Question

In the ground state of carbon atom has unpaired electrons: (a) 4 (b) 3 (c) 2 (d) \(\mathrm{No}\)

Short answer

There are 2 unpaired electrons (option c).

Step-by-step solution

Determine Electronic Configuration

To find the number of unpaired electrons in a carbon atom, determine its electronic configuration. Carbon has an atomic number of 6, which means it has 6 electrons. The electronic configuration is: \( 1s^2 2s^2 2p^2 \).

Analyze the p Orbital

In the electronic configuration \( 1s^2 2s^2 2p^2 \), focus on the 2p electrons because they are responsible for unpaired electrons. The 2p subshell can hold up to 6 electrons and consists of three degenerate orbitals: \( 2p_x, 2p_y, \) and \( 2p_z \).

Apply Hund's Rule

According to Hund's Rule, electrons will fill empty orbitals before pairing up. Since the 2p subshell has two electrons, one electron will go into each of two separate p orbitals (\( 2p_x \) and \( 2p_y \)), both remaining unpaired. Thus, carbon has two unpaired electrons.

Key concepts

Atomic Structure

Atomic structure is the arrangement of protons, neutrons, and electrons within an atom. Protons and neutrons form the nucleus at the center, while electrons orbit in shells or energy levels around the nucleus. The total number of protons, called the atomic number, defines the element.
For a carbon atom, the atomic number is 6, meaning there are 6 protons and, in a neutral atom, 6 electrons to balance the charge. These electrons arrangement is key to understanding how atoms interact with each other. Electrons are placed in various orbitals, following specific rules to form the electronic configuration.
In carbon's case, the electronic configuration is written as:

• 1s² (inner shell, 2 electrons)
• 2s² (second shell, next 2 electrons)
• 2p² (remaining 2 electrons in the second shell)

This configuration helps predict chemical bonding and magnetic properties of the atom, making it an essential part of chemistry.

Hund's Rule

Hund's Rule is a principle used to determine the electron arrangement in orbitals. It states that electrons will occupy separate orbitals of the same energy level before they start to pair up. This rule minimizes electron-electron repulsions, providing a more stable configuration.
Applying Hund's Rule to the carbon atom's 2p orbital requires considering how electrons fill these orbitals. The 2p orbital can hold a total of 6 electrons across its three sub-levels:

• 2pₓ
• 2p_y
• 2p_z

With only two electrons to fill these sub-levels, according to Hund's Rule, each of the electrons will fill an empty orbital (such as 2pₓ and 2p_y) rather than pair up in the same orbital. This left two electrons unpaired in carbon's ground state.

p Orbitals

p orbitals are one of the types of atomic orbitals where electrons are likely to be found. They come after the s orbitals when filling electron shells. Each p subshell contains three degenerate orbitals labeled as:

• 2pₓ
• 2p_y
• 2p_z

These orbitals have a unique dumbbell shape and can hold a maximum of two electrons each, following Pauli’s exclusion principle. Electrons fill these orbitals according to the aufbau principle and Hund’s rule.
For the carbon atom, which has a 2p² configuration, the p orbitals are partially filled, leading to two unpaired electrons because of the way electrons fill the orbitals in accordance with Hund's rule. Understanding p orbitals and their filling helps predict how atoms form bonds and interact with other atoms in chemical reactions.