Problem 19 - A Complete Resource Book in Chemistry for JEE Main

Question

A heavy element has atomic number \(\mathrm{X}\) and mass number Y. Correct relation between \(\mathrm{X}\) and \(\mathrm{Y}\) is (a) \(\mathrm{X}=\mathrm{Y}\) (b) \(\mathrm{X}>\mathrm{Y}\) (c) \(\mathrm{X}<\mathrm{Y}\) (d) \(\mathrm{X}=\mathrm{Z}(1-\mathrm{Y})\)

Step-by-Step Solution

Answer

The correct relation is (c) \(X < Y\).

Step 1: Understand the Atomic Number and Mass Number

The atomic number (\(X\)) of an element is the number of protons in its nucleus, while the mass number (\(Y\)) is the sum of protons and neutrons. Therefore, for any atom: \(Y = X + ext{number of neutrons}\) where the number of neutrons is non-negative.

Step 2: Analyze the Relation X < Y

Since neutrons contribute to the mass number (\(Y\)) and \(X\) counts only protons, usually \(Y > X\) unless there are no neutrons, which is generally not the case for heavy elements. Therefore, \(X < Y\) holds for a heavy element which has both protons and neutrons in the nucleus.

Step 3: Review the Answer Choices

(a) implies \(X = Y\), which does not account for neutrons. (b) suggests \(X > Y\), which would mean negative neutrons, which is not possible. (c) suggests \(X < Y\), aligning with our analysis. (d) offers a more complex formula not typically used in context with basic atomic number and mass number comparisons.

Key Concepts

Atomic Number

The atomic number of an element is a key fundamental property as it defines the identity of the element. This number correlates directly to the number of protons located in the nucleus of an atom.
The atomic number is often represented by the letter "Z" and it serves as a unique identifier for each element on the periodic table. For example, hydrogen, the simplest element, has an atomic number of 1, signifying it has one proton.
Here are some vital points regarding atomic number:

• Atomic number determines the element's position in the periodic table.
• It defines the number of electrons in a neutral atom.
• An increase in atomic number by one unit results in an element change.

Understanding the atomic number is crucial because it helps predict an element's chemical properties and behavior during reactions. Since protons carry a positive charge, their number impacts atomic interactions.

Mass Number

Mass number is another significant aspect of chemical elements often denoted by the letter "A". Unlike the atomic number, the mass number represents the sum of protons and neutrons in the nucleus.
This means that the mass number gives the total weight of the nucleus, although it's only a whole number approximation to the atomic mass. For example, carbon typically has a mass number of 12 because it has 6 protons and 6 neutrons.
Let's look at the key points about mass number:

• Mass number = Number of protons + Number of neutrons
• It is written as a superscript to the left of the element symbol.
• Mass number determines the isotope of an element.

By understanding the mass number, you can gauge the relative mass of an atom, which is often an essential aspect in nuclear physics and chemistry applications. This number helps differentiate between isotopes of the same element.

Protons and Neutrons

Protons and neutrons are two essential subatomic particles housed in the nucleus of an atom. While protons carry a positive charge, neutrons have no charge making them neutral. The balance between these particles is crucial in defining atomic properties.
Here are a few essential insights into protons and neutrons:

• Protons: They are responsible for the atomic number. The increase or decrease in proton number alters the identity of an element completely.
• Neutrons: Though they do not affect the identity of an element, they impact the atom's stability and decay patterns, affecting isotopes.
• Role in the nucleus: Heavy elements naturally have more neutrons to help stabilize the nucleus through nuclear binding energy.

These particles are bound together in the nucleus by nuclear forces, a strong attraction that counters the repulsive forces amongst protons due to their positive charges. The interaction between protons and neutrons leads to stability and different isotopic forms of an element ingrained within the mass number.