Unpaired electron number is one of the vital important terms used in the field of chemistry. Determination of unpaired electron number is very important in different kind of problems, such as for finding the magnetic moment (in B.M.), for finding spin multiplicity value etc. But evaluation of unpaired electron number using MOT or by drawing molecular orbitals, is time consuming. So, in this manuscript, I try to represent a simple and rapid way to calculate the unpaired electron number with the help of applied mathematics and some basic concepts of chemistry, which can be used specially for any competitive exam, that will be beneficiary for all students to save their valuable time. To use this new method, the student need not compulsorily know the MOT. This method is applicable for those diatomic molecules and ions, which have their total electron number (01-20).

1. _____________________________________________________________________________________________________
*Corresponding author: Email: pritam.oam@gmail.com;
Short Research Article
Journal of Applied Chemical Science International
6(4): 199-202, 2016
ISSN: 2395-3705 (P), ISSN: 2395-3713 (O)
International Knowledge Press
www.ikpress.org
AN INNOVATIVE AND RAPID METHOD FOR EVALUATION
OF UNPAIRED ELECTRON NUMBER OF HOMO AND
HETERO NUCLEAR DIATOMIC MOLECULES AND IONS
WITHOUT USING M.O.T
PRITAM DEBNATH1*
1
Department of Civil Engineering, National Institute of Technology Agartala, Tripura, Jirania 799046, India.
AUTHOR’S CONTRIBUTION
The sole author designed, analyzed and interpreted and prepared the manuscript.
Received: 17th
December 2015
Accepted: 13th
March 2016
Published: 22nd
June 2016
__________________________________________________________________________________
ABSTRACT
Unpaired electron number is one of the vital important terms used in the field of chemistry. Determination of
unpaired electron number is very important in different kinds of problems, such as for finding the magnetic
moment (in B.M.), for finding spin multiplicity value etc. But evaluation of unpaired electron number using
MOT or by drawing molecular orbitals, is time consuming. So, in this manuscript, I have tried to represent a
simple and rapid way to calculate the unpaired electron number with the help of applied mathematics and some
basic concepts of chemistry, which can be used especially for any competitive exam, that will be beneficial for
all students to save their valuable time. To use this new method, the student need not compulsorily know the
MOT. This method is applicable for those diatomic molecules and ions, which have their total electron number
(01-20).
Keywords: Even electron number; molecules; MOT; odd electron number; total electron number; value of δ.
1. INTRODUCTION
Using MOT or by drawing molecular orbitals, one can
find the unpaired electron number of any diatomic
molecules. The calculation of unpaired electron
number is very important in the field of inorganic
chemistry. The conventional method for evaluation of
unpaired electron number using MOT [1-9] is time
consuming. In case of the conventional method to
evaluate the unpaired electron number, at first, one
should draw the molecular orbitals for the
corresponding molecule. After that, one can calculate
the unpaired electron number present in that molecule
from the molecular orbitals by distribution of
electrons in those molecular orbitals. Concept of
MOT is great, but to use MOT, one should know
about the molecular orbitals and the distribution of
electron in those orbitals and also need to draw the
molecular orbitals for distribution of electrons, which
needs time. So with a very simple concept, the author
represents here a rapid way to calculate unpaired
electron number by using only the value of δ
(described below in section 2.1 & 2.2). One can easily
calculate the unpaired electron number of diatomic
molecules or ions only by finding value of δ, without
using MOT. By using this same concept, earlier two
rapid method has been introduced by the author
for easy prediction of ‘Magnetic Moment’ [12] and
‘Spin Multiplicity Value’ [13] for the benefit of
students.

2. Debnath; JACSI, 6(4): 199-202, 2016
200
This method contains four (4) new formulae with four
(4) sets of electron number. By placing only the value
of δ in the respective formula, one can easily calculate
the unpaired electron number of different diatomic
molecules and ions.
This rapid method will be very much helpful for all
students of chemistry, particularly for those situations,
where calculation of unpaired electron number is to be
done within a very short interval of time.
