Question

STATEMENT-1: The plot of atomic number (y-axis) versus number of neutrons ( \(x\) -axis) for stable nuclei shows a curvature towards \(x\) -axis from the line of \(45^{\circ}\) slope as the atomic number is increased. and STATEMENT-2: Proton-proton electrostatic repulsions begin to overcome attractive forces involving protons and neutrons in heavier nuclides. (A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT- 2 is True

Short answer

Both STATEMENTS are True, and STATEMENT-2 is a correct explanation for STATEMENT-1, making (A) the correct answer.

Step-by-step solution

Understanding the Relationship Between Neutrons and Atomic Number for Stable Nuclei

Stable nuclei typically follow the 'Belt of Stability', where the ratio of neutrons to protons changes such that lighter elements have approximately equal numbers of neutrons and protons, but heavier elements require more neutrons than protons to remain stable. As the atomic number increases (more protons), extra neutrons are required to mitigate the increased proton-proton repulsion due to their positive charge, which is why the plot curves towards the x-axis.

Analyzing Proton-Proton Repulsion in Heavier Nuclides

In heavier nuclides with more protons, the electrostatic repulsion between protons increases. The attractive nuclear force has a very short range and does not increase as fast as the repulsion with more protons. Thus, additional neutrons are necessary to provide an attractive force to counterbalance the repulsion and contribute to nuclear stability.

Determining the Correctness of the Statements

Both STATEMENT-1 and STATEMENT-2 are true. The curvature in the plot of atomic number versus number of neutrons for stable nuclei reflects the need for more neutrons to counterbalance the increasing proton-proton electrostatic repulsion in heavier nuclides, which is exactly what STATEMENT-2 explains.

Key concepts

Belt of Stability

Understanding the 'Belt of Stability' is critical when studying nuclear physics, particularly when explaining nuclear stability in heavier nuclides. The Belt of Stability is a graphical representation that shows the relationship between neutron numbers (on the x-axis) and proton numbers (on the y-axis) for stable atoms. Atoms within this band contain the optimal neutron-to-proton ratio that allows them to exist without undergoing radioactive decay rapidly. For lighter elements, this ratio is roughly 1:1, meaning they have nearly equal numbers of neutrons and protons.

However, as elements get heavier beyond Iron (with an atomic number of 26), the ratio of neutrons to protons starts increasing. Heavier elements require more neutrons than protons to help counter the effects of electrostatic repulsion between positively charged protons. This is why the Band of Stability curves towards the neutron, or x-axis. When elements stray too far from this belt, they tend to become unstable and can undergo radioactive decay to return to a more stable state.

Proton-Neutron Ratio

The proton-neutron ratio in an atomic nucleus plays a pivotal role in the stability of an atom. The correct balance between these subatomic particles is what prevents a nucleus from spontaneously breaking apart. In atoms with a lower atomic number, the ratio of neutrons to protons that equates to stability floats around 1:1.

As the atomic number increases and more protons are added to the nucleus, the proton-neutron ratio skews in favor of neutrons. The reason for this shift is due to the additional neutrons necessary to overcome the increased proton-proton repulsion that occurs with more protons sharing a confined space. If the number of neutrons is too low in comparison to protons, the nucleus experiences instability and may undergo decay series to achieve a balanced state.

Proton-Proton Repulsion

Proton-proton repulsion is a force that significantly influences the internal dynamics of an atomic nucleus. Protons, being positively charged, repel each other due to the electrostatic force, one of the four fundamental forces in nature. In smaller nuclei, with fewer protons, this repulsion is effectively counterbalanced by the strong nuclear force, which is provided by the presence of neutrons and acts to hold the nucleus together.

The strength of the electrostatic repulsion grows with the number of protons, becoming a dominant force in larger nuclei. Heavier nuclides thus require a larger number of neutrons to provide sufficient strong force to overcome this repulsion. This imperative for additional neutrons contributes to the upward curve of the Belt of Stability as the atomic number increases. Without enough neutrons, the repulsive forces between protons could lead to nuclear instability, potentially causing the nucleus to decay as it seeks a more stable configuration.