Question

The chance of finding an s-electron in any particular direction from the nucleus is (1) proportional to the value of its principal quantum number (2) the same (3) dependent on the direction (4) zero

Short answer

The same

Step-by-step solution

Understand the Role of an s-electron

An s-electron is an electron in an s-orbital. The s-orbitals are spherical, meaning the probability density of finding the electron is uniform in all directions from the nucleus.

Analyze the Spherical Symmetry

Since s-orbitals are spherical, the electron density does not depend on the direction. This means the probability of finding an s-electron is identical in all directions.

Compare each choice

1. Proportional to the value of its principal quantum number: Incorrect, the distribution does not depend on principal quantum number.2. The same: Correct, because s-orbitals have the same electron probability in all directions.3. Dependent on the direction: Incorrect, as explained the distribution is uniform.4. Zero: Incorrect as the probability is not zero in any direction.

Key concepts

s-orbital

An s-orbital is one of the basic types of orbitals in an atom. Each orbital defines a region around the nucleus where the probability of finding an electron is high.

Its shape is spherical, which means it is similar to a 3D ball centered around the nucleus.

Important points about s-orbitals:

• Exist in every electron shell of an atom.
• Have no angular nodes, meaning their probability density is uniformly distributed around the nucleus.
• Can hold a maximum of 2 electrons.

The spherical nature of s-orbitals explains why electrons within them have the same probability of being detected in any direction from the nucleus.

electron density distribution

Electron density distribution describes how electrons are spread out in an atom. In an s-orbital, this distribution is particularly simple and uniform.

When visualizing an s-orbital, imagine this:

• The nucleus is in the center.
• The electron density spreads out uniformly in a spherical manner around the nucleus.

This means that wherever you measure around this sphere, the likelihood of finding an electron is the same. It is crucial to remember:

• The higher the electron density in a region, the higher the probability of finding an electron there.
• In s-orbitals, there's no preferred direction, making the density evenly distributed.
• This even distribution leads to crucial properties such as equal electron probability in all directions.

Understanding this concept helps grasp the nature of chemical bonds and reactions.

spherical symmetry

Spherical symmetry is a vital characteristic of s-orbitals. It means that the system looks the same from any point on the surface of a sphere.

This can be visualized by thinking of a globe. If you were to stand on any point on the surface of a sphere (earth, for example) and look around, all directions would appear the same. This is analogous to the electron density in an s-orbital.

Key aspects of spherical symmetry:

• It does not matter where you look around the nucleus; the probability of finding an s-electron remains the same.
• This symmetry simplifies understanding atom behavior because it ensures uniformity.
• This property is unique and significant as other orbital shapes like p, d, and f do not exhibit such symmetry.

Spherical symmetry helps in predicting and explaining the behavior of electrons in different chemical scenarios.