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) \(\mathrm{X}=Z(1-\mathrm{Y})\)

Short answer

Option (c) \(X < Y\) is correct; atomic number is less than mass number.

Step-by-step solution

Understanding Atomic and Mass Numbers

Atomic number \(X\) is the number of protons in an atom's nucleus, while mass number \(Y\) is the sum of protons and neutrons. Therefore, since every atom has more mass comprising protons and neutrons, the mass number is usually larger than the atomic number.

Establishing the Relation

The atomic number \(X\) will always be less than the mass number \(Y\) in stable heavy elements because \(Y = X + \, \text{number of neutrons}\).

Choosing the Correct Option

Given the definitions, we can determine that the atomic number \(X\) is less than the mass number \(Y\). Hence, the correct relation is \(X < Y\).

Key concepts

Atomic Number

Understanding the atomic number is fundamental to the study of atomic structure. The atomic number, denoted as \( Z \), specifically refers to the number of protons in the nucleus of an atom. Each element has a unique atomic number, which defines the element. For instance, hydrogen, with one proton, has an atomic number of 1, while oxygen, with eight protons, has an atomic number of 8. Thus, the atomic number determines the identity of an element and its position on the periodic table.

Besides giving an element its identity, the atomic number also equals the number of electrons in a neutral atom. This balance between protons and electrons maintains the atom's electrical neutrality.

The concept of an atomic number remains crucial:

• It defines the element.
• It equals the number of protons.
• For neutral atoms, it's the same as the number of electrons.

Overall, recognizing the atomic number forms the basis for exploring other atomic properties, including chemical behavior and reactivity.

Mass Number

The mass number plays a different yet equally vital role in atomic structure. It's often represented by the symbol \( A \) and is the sum of two distinct atomic components: protons and neutrons in an atom's nucleus. Unlike the atomic number, the mass number is not unique to an element, as isotopes of an element have the same atomic number but different mass numbers due to varying neutron counts.

To calculate the mass number, simply add the number of protons (atomic number) and the number of neutrons: \[ A = Z + N \] where \( N \) is the number of neutrons. This formula highlights the reason why, in most cases, an atom's mass number is greater than its atomic number. While electrons have negligible mass contribution, both protons and neutrons significantly impact an atom's mass.

Key points about mass number include:

• It's the sum of protons and neutrons.
• Determines isotopes differentiation.
• Reflects the overall mass of an atom's nucleus.

By understanding mass numbers, students can gain insights into isotopes, nuclear reactions, and atomic stability.

Protons and Neutrons

Protons and neutrons, collectively known as nucleons, are the core components of an atom's nucleus. Understanding these subatomic particles is essential to grasp any aspect of atomic structure.

• Protons: Carry a positive electrical charge and have a mass of approximately 1 atomic mass unit (amu). They determine the identity of an element, corresponding directly to the atomic number \( Z \). Thus, altering the number of protons in a nucleus results in a different element altogether. Protons are central to the chemical behavior of atoms and interactions in chemical reactions. Without protons, the nucleus loses its identity as known by the periodic table.


• Neutrons: Uncharged particles with a mass similar to protons. Neutrons add to the atomic mass but do not influence the charge. Varied numbers of neutrons create isotopes, affecting only the mass and stability of atoms without changing the chemical properties.Neutrons play a critical role in the stability of the nucleus. They help counteract the electrostatic repulsion between positively charged protons, thus maintaining nuclear integrity.

Understanding protons and neutrons involves looking at their unique roles:

• They define nuclear stability and identity.
• Both have similar masses contributing to the atomic weight.
• Neutrons allow the formation of different isotopes.

In essence, the careful balancing of protons and neutrons fosters both the identity and stability of atoms across the periodic table.