Calculate the binding energy in J / nucleon of the deuterium nucleus whose mass is 2.0141 u.

Name: Problem 57, Chapter 20: Chemistry: The Molecular Nature of Matter
Uploaded: 2021-07-02T20:22:11-08:00
Duration: 1 min 24 s
Channel: David Collins
Description: Calculate the binding energy in J / nucleon of the deuterium nucleus whose mass is 2.0141 u.

step 1 To calculate the binding energy in units of joules per nucleon, we first need to calculate the m

Calculate the binding energy in J / nucleon of the deuterium...

Key Concepts

Binding Energy

Binding energy is the energy required to decompose a nucleus into its separate protons and neutrons. It is also the energy released when a nucleus is formed from these nucleons. In nuclear physics, this energy reflects the net attractive forces between the nucleons and is fundamental to understanding nuclear stability.

Mass Defect

Mass defect is the difference between the sum of the separate masses of the nucleons (protons and neutrons) and the actual measured mass of the nucleus. This deficit in mass arises because a portion of mass is converted into binding energy according to the mass-energy equivalence principle.

Mass-Energy Equivalence

Based on Einstein’s equation E=mc², mass-energy equivalence explains how a lost mass (the mass defect) can be equated to a specific amount of energy. This principle is used to convert the mass defect into binding energy by multiplying it by the square of the speed of light.

Unit Conversion

Conversion of mass units is essential in these calculations, particularly converting atomic mass units (u) to kilograms, since the standard SI unit for mass is the kilogram. This allows the use of E=mc² with the speed of light in meters per second, ensuring that the resulting energy is in Joules.

Binding Energy per Nucleon

Binding energy per nucleon is defined as the total binding energy of a nucleus divided by its number of nucleons. This measure provides insight into the stability of the nucleus; nuclei with higher binding energy per nucleon are generally more stable and require more energy per nucleon to be broken apart.

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