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Chapter 20: Problem 10

Define nuclear binding energy, mass defect, and nucleon.

Short Answer

Expert verified
Nuclear binding energy is the energy needed to separate a nucleus into its nucleons. Mass defect is the difference between nuclear mass and actual nucleon mass. Nucleons are protons and neutrons in the nucleus.

Step by step solution

01

Understanding Nuclear Binding Energy

Nuclear binding energy is the amount of energy required to disassemble a nucleus of an atom into its separate nucleons (protons and neutrons). It is the energy equivalent of the mass defect and signifies how strongly the nucleus is bound together.
02

Explaining Mass Defect

Mass defect refers to the difference between the mass of an atom's nucleus and the sum of the individual masses of the protons and neutrons that comprise it. The mass defect occurs because some of the mass is converted into binding energy that holds the nucleus together, as per Einstein's equation, \( E=mc^2 \).
03

Defining Nucleon

A nucleon is a collective term for the particles found in the nucleus of an atom, which are protons and neutrons. Nucleons are the building blocks of the nucleus.

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Key Concepts

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

Mass Defect
The concept of mass defect is pivotal in nuclear physics, providing insight into the intriguing world of atomic nuclei. Mass defect occurs because there is a discrepancy between the mass of a complete nucleus and the sum of its individual components. To break it down:
  • When protons and neutrons, collectively known as nucleons, come together to form a nucleus, they release energy. This energy corresponds to a small amount of mass, thanks to the principle outlined by Einstein's famous equation, \( E=mc^2 \).
  • As a result, the mass of the nucleus is slightly less than the total mass of its individual nucleons. This difference is what we call the mass defect.
This tells us that during the formation of a nucleus, some mass is converted into energy, which serves to bind the nucleons together. The mass defect is directly related to the binding energy of the nucleus and is crucial for understanding nuclear processes.
Nucleon
Nucleons are the fundamental constituents of an atomic nucleus. There are two types of nucleons:
  • Protons: Positively charged particles that determine the chemical element's identity.
  • Neutrons: Neutral particles that add to the mass of the atom without changing its chemical properties.
Together, protons and neutrons form the nucleus鈥攖hus, nucleons are essential for the creation and stability of every atom.
Their interaction and arrangement dictate the properties of the nucleus, including its stability and the degree of binding energy. Understanding nucleons is fundamental to comprehending the processes that occur in nuclear reactions and the formation of various isotopes.
Binding Energy
Binding energy is a crucial concept that determines how nuclei stay intact. It is the energy required to separate a nucleus into its individual protons and neutrons:
  • This energy is a measure of the stability of a nucleus; the greater the binding energy, the more stable the nucleus.
  • It reflects the strength of the forces that hold nucleons together within the nucleus.
Binding energy is essentially the "glue" that holds the nucleus together, preventing it from falling apart. It also explains why nuclear reactions, such as fission and fusion, can release immense amounts of energy. Given that this energy is equivalent to the mass defect, it is a vital parameter in understanding atomic structure and nuclear stability.

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Most popular questions from this chapter

Nuclei with an even number of protons and an even number of neutrons are more stable than those with an odd number of protons and/or an odd number of neutrons. What is the significance of the even numbers of protons and neutrons in this case?

Which of the following poses a greater health hazard: a radioactive isotope with a short half-life or a radioactive isotope with a long half-life? Explain. [Assume the same type of radiation \((\alpha\) or \(\beta)\) and comparable energetics per particle emitted.]

What is the difference between an electron and a positron?

Given that: $$ \mathrm{H}(g)+\mathrm{H}(g) \longrightarrow \mathrm{H}_{2}(g) \quad \Delta H^{\circ}=-436.4 \mathrm{~kJ} / \mathrm{mol} $$ calculate the change in mass (in \(\mathrm{kg}\) ) per mole of \(\mathrm{H}_{2}\) formed.

(a) Assuming nuclei are spherical in shape, show that the radius \((r)\) of a nucleus is proportional to the cube root of mass number \((A)\). (b) In general, the radius of a nucleus is given by \(r=r_{0} A^{1 / 3},\) where \(r_{0},\) the proportionality constant, is given by \(1.2 \times 10^{-15} \mathrm{~m}\). Calculate the volume of the \({ }^{238} \mathrm{U}\) nucleus.
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