How Can J Be a Fraction in Spectroscopic Notation?

In summary, spectroscopic notation is a system used to represent the energy levels and orbitals of electrons in an atom. It is important for communication and understanding of electron configuration, as well as providing insight into the properties and interactions of elements. It is written with numbers and letters representing energy levels and sublevels, and the number of electrons in each sublevel. It differs from orbital notation in that it does not show the spin of electrons, and it can be determined using the diagonal rule or Aufbau principle.
  • #1
MariusM
12
0

Homework Statement


Consider a [itex]^3D_X[/itex] where [itex]X=3/2[/itex] state.

a) What are the possible values of [itex]S, L, J[/itex] and [itex]J_z[/itex]?

Homework Equations


Spectroscopic notation for this LS coupling is [itex]^YL_J[/itex] where [itex]Y=2S+1[/itex]. [itex]J[/itex] ranges from[itex]|L-S|[/itex] to [itex]|L+S|[/itex]

The Attempt at a Solution


Since [itex]L=2[/itex] and [itex]S[/itex] must be equal to [itex]1[/itex], how can [itex]J[/itex] be a fraction? Shouldn't [itex]J[/itex] be either [itex]1, 2, 3[/itex]?
 
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  • #2
You are absolutely right. The problem is incorrect as it stands.
 
  • #3
Thanks for helping me clarify this!
 

FAQ: How Can J Be a Fraction in Spectroscopic Notation?

What is spectroscopic notation?

Spectroscopic notation is a system used to represent the energy levels and orbitals of electrons in an atom. It uses letters and numbers to denote the energy level, sublevel, and the number of electrons in that sublevel.

Why is spectroscopic notation important?

Spectroscopic notation allows scientists to easily communicate and understand the electron configuration of an atom. It also provides insight into the physical and chemical properties of elements and how they interact with other elements.

How is spectroscopic notation written?

Spectroscopic notation is written with the energy level number followed by the letter of the sublevel. The sublevel letters are s, p, d, and f, representing the different shapes of the orbitals. The number of electrons in the sublevel is written as a superscript next to the sublevel letter.

What is the difference between orbital notation and spectroscopic notation?

Orbital notation uses arrows to represent the spin of electrons in each orbital, while spectroscopic notation uses numbers to represent the number of electrons in each sublevel. Orbital notation is more detailed and specific, while spectroscopic notation is a more simplified representation.

How do you determine the electron configuration using spectroscopic notation?

To determine the electron configuration using spectroscopic notation, you can use the diagonal rule, also known as the Aufbau principle. This principle states that electrons fill orbitals in order of increasing energy, with the lowest energy level being filled first.

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