What is the Difference Between Linear and Quadratic Stark Effect?
🆚 Go to Comparative Table 🆚The Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external electric field. The key difference between linear and quadratic Stark effect lies in the nature of the dipole moment that arises from the external field and the relationship between the applied electric field and the energy level shift:
- Linear Stark Effect: This occurs due to a dipole moment that arises from the external field. The difference between the energy levels (Δε) is proportional to the square of the applied electric field (E). This type of Stark effect is characteristic of hydrogen and can be observed in hydrogen-like atoms such as He+, Li+2, and Be+3. The magnitude of the linear effect is relatively large, and it is typically found in atoms with symmetry and a constant dipole moment.
- Quadratic Stark Effect: This arises due to a dipole moment that is induced by the external field. The difference between the energy levels (Δε) is proportional to the square of the applied electric field (E^2). This type of Stark effect is common in many-electron atoms and is typically small in magnitude. It can be found in atoms with asymmetry and a changing dipole moment.
In summary, the main difference between linear and quadratic Stark effects lies in the nature of the dipole moment and the relationship between the applied electric field and the energy level shift. The linear Stark effect is characterized by a dipole moment that arises from the external field and is proportional to the square of the applied electric field, while the quadratic Stark effect arises due to an induced dipole moment and is proportional to the square of the applied electric field squared.
Comparative Table: Linear vs Quadratic Stark Effect
The Stark effect refers to the splitting of spectral lines observed when radiating atoms, ions, or molecules are subjected to a strong electric field. There are two types of Stark effects: linear and quadratic. Here is a table comparing the differences between the two:
| Linear Stark Effect | Quadratic Stark Effect |
|---|---|
| Occurs due to a dipole moment that arises from a selection rule | Arises due to a dipole moment induced by the external field |
| Characteristic of hydrogen and hydrogen-like atoms such as He+, Li+2, and Be+3 | Common in many-electron atoms |
| Magnitude is generally larger | Magnitude is generally smaller |
| Observed in atoms with symmetry and a constant dipole moment | Observed in atoms with asymmetry and a changing dipole moment |
| Energy shift is linearly proportional to the applied electric field | Energy shift is proportional to the square of the applied electric field |
The linear Stark effect is typically observed in hydrogen and hydrogen-like atoms, while the quadratic Stark effect is more common in many-electron atoms. The energy shift in the linear Stark effect is linearly proportional to the applied electric field, whereas in the quadratic Stark effect, the energy shift is proportional to the square of the applied electric field.
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