Question

Probability of finding the electron \(\psi^{2}\) of s orbital doesn't depend upon: (a) Azimuthal quantum number. (b) Energy of s orbital. (c) Principal quantum number. (d) Distance from nucleus (r).

Short answer

The probability does not depend on the azimuthal quantum number.

Step-by-step solution

Understand the Electron Probability Distribution

The probability of finding an electron in a given region is described by the square of the wave function, \(\psi^2\), which is related to the orbital shape and its associated symmetry.

Focus on S Orbital Characteristics

S orbitals are spherical in shape and their probabilities depend upon the distance from the nucleus (r). They exhibit equal probability distribution in all directions.

Identify Quantum Numbers Affecting S Orbital

The principal quantum number (n) affects the size and energy of the orbital, including the s orbital. The azimuthal quantum number (l), also known as the angular momentum quantum number, is zero for s orbitals.

Distance and Energy Dependence

The probability \(\psi^2\) is affected by the principal quantum number (n) because it changes with the radial distribution of electrons within the orbital. It also depends on the energy level as different energy levels have different radial distributions.

Determine What Does Not Affect \\(\psi^2\\)

For s orbitals, the azimuthal quantum number does not influence the shape or probability distribution since it is always zero, as they have radial symmetry.

Key concepts

S Orbital

The s orbital is an essential topic in the study of electron probability distribution in atoms. When looking at s orbitals, imagine a sphere surrounding the nucleus in which the electron is likely to be found. This spherical shape is unique to s orbitals and means the probability of finding an electron is uniform, or equal, in all directions around the nucleus.

The term "s orbital" refers to orbitals with zero angular momentum, meaning their azimuthal quantum number (\(l\)) is zero. This results in a complete spherical symmetry without any nodal planes. As electrons reach higher energy levels, they remain in spherical s orbitals with larger radii. These larger s orbitals still maintain their spherical symmetry but extend further from the nucleus, accommodating electrons of higher energy.

• Spherical shape of s orbitals enables a simple understanding of electron probability.
• S orbitals are found in every principal quantum level starting from the first level (n=1).
• The size of s orbitals increases with the principal quantum number.

Azimuthal Quantum Number

The azimuthal quantum number, also known as the angular momentum quantum number (\(l\)), is crucial for understanding the shape and characteristics of electron orbitals. For s orbitals, the azimuthal quantum number is always zero. This simplifies the calculations and behaviors associated with s orbitals, as their shape does not vary with different values of \(l\).

The value of \(l\) determines the number of angular nodes and the geometry of the orbitals. However, since \(l\) is zero for s orbitals, these orbitals do not have any angular nodes. Instead, they have a pure radial probability distribution.

• Azimuthal quantum number defines the sublevel of an electron within an atom.
• For s orbitals, \(l\) is always zero, indicating a spherical shape without angular nodes.
• This makes s orbitals unique and easy to work with because they have uninterrupted radial symmetry.

Principal Quantum Number

The principal quantum number (\(n\)) is significant when considering the size and energy levels of the electron orbitals. This number indicates the primary energy level of the electron within an atom and influences the size of the orbital.

As \(n\) increases, the size of the orbital and its distance from the nucleus also increase. This means that for higher principal quantum numbers, s orbitals are larger, allowing for a more extensive radial distribution of electrons.

Since \(n\) also describes the energy associated with the electron's location, it affects the electron probability distribution by altering the radial extent of the orbital.

• \(n\) values begin at 1 and increase as energy levels increase.
• Larger \(n\) results in larger orbital sizes and greater distance from the nucleus.
• Influences both the electron's energy and its probable location within an atom.