Question

The ionization energy of the ionized sodium atom \[N{a^{ + 10}}\] is-
A.\[13.6\,eV\]
B.\[13.6\,\, \times \,11\,eV\]
C.\[\left( {\dfrac{{13.6}}{{11}}} \right)\,eV\]
D.\[13.6\,\, \times \,{(11)^2}\,eV\,\]

Answer 1

Hint: In order to determine the ionization energy of the ionized sodium atom, we must have an idea about the ionization energy. Ionization energy is the minimum energy required to remove an electron from the gaseous atom or ion.

Complete answer:
Ionization energy simply indicates the tendency of an atom or ion to surrender an electron. It is basically the minimum energy required to remove an electron from the gaseous atom or ion. It is usually an endothermic process. It is also referred to as ionization potential.
So, we know that ionization is the process which involves the removal of an electron present in an orbit from the atom. The electron in each orbit has a characteristic energy. Ionization energy is equal to the difference of energy between the energy of the electron in the initial orbit and the energy of the electron outside the atom.
According to the Bohr model of an atom,
The energy of an electron in ‘n’th orbit is:
\[{E_n} = - \dfrac{{2{\pi ^2}m{e^4}}}{{{{(4\pi {\varepsilon ^o})}^2}{h^2}}} \times \dfrac{{{Z^2}}}{{{n^2}}}\]
\[{E_n} = - 13.6\, \times \,\,\dfrac{{{Z^2}}}{{{n^2}}}\,eV/atom\]
Where, \[Z\]is the atomic number of the atom and \[n\]indicates the number of electrons present.
The ionization energy of the ionized sodium atom \[N{a^{ + 10}}\] is
Here, \[n = 1\] and \[Z = 11\]
\[{E_n} = - 13.6\, \times \,\,\dfrac{{{{(11)}^2}}}{{{{(1)}^2}}}\,eV/atom\]
\[{E_n} = - 13.6\,\, \times \,{(11)^2}\,eV/atom\]

The correct answer is option (D).

Note:
If ionization energy is high, it is difficult to remove an electron. Ionization energy gives an idea about the reactivity of chemical compounds. It is used to determine the strength of a chemical bond. It is measured in units of electron volts or\[KJ/mol\]. Always remember that the second ionization energy is always higher than the first ionization energy. This is so because it is difficult to remove a second electron from an already positive ion. Similarly, third ionization will always be higher than second ionization energy.