So, on the basis of all these things, the author can
strongly recommend that this method will be most
rapid method for calculation of unpaired electron
number of homo and hetero nuclear diatomic
molecules or ions having total electron number
(01-20), without using M.O.T.
2. MATERIALS AND METHODS
First of all, we take certain range of total electron
number of different diatomic molecules and ions,
which are shown in four (4) sets as follows.
Set-1:- Molecules or ions having (1-10 and 16)
electrons, (consider only even electron
number in this range).
Set-2:- Molecules or ions having (11-20, ≠16)
electrons, (consider only even electron
number in this range).
Set-3:- Molecules or ions having (1-8) electrons,
(consider only odd electron number in this
range).
Set-4:- Molecules or ions having (9-20) electrons,
(consider only odd electron number in this
range).
The above four sets, with their corresponding
formulae for finding unpaired electron numbers are
shown in Table 1.
Table 1. Formulae for finding unpaired electron
number
Range of total electron number Formula
1-10 and 16 (consider only even electron
numbers in this range)
2δ
11-20(≠16) (consider only even electron
numbers in this range without 16)
2δ-2
1-8 (consider only odd electron numbers in
this range)
δ+1
9-20 (consider only odd electron numbers
in this range)
δ
The above table can also be represented by another
format as shown in Table 2.
2.1 Introduction to δ
δ is a variable, which can take only two value 0 or 1,
depending on the total electron number of a molecule
or ion.
If, the total electron number for a molecule or ion
lies between ‘1-8’, then value of δ = 0.
If, the total electron number for a molecule or ion
lies between ‘9-20’, then value of δ =1.
2.2 Source of Conception behind the Value
of δ
Actually this concept is taken from azimuthal
quantum number [10,11] of quantum chemistry;
where it is observed, for s orbital, quantum number δ
is taken as 0 (considering δ represents azimuthal
quantum number) and for p orbital δ is taken as 1. The
same concept has been used here. If an atom contains
only s orbital, the value of δ is taken as 0, and if an
atom contains both s and p orbital, then the value of δ
is taken as 1. The value of δ depends on the two atoms
of which a diatomic molecule is composed. But in
case of such diatomic molecules, where one atom has
only s orbital and another atom has both s and p
orbital, then it is observed that, if the atom consisting
both s and p orbital is taken under consideration, then
the calculation (using applied mathematics) goes in an
appropriate way and gives the desired result. But, if
the atom, which has only s orbital is taken under
consideration, then the process does not give any
suitable result. That is why; that atom is taken into
consideration, which contains both s and p orbital in
case of the ionic molecule or hetero nuclear diatomic
molecules (e.g. - HF) to find the value of δ.
Hence, from the above observations it can be said
that, the value of δ is 0 for those molecules, which
contain (1-8) total electrons and the value of δ is 1 for
those molecules, which contain (9-20) total electrons.
E.g.:
i. N + N = N2
Electronic configuration of N: 1S2
2S2
2P3
We can observe that N2 contain two N (nitrogen
atom), and both N atom contain both s and p orbital.
So, the value of δ for N2 molecule is taken as 1.
ii. H + F = HF
Electronic configuration of H: 1S1
Electronic configuration of F: 1S2
2S2
2P5

3. Debnath; JACSI, 6(4): 199-202, 2016
201
Table 2. Another representation of table 1 for finding unpaired electron number
Range of total electron number New
formula
Another representation of
new formula
A 1-10 and 16 (take only even electron numbers in this range) 2δ A=A1
(A1=2δ)
B 11-20( 16) (take only even electron
numbers in this range without 16)
2δ-2 B=(A1– coefficient of δ
of A1)=2δ-2
C 1-8 (take only odd electron numbers in this range) δ+1 C=A2
(A2= δ +1)
D 9-20 (take only odd electron numbers in this range) δ D=(A2– coefficient of δ
of A2)=δ
We can observe that HF contains one H (hydrogen)
atom and one F (fluorine) atom. And, H atom has only
s orbital, whereas F atom has both s and p orbital. So,
according to the considering rule, value of δ is taken
as 1.
