90 2 Quantum Mechanics – I
Table 2.1Hydrogen spectrum
Series Region First line (A) ̊ Series limit (A) ̊- Lyman Ultraviolet 1,215 911
ν ̃=^1 λ=R
(
1
12 −
1
n^2 i)
;ni= 2 , 3 , 4 ...- Balmer Visible 6,561 3,645
ν ̃=R
(
1
22 −1
n^2 i)
;ni=^3 ,^4 ,^5 ...- Pa s h e n Infrared 18,746 8,201
ν ̃=R
(
1
32 −1
n^2 i)
;ni= 4 , 5 , 6 ...- Brackett Infrared 40,501 14,580
ν ̃=R
( 1
42 −1
n^2 i)
;ni= 5 , 6 , 7 ...- Pfund Far infra-red 74,558 22,782
ν ̃=R
(
1
52 −
1
n^2 i)
;ni= 6 , 7 , 8 ...Positronium
Asystemofe+−e−is called positronium, the reduced mass,μ= 0. 5 me. Therefore,
the radii are expanded but energy levels are reduced by a factor of 2, compared to
the H-atom, and the entire spectrum is shifted toward the longer wavelength.
Uncertainty principle(Heisenberg)
ΔxΔpx (2.25a)
ΔEΔt (2.25b)
LzΔΦ (2.25c)Restricted uncertainty principle
ΔxΔpx/ 2 (2.26)Bohr magneton
μB=e
2 m(2.27)
Zeeman effect
The splitting of spectrum lines in a magnetic field is known as Zeeman effect.
Normal Zeeman effect(Strong magnetic field)
Each term is split up into 2J+1 terms by the magnetic field. When observed trans-
versely (magnetic field at right angle to the light path), the lines are observed to
be split up into three, the middle line linearly polarized parallel to the field, and
the outside lines at right angles to the field; but when observed longitudinally (field