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

8 electrons are present in \(l=1\) orbitals for Si.

Step 1: Understand Electron Configuration Basics

Silicon (Si) has an atomic number of 14, which means it contains 14 electrons when neutral. Electrons are arranged in different energy levels or shells around the nucleus of an atom. Each shell can hold a certain number of electrons, and these are filled according to specific rules.

Step 2: Review the Quantum Numbers

Quantum numbers are used to describe the position and energy of an electron in an atom. The azimuthal quantum number \(l\) specifies the shape of the orbital and can range from 0 to \(n-1\), where \(n\) is the principal quantum number. For \(l=1\), the orbitals are of type \(p\), which are found starting from the second energy level \(n=2\).

Step 3: Determine which Orbitals Correspond to \(l=1\)

Orbitals with \(l=1\) are \(p\) orbitals. They start at the second energy level, specifically in the \(2p\) and \(3p\) orbitals. Si has the electron configuration: \(1s^2 2s^2 2p^6 3s^2 3p^2\).

Step 4: Count the Electrons in \(p\) Orbitals

From the electron configuration \(1s^2 2s^2 2p^6 3s^2 3p^2\), we identify that the \(2p\) orbital has 6 electrons, and the \(3p\) orbital has 2 electrons. These are all the electrons present in \(l=1\) orbitals.

Step 5: Sum Up the Electrons

Add the electrons from the \(2p\) orbital and the \(3p\) orbital: \(6 + 2 = 8\) electrons. Therefore, there are 8 electrons in the \(p\) orbitals for silicon.

Key Concepts

Quantum Numbers

Quantum numbers play a crucial role in understanding how electrons are arranged within atoms. Think of them as an address system for electrons. Each quantum number gives a piece of information about an electron's position and energy:

• The principal quantum number, denoted by 'n', determines the primary energy level of an electron.
• The azimuthal quantum number, represented by 'l', specifies the shape of the orbital, which can range from 0 up to (n-1).
• The magnetic quantum number, symbolized as 'm', tells us about the orientation of the orbital within its shape.
• Finally, the spin quantum number indicates an electron's spin direction, which is either +1/2 or -1/2.

These quantum numbers together offer a detailed picture of where an electron resides in an atom.

Azimuthal Quantum Number

The azimuthal quantum number, designated as 'l', helps to define the shape of the electron cloud within an atom. It's like learning different shapes in a geometric class. The value of 'l' can be:

• 0 for 's' orbitals (spherical shape)
• 1 for 'p' orbitals (dumbbell shape)
• 2 for 'd' orbitals (more complex shapes)
• and so on.

For example, when 'l' is 1, we are dealing with 'p' orbitals, which play a significant role in determining the chemical properties of elements. Understanding this number is essential to predicting how atoms will interact in chemical bonding.

p Orbitals

When it comes to the 'p' orbitals, these are the spaces where electrons are likely to be found, and they have a distinctive dumbbell shape. 'p' orbitals are important for bonding and can hold a maximum of 6 electrons in total, distributed over three orientations. These three orientations, or different ways the orbital can be positioned, are labeled as 'p_x', 'p_y', and 'p_z'.

Each of these orientations can contain 2 electrons. 'p' orbitals begin from the second energy level; thus, starting from the 2p, we observe the filling of these orbitals. The unique shapes and orientations of 'p' orbitals allow elements to form different kinds of bonds, influencing molecular geometry and reactivity of the element.

Silicon Electron Configuration

Silicon, with its atomic number 14, has a specific way in which its electrons are arranged. The electron configuration provides a map of where all 14 electrons are distributed among the different orbitals. This arrangement is:

• 1s² ( 2 electrons in a spherical s-orbital in the first energy level)
• 2s² 2p⁶ ( 8 electrons in the second energy level, with 6 in the more complex p-orbitals)
• 3s² 3p² ( 4 electrons in the third energy level, again with 2 in the p-orbitals)

In silicon, this configuration plays a significant role in its properties, such as semiconducting characteristics and chemical behavior. Understanding this configuration helps us predict how silicon will bond and react with other elements.