Problem 13 - A Complete Resource Book in Chemistry for JEE Main

Question

Number of orbitals in \(L\) energy level (a) 1 (b) 2 (c) 3 (d) 4

Step-by-Step Solution

Answer

The correct answer is (d) 4.

Step 1: Identify the Energy Levels

The energy levels in an atom are denoted by the principal quantum number, represented by the letter \( n \). The letter \( L \) corresponds to \( n = 2 \).

Step 2: Determine the Sublevels for Principal Quantum Number

For a given principal quantum number \( n \), there are \( n \) sublevels identified by the azimuthal quantum number \( l \). For \( n = 2 \), we have \( l = 0 \) (s sublevel) and \( l = 1 \) (p sublevel).

Step 3: Count the Orbitals in Each Sublevel

The number of orbitals in a sublevel is given by \( 2l + 1 \). For \( l = 0 \) (s sublevel), there is \( 2(0) + 1 = 1 \) orbital. For \( l = 1 \) (p sublevel), there are \( 2(1) + 1 = 3 \) orbitals.

Step 4: Calculate Total Number of Orbitals

Add the orbitals from all sublevels within the \( n = 2 \) energy level: 1 (from the s sublevel) + 3 (from the p sublevel) = 4 orbitals.

Key Concepts

Principal Quantum Number

In atomic physics, the principal quantum number is one of the essential components for understanding atomic orbitals. It is denoted by the letter \( n \) and plays a pivotal role in defining the energy levels of an atom. The principal quantum number essentially determines the size and energy of an atomic orbital. The larger the value of \( n \), the further the electron's distance from the nucleus.

• The principal quantum number values range from 1 to infinity.
• Each value of \( n \) represents a specific electron shell.
• Higher \( n \) values signify higher energy levels.

When understanding the atomic structure, the principal quantum number holds the key to identifying the various energy levels in atoms. This knowledge lays the foundation for diving deeper into the atom's sublevel organization.

Azimuthal Quantum Number

The azimuthal quantum number, denoted by \( l \), is crucial for identifying sublevels within an electron shell. By specifying the subshell or sublevel type, it gives us more insight into the orbital shape and angular momentum than the principal quantum number alone.

• Its value ranges from 0 to \( n-1 \), where \( n \) is the principal quantum number.
• It determines the subshell or shape of the orbital: for example, \( l = 0 \) (s-subshell), \( l = 1 \) (p-subshell).
• The different subshells have distinct geometries: s-subshells are spherical, while p-subshells are dumbbell-shaped.
• Each subshell contains orbitals, specified by the azimuthal quantum number.

Understanding the azimuthal quantum number empowers students to comprehend the complex structure and classification of atomic orbitals.

Energy Levels in Atoms

Energy levels in atoms are a tiered and organized way of describing where electrons reside. These levels are determined by the principal and secondary quantum numbers, ensuring an electron's properties and position around the nucleus can be mapped out.

• Energy levels are labeled by the principal quantum number \( n \).
• Each main energy level can be subdivided into sublevels defined by the azimuthal quantum number \( l \).
• The combination of energy levels and sublevels dictates the electron configuration of an atom.

As these energy levels increase with higher \( n \) values, the energy required to keep an electron at that level also increases. Therefore, electrons fill or occupy these levels from the lower energy close to the nucleus and outward to higher energy levels. Decoding this structure is key in understanding chemical properties and bonding behaviors.