Problem 23 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

A \(3 p\) orbital has : (a) two non spherical nodes (b) two spherical nodes (c) one spherical \& one non spherical node (d) one spherical and two non spherical nodes

Step-by-Step Solution

Answer

(c) one spherical & one non spherical node

Step 1: Understanding Orbital Nodes

In quantum chemistry, orbital nodes are regions where the probability of finding an electron is zero. There are two types of nodes: radial nodes, which are spherical, and angular nodes, which are non-spherical.

Step 2: Determining Node Count Formula

The number of radial nodes in an orbital can be determined using the formula: \(\text{Radial nodes} = n - l - 1\) where \(n\) is the principal quantum number and \(l\) is the azimuthal quantum number. Angular nodes are equal to \(l\).

Step 3: Identifying Quantum Numbers for 3p Orbital

For a 3p orbital, the quantum numbers are: \(n = 3\) (principal quantum number) and \(l = 1\) (azimuthal quantum number because 'p' orbitals have \(l = 1\)).

Step 4: Calculating Radial Nodes

Using the formula \(\text{Radial nodes} = n - l - 1\):\[\text{Radial nodes} = 3 - 1 - 1 = 1\]Hence, there is one radial node.

Step 5: Calculating Angular Nodes

The number of angular nodes is equal to \(l\), which for a p orbital is 1. Therefore, there is one angular node.

Step 6: Summarizing Node Types

For a 3p orbital, there is one spherical (radial) node and one non-spherical (angular) node, matching option (c).

Key Concepts

Understanding Quantum Numbers

Quantum numbers are like the address for electrons in an atom, helping us know where they might be found. There are four kinds of quantum numbers, and each tells us something unique about an electron’s position and energy.

• Principal Quantum Number ( ): This number indicates the size of the orbital and relates directly to the energy level an electron occupies. It's often denoted by an integer (1, 2, 3, etc.).
• Azimuthal Quantum Number ( ): This tells us the shape of the orbital. For example, =0, 1, 2, 3 corresponds to s, p, d, f orbitals respectively.
• Magnetic Quantum Number ( ): Indicates the orientation of the orbital in space.
• Spin Quantum Number ( ): Represents the direction of the electron's spin. It can be either +1/2 or -1/2.

The principal ( ) and azimuthal ( ) quantum numbers are particularly important for understanding nodes in an orbital, as they directly influence the number of radial and angular nodes present.

What are Radial Nodes?

Radial nodes are spherical regions within an atom's orbitals where the likelihood of finding electrons is zero. The more radial nodes an orbital has, the more complex its structure and energy level.How to Calculate Radial Nodes:The formula to determine the number of radial nodes is simple: \[\text{Radial nodes} = n - l - 1\]Where:

• is the principal quantum number, indicating the energy level and size of the orbital.
• is the azimuthal quantum number, which defines the shape of the orbital.

In the case of a 3p orbital, =3 and =1. By plugging these values into the formula, we get 1 radial node, showing one sphere where finding an electron is impossible.

Exploring Angular Nodes

Angular nodes are non-spherical regions where the probability of finding an electron is zero. Unlike radial nodes, which are related to the distance from the nucleus, angular nodes correspond to specific orientations in space. Number of Angular Nodes: The number of angular nodes is equal to the azimuthal quantum number ( ), directly correlating to the shape of the orbital:

• For s orbitals, =0, meaning no angular nodes.
• For p orbitals, =1, resulting in one angular node.
• For d and f orbitals, =2 and =3 respectively, leading to more complex node patterns.

In the 3p orbital situation, there is one angular node. This non-spherical node helps define the 'lobes' characteristic of p orbitals.