Question

Short note on doublet structure of hydrogen atom

Answer 1

Answer:

Fine structure, in spectroscopy, the splitting of the main spectral lines of an atom into two or more components, each representing a slightly different wavelength. Fine structure is produced when an atom emits light in making the transition from one energy state to another. The split lines, which are called the fine structure of the main lines, arise from the interaction of the orbital motion of an electron with the quantum mechanical “spin” of that electron. An electron can be thought of as an electrically charged spinning top, and hence it behaves as a tiny bar magnet. The spinning electron interacts with the magnetic field produced by the electron’s rotation about the atomic nucleus to generate the fine structure.

Explanation :-

The amount of splitting is characterized by a dimensionless constant called the fine-structure constant. This constant is given by the equation α = ke2/hc, where k is Coulomb’s constant, e is the charge of the electron, h is Planck’s constant, and c is the speed of light. The value of the constant α is 7.29735254 × 10−3, which is nearly equal to 1/137.

In the atoms of alkali metals such as sodium and potassium, there are two components of fine structure (called doublets), while in atoms of alkaline earths there are three components (triplets). This arises because the atoms of alkali metals have only one electron outside a closed core, or shell, of electrons, while the atoms of alkaline earths have two such electrons. Doublet separation for corresponding lines increases with atomic number; thus, with lithium (atomic number 3), a doublet may not be resolved by an ordinary spectroscope, whereas with rubidium (atomic number 37), a doublet may be widely separated.

Answer 2

The transition wavelengths for the hydrogen atom are: ... For the allowed transitions and small values of n, the matrix element is of order the ... more important for higher Z