# Finding components of 2s2p configuration using LS coupling

• omicgavp
In summary, the lowest excited states of the Be atom have a 2s2p configuration with optically active electrons. The possible 2s+1Lj components in this configuration are 3P0, 3P1, 3P2, and 1P1. Using Hund's rules, the expected order of energy levels is 1P1, 3P0, 3P1, and 3P2, which matches the answer in the book.
omicgavp

## Homework Statement

The lowest excited states of the Be atom correspond to a 2s2p configuration of optically active electrons. What 2s+1Lj components originate in this configuration? Assume that Hund's rules hold for the multiplet and deduce the ordering of the energy levels. Refer to a table of beryllium levels to see if the ordering occurs as predicted.

## Homework Equations

l=|l1-l2|,|l1-l2|+1,...,l1+l2-1,l1+l2

j=|l-s|,|l-s|+1,...,l+s-1,l+s

## The Attempt at a Solution

spin-orbital assignments of 2s2p configuration:
(l1=0,s1=1/2) and (l2=1,s2=1/2)

So that,
total spin states: s=0 and 1
and
l=0,1, and 2
......?
I don't know what to do next.

Answer at the back of the book:
3P0,1,2,1P1

You pretty much have it. Except, I don't believe you calculated the possible l values properly.

|1-0|=1, so only l=1 works.

Now, all you have to do is use Hund's rules to find the order.

Last edited:

## 1. How do you determine the electron configuration of an atom using LS coupling?

To determine the electron configuration using LS coupling, you need to first identify the number of electrons in the atom. Then, you can use the Aufbau principle to fill the orbitals in order of increasing energy. For the 2s2p configuration, the 2s orbital is filled with 2 electrons and then the 2p orbital is filled with 2 electrons. This results in a total of 4 electrons in the 2s2p configuration.

## 2. What is the significance of LS coupling in determining electron configurations?

LS coupling, also known as Russell-Saunders coupling, is a model used to describe the electron configuration of an atom. It takes into account the spin and orbital angular momentum of electrons and allows for a more accurate representation of the atom's energy levels and electron arrangements.

## 3. How do you find the components of the 2s2p configuration using LS coupling?

To find the components of the 2s2p configuration using LS coupling, you can use the LS coupling scheme to determine the total angular momentum (J) and its corresponding energy level. This will give you the components of the configuration, which can be represented as (2S+1)LJ, where S is the total spin quantum number, L is the total orbital angular momentum quantum number, and J is the total angular momentum quantum number.

## 4. How does LS coupling differ from other coupling schemes?

LS coupling differs from other coupling schemes, such as jj coupling, by taking into account the spin and orbital angular momentum of electrons separately. In LS coupling, the spin and orbital angular momentum of electrons are first added together to get the total angular momentum, whereas in jj coupling, the individual angular momenta of each electron are added together to get the total angular momentum.

## 5. Can LS coupling be used for atoms with more than 4 electrons in the 2s2p configuration?

Yes, LS coupling can be used for atoms with more than 4 electrons in the 2s2p configuration. The same principles apply for determining the components of the configuration, but the total angular momentum quantum number (J) may be different depending on the number of electrons. For example, in the 2s2p3 configuration, the total angular momentum (J) would be 3/2 or 5/2, depending on the spin quantum number of the third electron in the 2p orbital.

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