Question

The ionisation energy of a hydrogen atom is 13.6 eV. The energy of the ground level in doubly ionised lithium is:
A. -28.7 eV
B. -54.4 eV
C. -122.4 eV
D. -13.6 eV

Answer 1

The energy required to remove the lowest orbiting electron from the influence of the central protons is the ionization energy.Ionization energy is the quantity of energy that an isolated, gaseous atom in the ground electronic state must absorb to discharge an electron, resulting in a cation.

Complete step by step answer: An atom consists of a central nucleus that contains positively charged protons and a number of neutrons specific to the given atom. A number of negatively charged electrons orbit the nucleus at various distances. The energy required to remove the lowest orbiting electron from the influence of the central protons is the ionization energy.
Comparison of ionization energies of atoms in the periodic table reveals two periodic trend:
-ionization energy generally increases from left to right within a given period (that is, row).
-ionization energy generally decreases from top to bottom in a given group (that is, column).
The latter trend results from the outer shell being progressively farther from the nucleus, with the addition of one inner shell per row as one moves down the column.
The nth ionization energy refers to the amount of energy required to remove an electron from the species having a charge of (n-1). For example, the first three ionization energies are defined as follows:
1st ionization energy is the energy that enables the reaction $\mathrm{X} \rightarrow \mathrm{X}^{+}+\mathrm{e}^{-}$
2nd ionization energy is the energy that enables the reaction $\mathrm{X}^{+} \rightarrow \mathrm{X}^{2+}+\mathrm{e}^{-}$
3rd ionization energy is the energy that enables the reaction $\mathrm{X}^{2+} \rightarrow \mathrm{X}^{3+}+\mathrm{e}^{-}$
The term ionization potential is an older name for ionization energy, because the oldest method of measuring ionization energy was based on ionizing a sample and accelerating the electron removed using an electrostatic potential. However this term is now considered obsolete. Bohr's model is used to find out the energy of the electron in an atom of hydrogen .
According to this E= $-13.6 \times\left(Z^{2} / \mathrm{n}^{2}\right)$ eV .
Now, coming to the numerical:
Given :Ionisation Energy of hydrogen atom= 13.6 eV
To find: the energy of the ground level in doubly ionised lithium.
A doubly ionized lithium atom is hydrogen like with atomic number 3.
So, in this the E is equal to the energy of the electron in the nth shell of an atom whose atomic number is Z.Now, the same amount of energy with opposite sign must be given to the electron in order to remove it.
I.E.= $-13.6 \times\left(Z^{2} / \mathrm{n}^{2}\right)$ eV (As n=1)
Since for Lithium, Z=3
Therefore, we get I.E.= −122.4 eV

The answer is (C).

Additional information: The most notable factors affecting the ionization energy include:
Electron configuration: this accounts for most element's IE, as all of their chemical and physical characteristics can be ascertained just by determining their respective electron configuration.
Nuclear charge: if the nuclear charge (atomic number) is greater, the electrons are held more tightly by the nucleus and hence the ionization energy will be greater.
Number of electron shells: if the size of the atom is greater due to the presence of more shells, the electrons are held less tightly by the nucleus and the ionization energy will be less.
Effective Nuclear charge($Z_{e f f}$): if the magnitude of electron shielding and penetration are greater, the electrons are held less tightly by the nucleus, the $Z_{e f f}$ of the electron and the ionization energy are smaller.
Type of orbital ionized: an atom having a more stable electronic configuration has less tendency to lose electrons and consequently has high ionization energy.
Electron occupancy: if the highest occupied orbital is doubly occupied, then it is easier to remove an electron.

Note: In this the E is equal to the energy of the electron in the nth shell of an atom whose atomic number is Z. Now, the same amount of energy with opposite signs must be given to the electron in order to remove it. The minus sign is very important as it is an attraction force.