Question

Write the electron configuration for the first excited state for \(\mathrm{N}_{2}\) - that is, the state with the highest-energy electron moved to the next available energy level. (a) Is the nitrogen in its first excited state diamagnetic or paramagnetic? (b) Is the \(\mathrm{N}-\mathrm{N}\) bond strength in the first excited state stronger or weaker compared to that in the ground state? Explain.

Short answer

The electron configuration of a nitrogen (\(\mathrm{N}_2\)) molecule in its first excited state is 1σ_g^21σ_u^22σ_g^22σ_u^23σ_g^23σ_u^21π_u^4. This configuration is diamagnetic, as there are no unpaired electrons. Compared to the ground state, the \(\mathrm{N-N}\) bond strength in the first excited state is weaker due to the presence of an additional antibonding orbital (3σ_u^1), which reduces the bond order.

Step-by-step solution

Ground-state electron configuration of nitrogen

First, we need to find the electron configuration for a single nitrogen (\(\mathrm{N}\)) atom in the ground state. Nitrogen has an atomic number of 7, which means it has 7 electrons. The electron configuration of nitrogen in the ground state is: 1s^22s^22p^3

First excited state of the nitrogen molecule

Next, we want to find the electron configuration for a nitrogen molecule (\(\mathrm{N}_2\)) in the first excited state. Since there are two nitrogen atoms in the molecule, we have a total of 14 electrons. The first excited state is obtained when we move the highest-energy electron (in this case, one of the 2p electrons) to the next available energy level (3s). The electron configuration of a nitrogen atom in its first excited state will be: 1s^22s^22p^23s^1 Now, considering both nitrogen atoms in the molecule, the electron configuration of the \(\mathrm{N_2}\) molecule in its first excited state will be: 1σ_g^21σ_u^22σ_g^22σ_u^23σ_g^23σ_u^21π_u^4

Paramagnetic or diamagnetic

To determine whether the nitrogen molecule in its first excited state is paramagnetic or diamagnetic, we should check whether its electron configuration has any unpaired electrons. In the given excited state configuration, every electron orbital has 2 electrons (paired electrons), so there are no unpaired electrons. Therefore, the nitrogen molecule in its first excited state is diamagnetic.

Comparing the bond strength

To compare the bond strength of the nitrogen molecule in its first excited state to that of the ground state, we will look at the electron configuration. In the ground state, the electron configuration of \(\mathrm{N}_2\) is: 1σ_g^21σ_u^22σ_g^22σ_u^21π_u^4 Comparing this with the electron configuration of the first excited state, we can see that the major difference is in the 3σ_u^1 for the excited state. This additional antibonding orbital will reduce the bond order in the first excited state, resulting in a weaker bond compared to the ground state. So, the \(\mathrm{N-N}\) bond strength in the first excited state is weaker compared to that in the ground state.

Key concepts

Excited States in Electron Configuration

When an atom or molecule like nitrogen ( \( \mathrm{N}_{2} \) ) transitions from a ground state to an excited state, it means that one or more electrons have moved from a lower energy level to a higher one.
This change happens when energy is absorbed, leading to an electron jumping to the next available orbital.

Think of it like the electron getting a temporary boost to climb up a ladder to a higher rung.

• Ground State: This is the lowest energy state of an atom or molecule, where electrons are in the nearest possible orbitals to the nucleus.
• First Excited State: In the case of the nitrogen molecule, an electron from the 2p orbital jumps to the 3s orbital.

The key outcome of this transition is seen in the electron configuration.
For example, in nitrogen's first excited state, the configuration includes a 3s orbital: \( 1s^22s^22p^33s^1 \).

Moving to an excited state is typically temporary, and the system will eventually return to its ground state by releasing energy. Understanding the excited states helps in analyzing the chemical behavior and properties of substances.

Paramagnetic vs. Diamagnetic States

Whether a substance is paramagnetic or diamagnetic depends on the electron configuration, specifically if there are unpaired electrons present.
The presence or absence of these unpaired electrons primarily influences the magnetic properties of the material.

• Paramagnetic: A paramagnetic substance has one or more unpaired electrons. These unpaired electrons align with external magnetic fields, making the substance attracted to magnets.
• Diamagnetic: A diamagnetic substance has all paired electrons, as seen in the first excited state of \( \mathrm{N}_{2} \). When all electrons are paired, they inherently cancel each other's magnetic moments. Thus, these substances are weakly repelled by magnetic fields.

In the case of nitrogen's first excited state, the lack of unpaired electrons makes it diamagnetic.
This property can be important in applications where materials need to minimize interactions with magnetic fields.

Understanding Bond Strength in Molecular States

The strength of a chemical bond indicates how tightly atoms are held together in a molecule. It is influenced by the number of bonding versus antibonding electrons.

Bond strength is represented by the bond order:

• Bond Order: Calculated as \((\text{Number of bonding electrons} - \text{Number of antibonding electrons})/2\).

When electrons are excited, they may occupy antibonding orbitals which can alter the bond strength.
For \( \mathrm{N}_{2} \), transitioning to the first excited state introduces electrons to a 3σ\_u orbital, being an antibonding orbital.
This addition weakens the bond because antibonding electrons counteract the stabilizing effect of bonding electrons.

Therefore, the nitroge-nitrogen bond in the excited state is weaker than in its ground state, because it lowers the overall bond order. A reduced bond order means the bond is less stable and more easily broken. Understanding this concept is crucial for predicting molecular behaviors in chemical reactions.