Ls coupling presentation

Russell-Saunders Coupling

Presentation by:

Group : Champions

Group members:

M. Usman Mustafa (Group leader) Zeeshan Anjum Zeeshan rauf Imran Khalid Sadam Hussain Kaleem ullah Mughal Zohaib Arshad

5th semester session 2013-17

2The Islamia University of Bahawalpur Department of PHYSICS

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What is coupling?

Coupling is the act of combining two things.

Couplings are mechanical elements that ‘couples’ two drive elements which

enables motion to be transferred from one element to another.

In order to transmit torque between two shafts that either tend to lie in the same

line or slightly misaligned, a coupling is used.

Of special interest is the coupling of two (or more) vibratory systems (e.g.

resonant circuits) by means of springs or magnetic fields

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Coupling in Physics

• There are two types of coupling

• L-S coupling & J-J coupling

In physics, two systems are coupled if they are interacting with each

other.


Russell-Saunders of L-S coupling notation for atomic states is a system ofnotating observed states for atoms, based upon a particular conception ofthe angular momentum possessed by each state, and the sources of suchangular momenta in the atom.

What is L-S coupling notation :

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Total angular Momentum of an atom

Total angular momentum associated with the

atom is measured along its projection along

observation axis (z-axis)

If more than one source of angular momentum (spin or orbital

motion contributes to A.M), we will only observe the total angular

momentum from this source included

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Different sources = Spin angular momentum &

Orbital angular momentum

The total angular momentum of an atom (a

vector J) can be shown to be consistent with

the vector addition of all the various sources of

angular momentum in the atom.


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Contributions come from various sources that “couple” or combine

together to give the resulting total.

Here we’ll discuss the angular momentum for many electron

system.

When more than one electron contributes orbital and spin angular

momenta to the total angular momentum J of an atom J is still the

vector sum of these individual momenta.

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Quantum numbers:

o Principal Quantum number (n).

o Orbital angular momentum quantum number (l).

o Magnetic Quantum number (m).

o Spin Quantum number(m).

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Quantum numbers:

The principal quantum number (n) describes the size of the orbital.

The angular quantum number (l) describes the shape of the orbital.

The magnetic quantum number (m) describe the orientation in space

of a particular orbital.

The Spin quantum number (m) describe the spin.

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In this scheme, the usual pattern for all atoms is that the orbital angularmomenta L of the various electrons are coupled together into a singleresultant L(combine vectorially).

The spin angular momenta si are also coupled together into another single resultant s.

𝐿 = 𝐿1 + 𝐿2 + 𝐿3 +⋯………

𝑆 = 𝑆1 + 𝑆2 + 𝑆3 +⋯………

Finding total Angular momentum:

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The momenta L and S then interact via the spin-orbit effect to form thetotal angular momentum J. This scheme is called LS coupling.

• The momenta L and S combine to form the total angular momentum J as

𝐽 = 𝐿 + 𝑆

Finding total Angular momentum:

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For a given value of L, the allowed values of J are

𝐽 = 𝐿 + 𝑆 , 𝐿 + 𝑆 − 1 ,… . , |𝐿 − 𝑆|

When two orbital angular momenta having quantum numbers l1 and l2combine, the allowed values of L are

𝐿 = 𝑙1 + 𝑙2 , 𝑙1 + 𝑙2 − 1 ,… . . , |𝑙1 − 𝑙2|

Similarly the allowed values are calculated for S and J.

For L>S, there are 2S+1 values of J.

For L<S, the number of possible values of J are 2L+1.

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The value of 2S+1 is called the multiplicity of the state.

Multiplicity of state:

For a two electron system (s1=s2=1/2), the total spin angular momentumquantum number S=0 (spin antiparallel) or 1 (spin parallel). When S=0, we have2S+1=1 and such states are referred to as singlet states.

Singlet state:

Triplet state:

when S=1 and 2S+1=3, these are referred to as triplet state.

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Term symbol of the state:

To describe states conveniently, one requires a notation. The symbol n Lj used

for a single electron is changed as follows.

State symbol or Term symbol = n 2S+1Lj

Where,

The superscript 2S+1 represents the multiplicity of the state,

Subscript J is the total angular momentum quantum number, and

L stand for S,P,D,…….

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J-J Coupling

Difference in J-J coupling, compared with L-S:

In J-J coupling l and s for each electron combine to form a separate J and allthe J-vectors are then vectorially added to form J. Thus for each activeelectron J1=l1 + s1; J2=l2 +s2; J3=l3 + s3,……etc. and J=J1 + J2 + J3 + … = ∑Ji. Thiscoupling scheme is known as J-J coupling which is distinctly different fromL-S coupling scheme.

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if S=1/2, L=1, J=3/2, 1/2. The corresponding states will be 2P3/2 and 2P1/2, read asdoublet P three halves and doublet P half.

How to read L-S coupling notation ?

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Modern Physics by G. Aruldhas (university of kerala ) & P. Rajagopal

(Mahatma Gandhi University).

Principles of Modern Physics by Ajay K Saxena.

Modern Physics by S. L. Kakani & Shubhra Kakani.

Physics of atoms and molecules by B. H. Bransden and C. J. Joachain.

Wikipedia

Reference:

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Any Question

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Can anyone define…….

What would you understand by the term Doublet state?

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Can any one solve it down?

A state is denoted as 4D5/2. Find,

(i) what are the values of L, S and J?

(ii) What is the minimum number of electrons which could give rise to this?

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Presentation by:

Group : Champions

Group members:

M. Usman Mustafa (Group leader) Zeeshan Anjum Zeeshan rauf Imran Khalid Sadam Hussain Kaleem ullah Mughal Zohaib Arshad

5th semester session 2013-17


ThankyouGood Bye for now

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Ls coupling presentation

Science

Transcript of Ls coupling presentation