Question

Which orbital is nearest to the nucleus after filling with electrons? (1) \(5 \mathrm{~d}\) (2) \(6 \mathrm{~s}\) (3) 6p (4) \(4 \mathrm{f}\)

Short answer

4f

Step-by-step solution

- Understanding Electron Orbitals

Electrons occupy different orbitals based on their energy levels. The principal quantum number (n) determines the energy level of an orbital, and within each energy level, the type of orbital (s, p, d, f) affects the energy order.

- Identifying Principal Quantum Numbers

Identify the principal quantum numbers (n) for each given orbital:(1) 5d: n = 5(2) 6s: n = 6(3) 6p: n = 6(4) 4f: n = 4

- Determining Energy Levels

The lower the principal quantum number, the closer the orbital is to the nucleus. For the given options, compare the principal quantum numbers:- 5d: n=5- 6s: n=6- 6p: n=6- 4f: n=4

- Identifying the Nearest Orbital

Since the 4f orbital has the lowest principal quantum number (n=4), it is the nearest to the nucleus after being filled with electrons.

Key concepts

Principal Quantum Number

The principal quantum number, represented by the symbol \(n\), is a fundamental concept in quantum mechanics that denotes the major energy levels in which an electron can exist. Each energy level corresponds to a different distance from the nucleus. Electrons in lower principal quantum numbers are closer to the nucleus and generally have lower energy.
The principal quantum number can take any positive integer value (1, 2, 3, ...), each representing a different electron shell. For example:

• \(n = 1\) is the first energy level.
• \(n = 2\) is the second energy level.
• \(n = 3\) is the third energy level.

Understanding the principal quantum number is crucial as it helps determine an electron's probable location around the nucleus and its associated energy.

Energy Levels

Energy levels are specific regions around an atom's nucleus where electrons reside. Each level corresponds to a different amount of energy. The concept of energy levels is essential to the Electron Configuration of atoms.
Electrons tend to occupy the lowest available energy levels first, which is known as the Aufbau principle. In the context of energy levels:

• Electrons in the lowest energy levels are closest to the nucleus.
• Higher energy levels are further away from the nucleus and have more energy.

For instance:

• The 1s orbital (=1) is closest to the nucleus.
• Other higher orbitals such as 2s, 2p, 3s, and so on, are farther away and have higher energy.

This principle helps us predict where electrons are generally located in an atom.

Orbital Types

Orbitals are regions in an atom where there is a high probability of finding electrons. Different types of orbitals (s, p, d, and f orbitals) have distinct shapes and orientations.
Here is a quick overview of each type:

• s-orbitals: Spherical in shape. One s-orbital per energy level.
• p-orbitals: Dumbbell-shaped and oriented along three axes (x, y, z). There are three p-orbitals per energy level after the first (starting at \( n=2 \)).
• d-orbitals: More complex shapes, including cloverleaf patterns. There are five d-orbitals per energy level starting at \( n=3 \).
• f-orbitals: Even more complex shapes. Seven f-orbitals per energy level starting at \( n=4 \).

Different orbital types within the same energy level have slightly different energies. For example, within the fourth energy level:

• =4, there can be 4s, 4p, 4d, and 4f orbitals.

This understanding is crucial for determining electron configurations and explaining the chemical behavior of elements.