Determining the First Excitation Potential of Li2

Understanding Excitation Potential

Excitation potential is the energy required to move an electron from a lower energy level to a higher energy level in an atom. This concept is fundamental in quantum mechanics and is crucial for understanding the behavior of electrons in atoms. The energy levels of electrons are quantized, meaning they can only occupy specific energy states. When an electron absorbs energy, it moves to the next available higher energy level, releasing that energy as light when it returns to a lower state.

Calculation for Li2

For lithium ion (Li2 ), we need to determine its first excitation potential. The first excitation potential is the difference in energy between the first excited state and the ground state. We can use the energy level formula for a hydrogen-like ion to find this difference.

Energy Level Formula for Hydrogen-like Ion

The energy level for a hydrogen-like ion is given by:

En -[Z2 · 13.6 eV / n2]

En is the energy of the electron in the nth level. Z is the atomic number of the element (3 for lithium). n is the principal quantum number, starting at 1 for the ground state.

Energy of the Ground State

The ground state of Li2 (n 1) is:

E1 -[(32 · 13.6 eV) / (12) -122.4 eV]

Energy of the First Excited State

The first excited state of Li2 (n 2) is:

E2 -[(32 · 13.6 eV) / (22) -30.6 eV]

Excitation Potential Calculation

The first excitation potential is the difference between the energy of the first excited state and the ground state:

Excitation Potential E2 - E1 (-30.6 eV) - (-122.4 eV) 91.8 eV

Thus, the first excitation potential of Li2 is 91.8 eV.

Alternative Formulation: Bohr Model

In the Bohr model, the energy change between two levels can also be calculated using the following formula:

ΔE 13.6 eV x 22 / [12 / (12) - 12 / (22)]

Substituting the values:

ΔE 13.6 eV x 9 / (1 - 1 / 4) 91.8 eV

This confirms the first excitation energy for the ground state of lithium ion is 91.8 eV.

Conclusion

Understanding excitation potential is essential in various applications, including spectroscopy and the study of atomic and molecular interactions. The calculation of excitation potential for lithium ion, Li2 , clearly shows that the first excitation potential is indeed 91.8 eV, not 132.4 eV, 13.6 eV, or 54.4 eV.