Question

write a note of priocipal quantun number ​

Answer 1

Explanation:

a no. which occur in the theoretical expression for the value of sone quantum property of subsubatomic particles like, atoms or molecules

Answer 2

Answer:

The principal quantum number is the quantum number denoted by n and which indirectly describes the size of the electron orbital.

Explanation:

The principal quantum number, usually designated by n, appears in the description of the electronic structure of atoms. The quantum number first arose in the Bohr-Sommerfeld theory of the hydrogen atom, but it is also part of the solution of the Schrodinger equation for hydrogen-like atoms. It is a positive integral number, n = 1, 2, 3, …, that indexes atomic shells. Historically, atomic shells were indicated by the capital letters K, L, M, … for n=1,2,3,…, respectively, but this usage is dying out.

In the Bohr-Sommerfeld ("old") quantum theory, the electron in a hydrogen-like (one-electron) atom moves in elliptic orbits. The principal quantum number appears in this theory at two places: in the energy En of the electron and in the length an of the major semi axis of the nth orbit,

where Ry is the Rydberg energy for infinite nuclear mass (= 13.605 6923 eV). Further, me is the mass of the electron, −e is the charge of the electron, Ze(e in subscript) is the charge of the nucleus, ε0 is the electric constant, and \h^bar is Planck's reduced constant.

In the "new" quantum mechanics (of Heisenberg, Schrodinger, and others) the energy En of a bound electron in a hydrogen-like atom satisfies the exact same equation, but the electron orbit is replaced by an electron orbital; the latter has no radius. However, in the new quantum theory the same expression for an appears in the form of the expectation value of r (the length of the position vector of the electron) with respect to a state with principal quantum number n. That is, quantum mechanics gives the same measure for the "size" of a one-electron atom (in state n) as the old quantum theory.

Strictly speaking, the principal quantum number is not defined for many-electron atoms. However, in a fairly good approximate description (central field plus independent-particle model) of the many-electron atom, the principal quantum number does appear and hence n is a label that is often applied to many-electron atoms as well.