P Chem 2 8C Atomic Spectra

What is a "transition" in the context of atomic spectra?

A change of state in which an atom's energy changes by ΔE.

How is the frequency of a transition related to energy change?

Frequency is equal to the change in energy divided by Planck’s constant (ν = ΔE/h).

What does the wavenumber represent in atomic transitions?

Wavenumber represents the change in energy divided by Planck’s constant and the speed of light (ṽ = ΔE/hc)

What are the terms in atomic spectra?

Terms refer to the energy levels of an atom.

What is a selection rule in atomic spectra?

A statement that dictates which transitions between energy levels are allowed.

What transitions are forbidden for an s-electron?

An s-electron (l=0) cannot transition to another s-orbital.

What must occur for an atom or molecule to absorb or emit light?

It must temporarily have an oscillating dipole moment that matches the frequency of the light.

When is a transition forbidden?

A transition is forbidden if the transition dipole moment is zero.

What are the selection rules for hydrogenic atoms?

Δl = ±1, Δm_l = 0, ±1.

What is the role of the electric dipole moment in atomic transitions?

It determines whether the transition will occur, depending on the interaction between the dipole moment and the electric field of light.

What is a Grotrian diagram?

A diagram representing the energy levels of an atom and the allowed transitions between them

How do parallel and paired electron spins affect the state of an atom?

The state with parallel spins lies lower in energy than the paired-spin state

What generally happens to the energy of terms arising from the same configuration?

The triplet term generally lies lower in energy than the singlet term.

What is spin-orbit coupling?

The interaction of the electron's spin magnetic moment with the magnetic moment from the orbital angular momentum.

How does the strength of spin-orbit coupling affect energy levels?

It depends on the orientation of the spin and orbital magnetic moments.

When are total angular momentum and energy high or low in relation to the spin and orbital angular momenta?

Total angular momentum is high when the spin and orbital angular momenta are parallel and low when they are opposed.

What is the total angular momentum quantum number j for l=0 and l=1?

For l=0, j=1/2​, and for l=1, j=3/2 or 1/2​.

How is the strength of spin-orbit coupling related to nuclear charge?

The strength of spin-orbit coupling depends on nuclear charge; the greater the nuclear charge, the stronger the spin-orbit interaction.

How does spin-orbit coupling affect the energy of an unpaired electron in the ground state of an alkali metal atom?

The unpaired electron in the ground state of an alkali metal atom has l=0 and j=1/2​, so the spin-orbit coupling energy is zero.

What is the role of the spin-orbit coupling constant A?

The spin-orbit coupling constant A is used to calculate the spin-orbit interaction energy for an electron

What are some common operations involving vectors in the context of angular momentum?

Addition, subtraction, scalar product, and finding the square magnitude of vectors are common operations when working with angular momenta.

How does coupling strength relate to atomic number and the position of electrons relative to the nucleus?

Coupling strength increases sharply with atomic number because inner electrons are closer to the nucleus, except in hydrogen (H) and helium (He), where it is weak

What are the two spectral lines observed for alkali transitions to the s-orbital?

Two spectral lines are observed: one for j=3/2 and one for j=1/2.

What does the term symbol represent in atomic spectra?

The term symbol represents the total spin, total orbital angular momentum, and total overall angular momentum.

What are the components of a term symbol, such as 2P3/2​?

In 2P3/2​, the number 2 represents multiplicity (2S + 1), P represents total orbital angular momentum (L), and 3/2 represents total angular momentum (J)

What values can the magnetic quantum number (mL​) take?

The magnetic quantum number mLm_LmL​ can take values from −L to +L, including zero.

What does the total angular momentum quantum number J represent?

The total angular momentum quantum number J represents the combined spin and orbital angular momenta, with possible values ranging from L+SL to |L - S|

How is the total orbital angular momentum (L) determined for an electron configuration?

The total orbital angular momentum L is determined by adding and subtracting the individual orbital angular momenta of electrons, forming a series of values known as the Lande interval.

What are the orbital designations for L values?

The L values correspond to the following orbitals: L=0 (S), L=1 (P), L=2 (D), L=3 (F), L=4 (G), L=5 (H), L=6 (I).

What terms arise for a p² electron configuration in terms of total orbital angular momentum (L)?

