Problem 151 - A Complete Resource Book in Chemistry for JEE Main

Question

How many electrons are present in Si atom corresponding to \(l=1\) ?

Step-by-Step Solution

Answer

Silicon has 6 electrons with quantum number \(l=1\).

Step 1: Understand the Electron Configuration of Silicon

Silicon (Si) has an atomic number of 14, which means it has 14 electrons. The distribution of these electrons in its atomic orbitals follows the principle of filling from lower to higher energy levels: 1s, 2s, 2p, 3s, and finally 3p.

Step 2: Identify Orbitals with Quantum Number l = 1

Quantum number \(l\) represents the orbital angular momentum and \(l=1\) corresponds to the 'p' orbitals. In silicon, this includes the 2p and 3p orbitals.

Step 3: Count Electrons in l = 1 Orbitals

Silicon has 6 electrons in total within the \(l=1\) orbitals: 2 electrons in the 2p orbital and 4 electrons in the 3p orbital.

Key Concepts

Quantum Numbers

Quantum numbers are like addresses for electrons. They tell us where we might find an electron within an atom. In essence, they help describe the size, shape, and orientation of the atomic orbitals, where electrons are likely to be found.

There are four types of quantum numbers:

• The principal quantum number (\( n \)) describes the energy level of an electron, determining its distance from the nucleus. Larger \( n \) values mean electrons are farther away.
• Angular momentum quantum number (\( l \)) is related to the shape of the orbital. Specifically, when \( l = 0 \), it's an 's' orbital; \( l = 1 \) indicates 'p' orbitals; \( l = 2 \) corresponds to 'd', and \( l = 3 \) correlates with 'f'. Each type has a unique shape.
• Magnetic quantum number (\( m_l \)) specifies the orientation of the orbital in space. It can take on values from \( -l \) to \( +l \)
• The spin quantum number (\( m_s \)) can either be \( +\frac{1}{2} \) or \( -\frac{1}{2} \), denoting the direction of the electron's spin.

Atomic Orbitals

Atomic orbitals are zones where electrons are most likely to be found around an atom's nucleus. Think of these as 'clouds' of probable locations for electrons.

Each type of orbital has a distinct shape:

• s orbitals are spherical, like a round balloon around the nucleus. They exist at every energy level (all \( n \) values).
• p orbitals are peanut-shaped and appear from the second energy level upwards.\( l = 1 \) describes these p orbitals, and they can hold a maximum of six electrons, spread across three sub-orbitals.
• d orbitals are more complex, resembling clover shapes, and appear from the third energy level.
• f orbitals are even more intricate, emerging from the fourth energy level.

Atomic Number

The atomic number of an element is a fundamental property that tells us the number of protons found in the nucleus of an atom. For neutral atoms, it also indicates the number of electrons.

This number is crucial because:

• It determines the identity of the element. For instance, silicon (Si) has an atomic number of 14, meaning each silicon atom has 14 protons.
• It gives a clue about the electron configuration. With 14 electrons, silicon fills its orbitals starting from the lowest energy level.
• It's used to order elements in the Periodic Table. This ordering helps predict and understand chemical behaviors.