Problem 35 - A Complete Resource Book in Chemistry for JEE Main

Question

An element has 2 electrons in its \(\mathrm{K}\) shell, 8 electrons in \(\mathrm{L}\) shell, 13 electrons in \(\mathrm{M}\) shell and one electron in N shell. The element is (a) \(\mathrm{Cr}\) (b) \(\mathrm{Fe}\) (c) V (d) \(\mathrm{Ti}\)

Step-by-Step Solution

Answer

The element is Chromium (\( \mathrm{Cr} \)).

Step 1: Understand Electron Configuration

The electron configuration of an atom describes the distribution of electrons in the atomic orbitals. The given shell configuration is: 2 electrons in the \( K \) shell, 8 in the \( L \) shell, 13 in the \( M \) shell, and 1 in the \( N \) shell. This corresponds to a total count of electrons.

Step 2: Calculate Total Electrons

Add the number of electrons from each shell: \( 2 + 8 + 13 + 1 = 24 \) electrons. This means the atomic number of the element is 24.

Step 3: Identify the Element

Utilize the periodic table to determine which element has an atomic number of 24. Chromium (\( \mathrm{Cr} \)) is the element with atomic number 24.

Key Concepts

Atomic Number

The atomic number of an element is crucial in determining its identity. It is the count of protons in the nucleus of an atom, and in a neutral atom, it also equals the number of electrons. This direct one-to-one relationship helps categorize the elements. Atomic number defines not only the element's chemical properties but also its position on the periodic table.
To find an element using its atomic number, count the electrons in its various electron shells. For instance, if an element has 24 electrons, its atomic number is also 24. Since the atomic number is unique for every element, it effectively distinguishes them in the vast periodic table. This direct link between electrons and atomic number makes it easy for students to identify elements and predict chemical behaviors.

Periodic Table

The periodic table is a powerful tool for understanding the placement and properties of elements. Elements are arranged in order of increasing atomic number, and those with similar properties are grouped together in columns known as groups.
The periodic table is divided into several blocks based on electron configuration:

• s-block: Groups 1 and 2, plus helium, where outer-shell electrons fill s orbitals.
• p-block: Groups 13-18, with outer-shell electrons filling p orbitals.
• d-block: Transition metals, where electrons fill d orbitals.
• f-block: Lanthanides and actinides, filling f orbitals.

The element with atomic number 24 is chromium (Cr), found in the d-block, known for having partially filled d orbitals, which contribute to the unique properties of transition metals. By understanding an element's position on the table, you can predict its reactivity, state of matter, and even its melting and boiling points.

Electron Shells

Electron shells are layers around the nucleus where electrons reside. They are denoted by the letters K, L, M, N, and so on. Each shell can hold a specific number of electrons:

• K shell: up to 2 electrons.
• L shell: up to 8 electrons.
• M shell: up to 18 electrons.
• N shell: up to 32 electrons.

In practice, the electrons fill the lowest energy levels first (starting with the K shell). This is known as the aufbau principle. Understanding electron shells is essential not just for identifying an element, but also for predicting how it will interact in chemical reactions.
For example, chromium (Cr) has a unique configuration of electrons filling up to the 1st electron in the N shell (2 in K, 8 in L, 13 in M, and 1 in N). This arrangement explains why it behaves a certain way chemically, specifically in how it forms bonds and its oxidation states.