Question

How much energy is required to ionise a H atom if the electron occupies n = 5 orbit? Compare your answer with the ionization enthalpy of H atom (energy required to remove the electron from n = 1 orbit).

Answer 1

Energy for n=5 Orbit

The energy of an electron in the hydrogen atom at level \( n \) is given by \( E_n = -\frac{13.6}{n^2} \) eV.

 

For ionization from \( n=5 \) to \( n=\infty \), the required energy is \( |E_5| = \frac{13.6}{25} = 0.544 \) eV [3][4].

In joules, this is \( 8.72 \times 10^{-20} \) J.

 

Ground State (n=1)

The ionization energy from the ground state (\( n=1 \)) is 13.6 eV.

 

In joules, it is \( 2.18 \times 10^{-18} \) J.

 

Comparison

The energy required from \( n=5 \) is \( \frac{1}{25} \)th (or 0.04 times) that from \( n=1 \), since ionization energy scales as \( \frac{1}{n^2} \).

 

Thus, 25 times less energy is needed for the n=5 orbit compared to the ground state.