# What is the cause for the fine structure?

What is the cause for the fine structure? I know that it describes the splitting of the spectral lines of atoms but I don't understand its cause, any help is appreciated

• In quantum mechanics, the spectral lines are usually derived using the Schrodinger equation which is non-relativistic. The fine structure is obtained when taking into account relativistic corrections. Jul 3, 2019 at 8:43
• @Christophe Strange comment because the atomic structure with their spins and magnetic dipoles are responsible for the fine splitting of energy levels of spectra. The Schrödinger equation is among others the result of the observation of fine structures. Jul 3, 2019 at 9:49
• have a look at the simple hydrogen hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydfin.html Jul 3, 2019 at 10:35
• @HolgerFiedler The (relativistic) Dirac equation is expected to give the exact spectral lines. The lowest-order expansion in $v/c$ gives the Schroedinger equation and then the usual spectral lines. The next order gives three additional terms in the Schroedinger equation: the first correction to the kinetic energy, the spin-orbit coupling (coupling of the spin with the orbital kinetic momentum) and the so-called Darwin term. The contribution of these three terms to the spectral lines are known as the fine structure. Jul 3, 2019 at 13:55
• @Christophe No offense. And your last comment could be a good answer. I only came across the fact that you called the formula the cause of the fine structure spectra. Jul 3, 2019 at 14:52

When we observed the emission spectrum of hydrogen, we were able to see a fine splitting in the spectrum. This was something where Bohr's model of atom failed to explain. This was arising due to the interaction of the intrinsic spin of the electron with the magnetic field created by the orbital motion of the electron around the atom. The angular momentum of electrons the units of reduced plank's constant is 1/2. this has only 2 possible Stern-Gerlach experiment showed (space quantization) direction either parallel or antiparallel to the magnetic field of the atom. Which increases or decreases the energy of the electron. Hope this solved your doubt.