# Magnetic Behavior of Diatomic Species

Generally magnetic properties of diatomic molecules or ions whose total number electrons lie in the range (1-20) can be evaluated with the help of Molecular orbital theory (MO theory)1,2. The present study involves3-5 three (03) new formulae by just manipulating the number of unpaired electrons (n) for determination of magnetic properties without MO theory using mod function (based on Applied Mathematics) and by means of these n values one can easily stumble the magnetic moment values in Bohr-Magneton using spin only formula

$\mu_s = \sqrt{n(n+2)} \mu_B$

where

• $$\mu_B$$ is the Bohr Magneton (unit of magnetic moment) and
• $$n$$ is the number of unpaired electrons.

## Classification

First of all we classify the molecules or ions depending on the total number of electrons present in them in the following three (03) sets.

• Set 1: Molecules or ions with (1-3), (3-5), (5-7), (7-10), or (13-16) electrons
• Set 2: Molecules or ions with (10-13) or (16-19) electrons
• Set 3: Molecules or ions with 20 electrons

Then for different set we have to use three different formulae to calculate the number of unpaired electrons which have been presented in Table 1 and thus magnetic moment ($$\mu_s$$) can be evaluated in the following way:

## SET 1: Species with (1-3), (3-5), (5-7), (7-10), or (13-16) Electrons

For the prediction of number of unpaired electrons (n) of molecules or ions having total number of electrons (1-3),(3-5),(5-7),(7-10) and (13-16)electrons:

In this case, the number of unpaired electrons n = [ I (ND - total electrons) I ]

Here, ND = next digit i.e. digit next to minimum digit and ‘I I’ indicates mod function.

Eg:Molecules or ions having (1-3)electrons, in this case ND = 2 because here minimum digit is 1.

Example 1: He2+

He2+ (3electrons), the total number of electrons will be 3, ND = 2, Hence, unpaired electron n = I (ND - total electrons) I = I (2-3) I = 1. Hence, Magnetic Moment μs = √n(n+2) $$\mu_B$$ = √ 1(1+2) BM = √3 BM = 1.73BM.

For the molecules or ions containing (3-5)electrons, (5-7)electrons, (7-10)electrons, and (13-16)electrons the ND value will be 4, 6, 8 and 14 respectively. Hence, the value of n = [ I (4-total electrons) I ]; [ I (6- total electrons) I ] [ I (8- total electrons) I ] and [ I (14- total electrons) I ] respectively.

## SET 2: Species with (10-13) or (16-19) Electrons

For the prediction of number of unpaired electrons (n) of molecules or ions having total number of electrons (10-13) and (16-19):

In this case, the number of unpaired electrons n = [ I (PD - total electrons) I ]

Here, PD = Penultimate electron digit (i.e. before last electron).

Example 2: C2-

The $$C_2^-$$ diatomic ion has 13 electrons, so PD = 12. Hence, unpaired electron n = I (12 - total electrons) I = I (12-13) I = 1

Hence, Magnetic Moment μs = √n(n+2) $$\mu_B$$ = √ 1(1+2) BM = √3 BM = 1.73BM

Example 3: F2

The $$F_2$$ diatomic molecules has 18 electrons, the total number of electrons will be 18, PD = 18. Hence, unpaired electron n = I (18 - total electrons) I = I (18-18) I = 0

Hence, Magnetic Moment μs = √n(n+2) $$\mu_B$$ = √ 0(0+2) BM = 0 BM = Diamagnetic in nature.

## SET 3: Species with 20 Electrons

For the prediction of number of unpaired electrons (n) of molecules or ions having total number of electrons 20:

In this case, the number of unpaired electrons n = [ (20 - total electrons) ]

Example 4: Ne2

The $$Ne_2$$ diatomic molecules has 20 electrons, the total number of electrons will be 20. Hence, unpaired electron n = (20 - total electrons) = (20-20) = 0

Hence, Magnetic Moment μs = √n(n+2) $$\mu_B$$ = √ 0(0+2) BM = 0 BM = Diamagnetic in nature.

Table 1: Magnetic moments of homonulcear and heteronuclear diatomic species

Species (Molecules or ions)

Total Number of electrons

Number of unpaired electrons (n)

Magnetic moment (μs) in Bohr Magneton ($$\mu_B$$)

Magnetic Behavior

H2+

1

1

1.73

Paramagnetic

H2, He22+

2

0

0

Diamagnetic

H2-,He2+

3

1

1.73

Paramagnetic

He2,

4

0

0

Diamagnetic

Li2+,He2-

5

1

1.73

Paramagnetic

Li2, He22-, Be22+

6

0

0

Diamagnetic

Be2+,Li2-

7

1

1.73

Paramagnetic

Be2,Li22-

8

0

0

Diamagnetic

Be2-,B2+

9

1

1.73

Paramagnetic

B2, Be22-, HF

10

2

2.82

Paramagnetic

B2-,C2+

11

1

1.73

Paramagnetic

C2,B22-,N22+, CN+

12

0

0

Diamagnetic

C2-,N2+

13

1

1.73

Paramagnetic

N2,CO,NO+,C22-,CN-,O22+

14

0

0

Diamagnetic

N2-,NO,O2+

15

1

1.73

Paramagnetic

NO-,O2

16

2

2.82

Paramagnetic

O2-

17

1

1.73

Paramagnetic

F2,O22-,HCl

18

0

0

Diamagnetic

F2-

19

1

1.73

Paramagnetic

Ne2

20

0

0

Diamagnetic

## References

1. “Spectroscopy. Molecular Orbitals and Chemical Bonding”, Nobel Lectures, Chemistry 1963-1970,Elsevier Publishing Company, 1972-1966
2. Hall, George G. Lennard-Jones Paper of “Foundations of Molecular Orbital Theory”,Advances in Quantum Chemistry,1929,22. Bibcode:1991AdQC…22…1H. doi:10.1016/S0065-3276(08)60361-5, ISBN-978-0-12-034822-0, ISSN 0065-3276
3. Arijit Das,‘Simple Thinking Makes Chemistry Metabolic And Interesting- A Review Article’, IOSR-JAC,2013,6(4), 8-15, e-ISSN: 2278-5736, doi:10.9790/5736-0640815
4. Arijit Das, ‘A rapid and innovative method for the easy prediction of Magnetic behavior of homo and heteronuclear mono and diatomic molecules or ions without MOT’,IJAR,2013, 3(10), 1, ISSN-2249-555X
5. Arijit Das, R.Sanjeev and V.Jagannadham, “Innovative And Time Economic Pedagogical Views In Chemical Education – A Review Article”, World Journal of Chemical Education, 2014, 2(3), 29-38, Science and Education Publishing , USA, DOI:10.12691/wjce-2-3-1