Understanding Helium Ion (He⁺) Excitation Potential
The excitation potential of helium ion (He⁺) refers to the energy required to move an electron from its ground state to the first excited state. This process is crucial in understanding atomic structure and spectral lines.
Energy Levels in He⁺
- Hydrogen-like Ion: He⁺ is a hydrogen-like ion with one electron in a potential field created by a nucleus with a charge of +2e.
- Energy Formula: The energy levels of hydrogen-like ions are given by the formula:
E_n = -Z² * (13.6 eV) / n², where Z is the atomic number and n is the principal quantum number.
First Excitation Level
- Ground State (n=1): For He⁺, the ground state energy (n=1) is:
E_1 = -2² * (13.6 eV) / 1² = -54.4 eV.
- First Excited State (n=2): The energy at the first excited state (n=2) is:
E_2 = -2² * (13.6 eV) / 2² = -13.6 eV.
Calculating the Excitation Potential
- Energy Difference: The excitation potential is the difference between the first excited state energy and the ground state energy.
- Calculation:
Excitation Potential = E_2 - E_1 = (-13.6 eV) - (-54.4 eV) = 40.8 eV.
Conclusion
- The first excitation potential of He⁺ is 40.8 eV. This value is essential for understanding the behavior of helium ions in various applications, such as spectroscopy and quantum mechanics.