Question

How to calculate the first and second ionisation energies of Helium?

Answer 1

Hint: The answer here is dependent on the definition of ionisation energy which is nothing but the energy required to remove an electron from the outermost orbit of the electron shell of an atom.

Complete step by step answer:
In the previous classes of inorganic chemistry, we have studied about the concepts of the trends in the periodic table which includes several calculations such as ionization energies, electron affinity, atomic radius etc.
We shall see the calculation of ionization energy of the given atom Helium based on these concepts.
- Ionization energy is defined as the minimum amount of energy which is required to remove an electron from the outermost orbit of an atom or in other words it is the minimum amount of energy required to remove the loosely bound electron of an isolated gaseous atom or molecule.
- Usually Bohr’s equation predicts the ionization energy for the hydrogen like atoms and this is not valid for the multi electron system like helium and the first and second ionization energy values predicted for this were the same.
- As a matter of fact usually the first ionization energy is lower than the second one because the second electron will be strongly attracted by the nucleus than the first.
Thus, for multi electron system, the value $Z$ must be replaced by ${{Z}_{eff}}$ (effective nuclear charge)
Therefore, the Bohr’s equation becomes,
\[{{E}_{n}} = -{{R}_{H}}\times \dfrac{Z_{eff}^{2}}{{{n}^{2}}}\]
- Now, according to calculations, Helium’s second 1s electrons have an attractive nuclear charge equal to 1.7 and then this is substituted in above equation the first ionization energy will be $3791kJ/mol$ which was near to the experimental value $2372kJ/mol$
- Similarly, if experimental value was plugged backwards in the equation then effective nuclear charge was found to be 1.34 and was lower than 1.7 and therefore the ionization energy cannot be calculated easily and there is no correct accepted method for this.

Note: Note that the ionization energy is usually measured in the gaseous phases because in the gaseous phase there is a little attraction of these molecules between the other particles that would affect the ionization energy.