Question

The ionization potential energy of a hydrogen atom is 13.6 eV. The energy required to remove an electron from the second orbit of hydrogen will be
(A). 27eV
(B). 13.6eV
(C). 3.4eV
(D). None of these

Answer 1

Hint- Ionization energy is simple terms that can be described as a measure of the difficulty in removing an electron from an atom or ion or the tendency of an atom or ion to surrender an electron. The loss of electrons usually happens in the ground state of the chemical species. Alternatively, we can also state that ionization or ionization energy is the measure of strength (attractive forces) by which an electron is held in a place.

Complete step-by-step solution -
What can be further concluded is that ionizing energy brings a sense of chemical compound reactivity. It can also be used to determine the strength of chemical bonds. It is either expressed in electron volt units or in kJ / mol.
Ionization energy for the removal of an electron from a neutral atom can be calculated, by substituting, the orbit number of the electron before transition as ‘$n_1$‘ and orbit number of the electron after transition as ‘∞'(infinity) as $n_2$ in Bohr’s energy equation.
$
  {E_{ion}} = {E_\infty } - {E_n} \\
   = 13.6\dfrac{{{Z^2}}}{{{n^2}}} \\
$
Now as we know that the energy required to move the electron from ground state to infinity is
$n = \infty $
Energy required to remove electron from 2nd bohr orbit is
$
  \Delta E = {E_0} \times \left( {\dfrac{1}{{{2^2} - \dfrac{1}{\infty }}}} \right) \\
   = \dfrac{{{E_0}}}{4} = \dfrac{{13.6}}{4}ev \\
  \Delta E = 3.4ev \\
$
Hence, the correct option is “C”.

Note- Depending on the ionization of molecules which often leads to changes in molecular geometry, ionization energy can be either adiabatic ionization energy or vertical ionization energy. Ionization energy helps in understanding the concept of bonds formed between the metal compounds and due to the difference in the ionization energy we can say whether the bond formed will be ionic or covalent.