Problem 63 - A Complete Resource Book in Chemistry for JEE Main

Question

The atomic numbers of elements \(\mathrm{X}, \mathrm{Y}, \mathrm{Z}\) are \(19.21\) and 25 respectively. The number of electrons present in the 'M' shells of these elements follow the order (a) \(\mathrm{Z}>\mathrm{Y}>\mathrm{X}\) (b) \(\mathrm{X}>\mathrm{Y}>\mathrm{Z}\) (c) \(\mathrm{Z}>\mathrm{X}>\mathrm{Y}\) (d) \(\mathrm{Y}>\mathrm{Z}>\mathrm{X}\)

Step-by-Step Solution

Answer

Option (a): Z > Y > X

Step 1: Understanding Electron Configuration

Each electron shell corresponds to a principal quantum number, and the first three shells (K, L, M) can hold 2, 8, and 18 electrons respectively. The 'M' shell corresponds to the third energy level, which can hold up to 18 electrons.

Step 2: Determine Electron Configuration for Element X (Atomic Number 19)

For element X: The electron configuration will distribute the 19 electrons as follows: - K shell: 2 electrons - L shell: 8 electrons - M shell: 9 electrons Thus, there are 9 electrons in the M shell.

Step 3: Determine Electron Configuration for Element Y (Atomic Number 21)

For element Y: The electron configuration will distribute the 21 electrons as follows: - K shell: 2 electrons - L shell: 8 electrons - M shell: 11 electrons Thus, there are 11 electrons in the M shell.

Step 4: Determine Electron Configuration for Element Z (Atomic Number 25)

For element Z: The electron configuration will distribute the 25 electrons as follows: - K shell: 2 electrons - L shell: 8 electrons - M shell: 13 electrons Thus, there are 13 electrons in the M shell.

Step 5: Compare the Number of Electrons in the M Shell

Comparing the number of electrons in the M shell: - Element Z: 13 electrons - Element Y: 11 electrons - Element X: 9 electrons The order is Z > Y > X.

Key Concepts

Principal Quantum Number

The principal quantum number is a critical concept in atomic structure and electron configuration. It is denoted by the symbol \( n \) and indicates the size of the electron shell. Each electron shell is assigned a principal quantum number, with \( n = 1 \) for the first shell (K shell), \( n = 2 \) for the second shell (L shell), and \( n = 3 \) for the third shell (M shell).
The principal quantum number signifies the primary energy level of an electron. As the value of \( n \) increases, the shell is positioned further away from the nucleus, and the potential energy increases as well. This is because higher energy levels or shells have more space and thus accommodate more electrons. The numbers of electrons each shell can hold are as follows:

• K shell (\( n = 1 \)): 2 electrons
• L shell (\( n = 2 \)): 8 electrons
• M shell (\( n = 3 \)): 18 electrons

Understanding the concept of principal quantum numbers helps us determine how electrons are distributed throughout an atom's electron shells.

Electron Shells

Electron shells are like layers surrounding an atom's nucleus, where electrons reside. Each shell corresponds to a specific energy level, and the closer the shell is to the nucleus, the lower its energy. The shells are often labeled as K, L, M, and so forth.
Each shell can hold a fixed number of electrons, determined by its maximum capacity. This is crucial to the stability and properties of the atom. The electron configuration that describes how electrons are distributed among these shells reflects both energy considerations and the principle of electron pairing. Here is the maximum number of electrons each shell can hold:

• K shell (1st shell): 2 electrons
• L shell (2nd shell): 8 electrons
• M shell (3rd shell): 18 electrons

As more electrons are added to an atom, they fill the inner shells first before moving to outer shells. This orderly filling is dictated by energy efficiency and stability of the electron arrangement.

Atomic Number

The atomic number of an element is fundamental to its identity and properties. It is the number of protons present in the nucleus of an atom, and it uniquely defines an element. For neutral atoms, the atomic number also equals the number of electrons orbiting the nucleus.
Knowing the atomic number allows us to determine the electron configuration of an element, which in turn influences the chemical behavior of the element. For example, in the exercise, elements X, Y, and Z have atomic numbers 19, 21, and 25, respectively. This sequence informs us of their electron distributions across different shells.
Since the atomic number affects electron configuration, it plays a crucial role in periodic table arrangements and helps predict the properties and reactivities of elements.

Electron Distribution

Electron distribution refers to how electrons are arranged in an atom's electron shells. This distribution is key to understanding the chemical properties and reactivity of the element.
Electrons are added to shells starting from the innermost, based on the principle of minimum energy. In our specific exercise involving elements X, Y, and Z:

• X, with 19 electrons, distributes these as 2 in the K shell, 8 in the L shell, and the remaining 9 in the M shell.
• Y, with 21 electrons, has 2 electrons in the K shell, 8 in the L shell, and 11 in the M shell.
• Z, with 25 electrons, is distributed as 2 in the K shell, 8 in the L shell, and 13 in the M shell.

This electron distribution is vital, as it determines how chemically reactive each element is and influences their potential to form bonds with other elements forming compounds.