Question

In high school chemistry, students are taught that the convergence limit in the emission spectrum of an element can be used to determine the first ionization energy.

However, what about the second, third or nth ionization energy? Wouldn't that be a higher energy and therefore appear as a higher energy / smaller wavelength spectral line? Shouldn't the convergence limit be the ionization energy for the 1s1 electron?

Answer 1

The convergence limit in the emission spectrum generally corresponds to the first ionization energy. However, the second, third, or nth ionization energies involve removing additional electrons from an ion and require more energy.

Step-by-step explanation:

The convergence limit in the emission spectrum, indeed, refers to the situation where the electron is removed completely from an atom, the first ionization energy.

To determine higher ionization energies, such as the second, third, or nth ionization energy, more energy is needed to remove additional electrons, especially because these electrons are being removed from increasingly positive ions, which hold onto their electrons more tightly.

For example, the first ionization energy is the energy required to remove the outermost, or least tightly bound, electron from a neutral atom. As electrons are removed, the ion becomes more positively charged, and subsequent electrons are removed from an ion rather than a neutral atom.

This process requires more energy for each subsequent electron, leading to successive ionization energies being higher and appearing at smaller wavelengths in the emission spectrum.

The reason the convergence limit is often discussed in relation to the first ionization energy is that it represents the point when an electron is completely removed from an atom, any additional energy input wouldn't be bound to a specific transition between quantized energy levels.