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Chapter 18: Problem 27

Statement-1 : The plot of atomic number (y-axis) versus number of neutrons (x-axis) for stable nuclei shows a curvature towards \(\mathrm{x}\)-axis from the line of \(45^{\circ}\) slope as the atomic number is increased. 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

Expert verified
(b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

Step by step solution

01

Analyze Statement-1

Statement-1 indicates that as the atomic number increases, the plot of atomic number versus the number of neutrons shifts downward from a 45-degree line. Initially, light nuclei have nearly equal numbers of protons and neutrons, but as atomic number increases, more neutrons are needed to overcome proton-proton repulsion, hence, the curvature towards the x-axis represents this neutron-rich condition.
02

Evaluate Statement-2

Statement-2 explains that in heavier nuclei, the electrostatic (Coulomb) repulsion between protons becomes significant enough to affect nuclear stability. To maintain stability, additional neutrons are necessary to provide enough strong nuclear force, which is an attractive force, thereby compensating for these repulsions.
03

Determine the Truth of Statements

Both statements are true as they are well-established principles in nuclear physics. The curve described in Statement-1 is a recognized observation in nuclear stability studies, and Statement-2 accurately describes a reason nuclei become neutron-rich with increased atomic number.
04

Assess the Explanation

Although Statement-2 involves additional neutrons overcoming electrostatic repulsion, it specifically deals with what happens in heavier nuclei rather than being the direct reason for the curvature mentioned in Statement-1. Rather, the curve results from the need for increased nuclear force to maintain stability, not primarily the repulsion itself.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Atomic Number
The concept of the atomic number is fundamental to understanding the behavior of elements. The atomic number represents the number of protons found in the nucleus of an atom. It defines the element and determines its position in the periodic table. For example, carbon has an atomic number of 6, which means it has six protons in its nucleus.

As we explore elements with higher atomic numbers, we notice changes in nuclear stability. Small atomic numbers correlate with nuclei containing almost equal numbers of protons and neutrons. This balance helps maintain stability. However, with increasing atomic numbers, more neutrons are required to maintain stability. This need arises because more protons lead to increased electrostatic repulsion among protons.

The plot of atomic number versus number of neutrons reflects these changes. When graphed, the line begins to curve as atomic numbers grow, showing a trend towards needing more neutrons. This curve reflects a deviation from the 45-degree line observed in lighter elements, highlighting a need for greater neutron presence to maintain nuclear stability.
Neutron-Proton Ratio
The neutron-proton ratio is critical in assessing atomic stability. In lighter elements, the ratio is close to 1:1, indicating an almost equal presence of neutrons and protons. This balance contributes to strong nuclear stability.

However, as we explore heavier elements, this ratio shifts. For nuclei with high atomic numbers, it's essential to have more neutrons compared to protons. The added neutrons play a significant role in counteracting the electrostatic repulsion between numerous protons.
  • Neutrons act as a buffer, reducing repulsion.
  • They increase the nuclear binding energy due to the strong nuclear force.
  • This results in a stable nucleus despite higher proton numbers.
The shift in this ratio is visibly reflected in the curvature observed on the graph when plotting atomic numbers against the number of neutrons. This curvature signifies an increase in neutron content as the atomic number rises, ensuring nuclear stability is preserved.
Electrostatic Repulsion
Electrostatic repulsion refers to the force pushing protons apart within a nucleus. It arises because like charges repel each other according to Coulomb's law. This force becomes more pronounced in elements with higher atomic numbers because they contain more protons.

In heavier elements, this electrostatic repulsion is significant enough to challenge the nuclear stability. The nucleus needs to have additional mechanisms to maintain integrity. This is where neutrons become crucial, providing an attractive strong nuclear force that pairs with protons to add stability.
  • Protons repel each other due to positive charges.
  • The nuclear strong force provided by neutrons counters this repulsion.
  • Neutrons do not contribute to electrostatic repulsion.
This balance of forces means that as electrostatic repulsion increases, so too does the necessity for additional neutrons. This is what keeps heavier nuclei from unraveling under the stress of their own positive charges, ensuring that elements with high atomic numbers can exist stably.

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Most popular questions from this chapter

The following statement(s) is (are) correct : [1999 - 3 Marks] (a) A plot of \(\log K_{p}\) versus \(1 / T\) is linear (b) A plot of \(\log [X]\) versus time is linear for a first order reaction, \(X \rightarrow P\) (c) A plot of \(P\) versus \(1 / T\) is linear at constant volume (d) A plot of \(P\) versus \(1 / V\) is linear at constant temperature

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If uranium (mass number 238 and atomic number 92) emits an \(\alpha\) particle, the product has mass no. and atomic no. (a) 236 and 92 (b) 234 and 90 (c) 238 and 90 (d) 236 and 90

A nuclear explosion has taken place leading to increase in concentration of \(C^{14}\) in nearby areas. \(C^{14}\) concentration is \(C_{1}\) in nearby areas and \(C_{2}\) in areas far away. If the age of the fossil is determined to be \(T_{1}\) and \(T_{2}\) at the respective places then (a) The age of the fossil will increase at the place where explosion has taken place and \(T_{1}-T_{2}=\frac{1}{\lambda} \ln \frac{C_{1}}{C_{2}}\) (b) The age of the fossil will decrease at the place where explosion has taken place and \(T_{1}-T_{2}=\frac{1}{\lambda} \ln \frac{C_{1}}{C_{2}}\) (c) The age of fossil will be determined to be same (d) \(\frac{T_{1}}{T_{2}}=\frac{C_{1}}{C_{2}}\)

Rate of a reaction \(A+B \rightarrow\) products, is given below as a function of different initial concentrations of \(A\) and \(B\) : [1982-4 Marks] 119 \(\begin{array}{lll}{[A](\operatorname{mol} / l)} & {[B](\mathrm{mol} / l)} & \text { Initial rate }(\mathrm{mol} / l / \mathrm{min}) \\ 0.01 & 0.01 & 0.005 \\ 0.02 & 0.01 & 0.010 \\ 0.01 & 0.02 & 0.005\end{array}\) 1
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