3. RESULTS AND DISCUSSION
3.1 Discussion for Set 1
Total electron range: 1- 10 and 16 (consider only
even electron number).
In this case, Formula for finding unpaired electron
number = 2δ.
E.g.: O2, which has total electron number 16,
therefore value of δ = 1.
Hence, unpaired electron number for O2 = 2×1 = 2.
3.2 Discussion for Set 2
Total electron range: 11- 20,≠16 (consider only even
electron number).
In this case, Formula for finding unpaired electron
number = 2δ – 2.
E.g.: N2, which has total electron number 14,
therefore value of δ = 1.
Hence, unpaired electron number for N2 = 2×1 – 2 =
0.
3.3 Discussion for Set 3
Total electron range: 1- 8 (consider only odd electron
number).
In this case, Formula for finding unpaired electron
number = δ + 1.
E.g.: Be2
+
, which has total electron number 7,
therefore value of δ = 0.
Hence, unpaired electron number for Be2
+
= 0 + 1 =
1.
3.4 Discussion for Set 4
Total electron range: 9- 20 (consider only odd
electron number).
In this case, Formula for finding unpaired electron
number = δ.
E.g.: NO, which has total electron number 15,
therefore value of δ = 1.
Hence, unpaired electron number for NO = 1.
The unpaired electron number of different molecules
and ions are shown in Table 3.
Table 3. Unpaired electron number of different molecules with calculation by using new method
Different
molecules
Total electron
number
Unpaired electron
number (n) using MOT
Value of ‘δ’ Unpaired electron number
(n) using new formula
H2 2 0 0 2×0 = 0
He2 4 0 0 2×0 = 0
Li2 6 0 0 2×0 = 0
Be2 8 0 0 2×0 = 0
B2 10 2 1 2×1 = 2
C2 12 0 1 2×1 – 2 = 0
N2 14 0 1 2×1 – 2 = 0
O2 16 2 1 2×1 = 2
F2 18 0 1 2×1 – 2 = 0
Ne2 20 0 1 2×1 – 2 = 0
H2
+
1 1 0 0 + 1 = 1
H2
-
3 1 0 0 + 1 = 1

4. Debnath; JACSI, 6(4): 199-202, 2016
202
Different
molecules
Total electron
number
Unpaired electron
number (n) using MOT
Value of ‘δ’ Unpaired electron number
(n) using new formula
He2
+
3 1 0 0 + 1 = 1
Li2
+
5 1 0 0 + 1= 1
Be2
+
7 1 0 0 + 1 = 1
HF 10 2 1 2×1 = 2
C2
+
11 1 1 1
C2
-
13 1 1 1
N2
+
13 1 1 1
N2
-
15 1 1 1
O2
+2
14 0 1 2×1 – 2 = 0
O2
-2
18 0 1 2×1 – 2 = 0
O2
-
17 1 1 1
O2
+
15 1 1 1
NO+
14 0 1 2×1 – 2 = 0
NO-
16 2 1 2×1 = 2
CN 13 1 1 1
CN+
12 0 1 2×1 – 2 = 0
4. CONCLUSION
In the conclusion, it can be stated that, the new
method offers the student an innovative as well as a
rapid process to evaluate the unpaired electron
number of homo and hetero nuclear diatomic
molecules and ions without using MOT. This method
proposes an enhanced, simpler process which will
curtail the calculation time.
ACKNOWLEDGEMENTS
The corresponding author Mr. Pritam Debnath, would
be grateful to Dr. Subhajit Das, Department of
chemistry, NIT Agartala, Tripura (west) for his
advices in this regard and also very much thankful to
all his teachers and faculties and also his friends,
particularly Mr. Rahul Raj Chowdhori and family
members Sri Bikramjit Debnath (Father), Smt. Fulu
Rani Debnath (Mother) & Miss. Smriti
Debnath (Elder Sister) for their great inspiration in
this regard.
COMPETING INTERESTS
Author has declared that no competing interests exist.
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e-ISSN: 2278-5736
DOI: 10.9790/5736-081112730
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