Journal of Basic & Applied Sciences, 2018, 14, 113-118 113
ISSN: 1814-8085 / E-ISSN: 1927-5129/18 © 2018 Lifescience Global
Rydberg Energy Levels and Quantum Defects of some
Semiconductor Elements
Ejaz Ahmed
*
and Jehan Akbar
Hazara University, Mansehra, Pakistan
Abstract: Weakest bound Electron Potential Model Theory has turned out to be a successful theory in explaining many
atomic properties, namely, energy levels, transition probabilities and oscillator strengths. The theory has also been used
to calculate Rydberg energy levels and quantum defects. In this paper we studied semiconductor elements Boron and
Silicon. We calculated energy levels of Rydberg atoms of Boron and Silicon up to n = 50 levels using WBEPMT. We also
calculated quantum defects in principle quantum number for various configurations of these elements.
Keywords: Weakest bound Electron Potential Model Theory, Rydberg Atoms, Rydberg energy levels, Boron,
Silicon.
INTRODUCTION
Weakest bound Electron Potential Model Theory
has turned out to be a successful theory in explaining
many atomic properties, namely, energy levels,
transition probabilities and oscillator strengths. The
theory has also been used to calculate Rydberg energy
levels and quantum defects. In the following section we
have given a brief introduction of WBEPMT [1-2]. One
atom System energy of an atom system can be
expressed as;
T = T(ionization limit) + E(energy of the weakest bound
electron) (WBE)
T = T
limit
+ E (1)
1
2
d
2
R
dr
2
+
1
r
dR
dr
+ E ! V (r ) !
l (l + 1)
2r
2
"
#
$
%
&
'
! R = 0 (2)
The potential by Weakest Bound electron as [3]
V (r ) = !
" Z
r
+
k ( k + 1) + 2 kl
2r
2
(3)
By comparative & substitutive sketch of eq-3 & eq-
2, the new format of radial equation turns out to be;
1
2
d
2
R
dr
2
+
1
r
dR
dr
+ E !
" Z
r
!
l (l + 1)
2r
2
#
$
%
&
'
(
! R = 0 (4)
Where
! l = l + K (5)
*Address correspondence to this author at the Hazara University, Mansehra,
Pakistan; E-mail: blueshiftlife@gmail.com
The equation-4 can be simplified as
R
nl
(r ) = A exp !
" Zr
" n
#
$
%
&
'
( L
n!l !1
2 " l +1
2 " Zr
" n
#
$
%
&
'
( (6)
E = !R
" Z
" n
#
$
%
&
'
(
2
(7)
where “R” is Rydberg constant
! Z
! n
=
Z
net
n " #
n
(8)
Where Z
net
represents the Net-charge # of Atomic
Kernel and its value is one for atoms and δn
Represents the quantum defect;
T = T
limit
+ E = T
limit
+
Z
net
n ! "
n
#
$
%
&
'
(
2
(9)
Where !
n
can be represented as; by the reference
of Martin’s formula
!
n
=
a
i
(n " !
o
)
2i
i=0
3
#
(10)
Where !
o
represents quantum defect of lowest
energy level, and a
i
are the parameters, these
parameters can be obtained by the minimum possible
square fitting of equation (9) using minimal
experienmental data obtained at first reading of the
given spectrum series. [3]
Boron in a chemical element is symbolically
represented by “B” and has atomic number” 5”. It is
completely produced by spallation of Cosmic rays,
having low abundance in Solar system including