Problem 11 - A Complete Resource Book in Chemistry for JEE Main

Question

The values of four quantum numbers of valence electron of an element are \(\mathrm{n}=4, l=0, \mathrm{~m}=0\) and \(\mathrm{s}=+1 / 2\) The element is (a) Ti (b) \(\mathrm{K}\) (c) \(\mathrm{Na}\) (d) \(\mathrm{Sc}\)

Step-by-Step Solution

Answer

The element is Potassium (K).

Step 1: Understand the Quantum Numbers

Quantum numbers describe the position and energy of an electron in an atom. Here, the given values are: Principal quantum number \( n = 4 \), azimuthal quantum number \( l = 0 \), magnetic quantum number \( m = 0 \), and spin quantum number \( s = +1/2 \). These indicate a configuration in a 4s orbital.

Step 2: Identify the Orbital from Quantum Numbers

With \( n = 4 \) and \( l = 0 \), the electron is in a 4s orbital. The possible orbitals when \( l = 0 \) corresponds to an 's' subshell. Therefore, the electron is uniquely positioned in the 4s orbital.

Step 3: Determine Which Element Has a 4s Valence Electron

The 4s orbital starts filling before the 3d when moving through the fourth period of the periodic table. The first element to house an electron in the 4s orbital is Potassium (\( K \)) as it is represented by the electron configuration [Ar] 4s¹, where the valence electron is in the 4s orbital.

Key Concepts

Valence Electron

Valence electrons are the electrons found in the outermost shell of an atom. These are crucial for determining an atom's chemical properties and its ability to form bonds with other atoms. Valence electrons are often responsible for the chemical reactivity and conductivity of an element.

• They participate in chemical bonding, both ionic and covalent.
• For example, in the case of potassium (K), the valence electron is located in the 4s orbital, which is its outermost electron that can participate in forming bonds.

Understanding which electrons are valence electrons helps in predicting how an element will react with others, and is fundamental in studying any element's behavior.

4s Orbital

Orbital refers to the region in an atom where an electron is likely to be found. When we talk about the 4s orbital, it means that the electron is located in the fourth energy level (n=4) and specifically in the 's' subshell, which is spherical in shape. The 's' orbital can hold up to 2 electrons.

• The 4s orbital is filled before the 3d orbital, even though 3d belongs to a lower principal energy level (n=3).
• This phenomenon is due to energy levels overlapping, where 4s is lower in energy compared to 3d.

Understanding the behavior of the 4s orbital is important when discussing how electrons fill up energy levels in atoms.

Periodic Table

The periodic table is an organized chart of all chemical elements based on increasing atomic number. It helps predict the chemical properties of elements based on their position in the table. The arrangement highlights recurring trends in element behavior, known as periodicity.

• Elements in the same group (vertical columns) have similar valence electron configurations, affecting their chemical reactivity.
• Moving from left to right, the electron configuration gradually fills the same principal energy level until reaching noble gases.

The position of potassium in the periodic table is particularly informative in terms of its reactivity and properties as it contains 1 electron in the 4s orbital in its outermost shell.

Electron Configuration

Electron configuration describes how electrons are distributed in an atom's orbitals. This is key to understanding both the atom's structure and its reactive properties. Standard notation for this involves listing each occupied subshell and the number of electrons in it.

• For example, the electron configuration of potassium is written as: [Ar] 4s¹.
• The notation [Ar] represents the argon core, displaying that lower energy shells are already filled like argon.

This configuration informs us that after filling the previous shells like argon, the next electron enters the 4s orbital. Recognizing electron configurations helps in predicting an element's behavior in atomic interactions.