Quantum Numbers

Presentation Headings

1

2

3

4

Introduction

The General Quantum Numbers

Quantum Numbers Specifying States of Particles

Conclusion

The General Quantum Numbers

Principle Quantum Number (n)

Angular Quantum Number (l)

Magnetic Quantum Number (m)

Spin Quantum Number (s)

Quantum Number of Electrons

Principle Quantum Number

Describes the Size of the Orbital.

Distance from electron to the nucleus is directly

proportional to the energy of the electron.

Angular Quantum Number (l)

describes the Shape of the orbital.

Magnetic Quantum Number (m)

describes the orientation of the orbital.

for s orbital l = 0 and m = 0. and if l = 1 and m =

+1,0,-1 and if l = 2 and m = -2,-1,0,+1,+2.

Spin Quantum Number (s)

describes the spin or direction (clockwise or

anticlockwise) in which an electron spin.

the two possible spin values are +1/2 and -1/2.

Rules of Allowed Quantum Numbers

3 quantum number (n, l, m) must be an integer.

‘n’ cannot be zero.

‘l’ can be an integer b/w 0 > l > (n-1).

‘m’ can be an integer b/w -l > m > +l.

‘s’ can take only …….

no two electrons in same atom can have the same 4

Quantum Numbers.

Tabular Representation

Shell n Sub Shell l Sub-shell notation Orientation m

No. of Orbita

ls

1 0 1s 0 1

20 2s 0 1

1 2p -1, 0, +1 3

3

0 3s 0 1

1 3p -1, 0, +1 3

2 3d -2, -1, 0, +1, +2 5

4

0 4s 0

1 4p -1, 0, +1

2 4d -2, -1, 0, +1, +2

3 4f -3, -2, -1, 0, +1, +2, +3

Quantum Numbers Specifying States of Particles

Nucleon Number (N)

Lepton Number (L)

Baryon Number (B)

Spin Quantum Number (s)

Iso-spin (IS)

Strangeness Number (S)

Hypercharge (Y)

Nucleon Number (N)

The Nucleon is ….

N = (no. of nucleons) – (no. of anti-nucleons).

But remains constant in decay process.

during any conversion (n - p) the no. of nucleons

remains the same.

Lepton Number (L)

The Leptons are ….

L = (no. of Leptons) – (no. of anti-leptons).

In any decay process it remains the same.

Mass >= pion mass.

Baryon Number (B)Rest mass >= nucleon mass < deutron mass

describes the behavior of nucleon, lepton and

hyperons.

the allowed values are

B = +1 => nucleon & hyperons (baryons)

B = -1 => anti baryons

B = 0 => all other elementary particles

Spin quantum Number (s)

it expresses the intrinsic spin of particle. spin angular quantum number.  

ℏ

s – half integral values for fermions. (anti – symmetric wave function)

S – integral values for bosons. (symmetric wave function)

The intrinsic spin is due to the invariance of particle wave function under

rotation.

This variation may be symmetric or anti symmetric that is even or odd

parity..

Isospin (IS)

charge of the nucleon is treated as variable for different

states of nucleon.

I = ½ for nucleon and I = 1 for pions and the the

different states are denoted by the z – component of the

Isospin vector.

IS = ½ proton state & - ½ neutron state.

IS = +1 pi+ state & 0 for pi0 state & -1 for pi- state.

Strangeness Quantum Number (S)

it describes that if the particle that have any strange

behavior.

eg: - observed a strange behavior of k – meson & hyperons. produce in high energy n – n collision.

decay by weak interaction

produced in pairs.

0 or finate to indicate the strangeness

Strangeness Quantum Number (S)

Elementary Particles Strangeness Number (S)

Pi – meson, Nucleon, Anti – nucleon 0

K0 – meson, Anti – Lambda hyperons, Anti- Sigma Hyperons +1

K0* - meson, Lambda Hyperons, Sigma Hyperons -1

Ki – Hyperons -2

Anti Ki – Hyperons +2

Hypercharge (Y = B + S)

The Hypercharge = Baryon Number + Strangeness Number.

Its Conserved for all strong and electromagnetic

interactions. For pions Y = 0

Kaons & nucleons Y = +1

Y = 2 (Q - IZ)

So the Hypercharge is equal to twice the difference between

the actual charge and the Isospin.

Thank You.ByDominic Joseph T10PPH818