Question

The orbital diagram in which Aufbau principle is violated is: (a) \(\prod \downarrow|\widehat{\uparrow} \downarrow| \uparrow \mid\) (b) \(\widehat{\uparrow} \prod \downarrow \uparrow \mid \uparrow\) (c) \(\left.\prod \downarrow\right]{\uparrow} \uparrow \mid \uparrow\) (d) \(\prod \downarrow[\uparrow \downarrow \mid \uparrow \downarrow \uparrow\)

Short answer

Option (b) violates the Aufbau principle.

Step-by-step solution

Understanding the Aufbau Principle

The Aufbau Principle states that electrons fill orbitals starting from the lowest energy level to the highest. Electrons fill orbitals in a specific order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, etc. Electrons do not fill higher energy orbitals if a lower energy orbital is empty.

Analyze Option (a)

The diagram (a) \( \prod \downarrow|\widehat{\uparrow} \downarrow| \uparrow \mid \) indicates that there is an electron in a higher energy orbital while a lower energy orbital should have been filled earlier. However, since we do not have energy levels specified here, further analysis in the other options might be necessary.

Analyze Option (b)

For option (b) \( \widehat{\uparrow} \prod \downarrow \uparrow \mid \uparrow \), observe that a higher energy orbital appears to be occupied by electrons without due progression from lower energy levels in the absence of specified energy levels, suggesting a potential problem.

Analyze Option (c)

In option (c) \( \left.\prod \downarrow\right]{\uparrow} \uparrow \mid \uparrow \), this appears to follow the normal flow of electron placement but lacks specific context on energy levels.

Analyze Option (d)

The diagram (d) \( \prod \downarrow[\uparrow \downarrow \mid \uparrow \downarrow \uparrow \) suggests proper filling in terms of electron orbital occupation as all lower energy orbitals seem filled before proceeding to higher ones.

Draw Conclusion

Without specific levels, assumptions must be drawn from given options. It seems that in (b), electrons do not fill orbitals as expected through the normal low-to-high scheme of energy level filling per Aufbau. Therefore, option (b) violates the Aufbau Principle the most based on the given sequence.

Key concepts

Electron Configuration

Electron configuration is the arrangement of electrons within an atom or molecule. It is crucial to understand it because it determines how atoms will interact with each other, influencing chemical reactions and bonding.
In most atoms, electrons occupy energy levels or shells, closest to the nucleus first, before filling more distant shells. This ordering is guided by principles such as the Aufbau Principle.
To represent electron configuration, physicists use a notation consisting of numbers, letters, and superscripts. The numbers denote energy levels, letters specify the type of orbital (s, p, d, f), and superscripts indicate the number of electrons in those orbitals.

• For example, the electron configuration of carbon is written as: 1s² 2s² 2p², illustrating that carbon has two electrons in the 1s orbital, two in the 2s orbital, and two in the 2p orbital.

Orbital Diagrams

Orbital diagrams offer a visual representation of electron configurations, illustrating how electrons are distributed among the orbitals of an atom.
These diagrams use boxes or circles to depict orbitals and arrows to show electrons.
Each arrow represents an electron, and the arrow’s direction indicates its spin.

• For example, an orbital diagram for helium would show one box with two arrows pointing in opposite directions, since helium has two electrons filling a single 1s orbital.

Orbital diagrams can be very useful when examining whether an atom complies with the electron filling rules, such as the Aufbau Principle and Hund's Rule.
This makes them essential for recognizing any violations in electron configurations that might occur if these rules aren't followed.

Energy Levels

Energy levels, often referred to as electron shells, are fixed distances from the nucleus of an atom where electrons are likely to be found.
Each level can hold a certain maximum number of electrons: the closer the energy level to the nucleus, the fewer electrons it can accommodate.

• The first energy level can hold up to 2 electrons.
• The second can hold up to 8 electrons.
• As you move to higher energy levels, the capacity increases, allowing for more complex electron arrangements.

When electrons fill an atom's energy levels, they typically start at the lowest available energy level and fill higher levels only when lower ones are at full capacity.
This ordered filling is crucial for maintaining the most stable electron configuration possible. The understanding of this structure helps in predicting how an atom will react chemically and form bonds with other atoms.