For a p² configuration, L can have values of 2, 1, or 0, leading to D, P, and S terms, respectively.

Why do terms differ in energy for the same electron configuration?

Terms differ in energy due to differences in the spatial distribution of electrons and the repulsion between them

How is the orbital angular momentum of closed shells treated in atomic spectra?

Closed shells have zero orbital angular momentum and are typically not considered when calculating total angular momentum

How is the total spin quantum number (S) determined for multiple unpaired electrons?

S is determined by summing the individual spin quantum numbers of all unpaired electrons: S=S1+S2+S3−...

What is the multiplicity of a term, and how is it calculated?

The multiplicity of a term is given by 2S+1, where S is the total spin quantum number. A larger multiplicity corresponds to more unpaired electrons.

What must be considered if there are multiple electrons outside a closed shell?

The coupling of all spins and all orbital angular momenta must be considered when multiple electrons are outside a closed shell.

What is the difference between weak and strong spin-orbit coupling?

When spin-orbit coupling is weak, the R-S (Russell-Saunders) coupling scheme is used, where orbital angular momenta are coupled together separately from spins.

What is Russell-Saunders coupling, and when is it effective?

Russell-Saunders coupling is effective when spin-orbit coupling is weak, and all orbital angular momenta are added together to form a total orbital angular momentum, L, while spins are coupled separately.

How is the total angular momentum (J) calculated in the R-S coupling scheme?

Total angular momentum (J) is calculated by combining L and S, where J = L + S, L + S - 1, ..., |L - S|

What happens when L is less than S in a Russell-Saunders coupling?

When L is less than S, the multiplicity is equal to the number of levels, resulting in a series of terms.

What is jj-coupling, and when is it used?

jj-coupling is used when spin-orbit coupling is strong, particularly in heavy atoms with high atomic number (Z). In this scheme, each electron’s spin and orbital angular momenta are coupled individually.

What is Hund's first rule?

For a given electron configuration, the term with the greatest multiplicity lies lowest in energy.

What is Hund's second rule?

For a given multiplicity, the term with the highest value of L lies lowest in energy.

What is Hund's third rule?

For atoms with less than half-filled shells, the level with the lowest value of J lies lowest in energy, and for more than half-filled shells, the highest value of J lies lowest.

What are the selection rules for light atoms in atomic spectra?

The selection rules are:

• ΔS=0

• ΔL=0,±1

• ΔJ=0,±1

• J=0↔J=0 is forbidden.

What is a Grotrian diagram?

A Grotrian diagram is a graphical representation of the energy levels of an atom and the allowed transitions between them. It shows how electrons move between different energy states by absorbing or emitting photons.

What is spin-orbit coupling?

Spin-orbit coupling is a magnetic interaction between the electron's spin magnetic moment and its orbital magnetic moment, causing energy level splitting within an atom. The strength of the coupling depends on the atomic number, with heavier atoms experiencing stronger coupling.

How does spin-orbit coupling affect energy levels?

Spin-orbit coupling causes a term to split into multiple energy levels based on the relative orientation of spin and orbital angular momenta. States with parallel angular momenta have higher energy, while states with opposed angular momenta have lower energy.

What are term symbols, and what do they indicate?

Term symbols specify the angular momentum states of an atom. They indicate the total orbital angular momentum (L), multiplicity (2S+1), and total angular momentum (J). An example is 2P₃/₂, where 2 is the multiplicity, P corresponds to L = 1, and 3/2 is J.

What are the selection rules for transitions in light atoms?

The selection rules for light atoms are:

1. ΔS = 0

2. ΔL = 0, ±1 (but L = 0 ↔ L = 0 is forbidden)

3. ΔJ = 0, ±1 (but J = 0 ↔ J = 0 is forbidden)

What is the relationship between singlet and triplet terms?

Singlet terms arise when two electrons have paired spins, resulting in zero total spin angular momentum (S = 0). Triplet terms arise when two electrons have parallel spins, giving a total spin angular momentum of S = 1. Triplet terms are usually lower in energy than singlet terms.

What is the sodium D-line doublet, and why does it occur?

The sodium D-line doublet occurs due to spin-orbit coupling, which splits the p-orbital's energy levels into two distinct levels with slightly different energies. This causes two closely spaced spectral lines to appear in the visible spectrum around 589 nm.