jump indicates removing an electron from a core orbital requiring much more energy. This aligns with the high IE of noble gases (Group 18) due to their full valence shells.

\(E_5\): This very low value is characteristic of removing an electron from a filled outer shell, resulting in a stable inert gas configuration (Group 1 - Alkali metals).

Other Options Explained:

Successive Ionization Energies for Element 5 (Boron): The jump between \(E_1\) and \(E_2\) is smaller than expected for consecutive ionization energies of a single element.

First IE for Elements 1-5: The increase between \(E_1\) and \(E_2\) is smaller than expected for elements with increasing atomic numbers across a period.

Successive IE for Transition Elements: The significant jump between \(E_4\) and \(E_5\) is not typical for gradual increases observed in transition elements within a group.

Conclusion:

By analyzing the trends in IE and the pattern observed in these values, it's most likely that they represent the first ionization energies for elements across different groups in the periodic table, showcasing the influence of electron configuration and atomic radius on ionization energy.