Nuclear Binding Energy Per Nucleon & Mass Defect Problems - Nuclear Chemistry

The Organic Chemistry Tutor
14 Jan 201819:53
EducationalLearning
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TLDRThis educational video script explains the concept of mass defect and nuclear binding energy per nucleon, using carbon-12 as an example. It details the steps to calculate the mass defect by comparing the mass of the nucleus to the combined mass of its constituent protons and neutrons. The script also demonstrates how to compute the nuclear binding energy using Einstein's famous equation, E = mc^2, and convert it to mega electron volts per nucleon. Additionally, it challenges viewers to apply these concepts to calculate the energy released when 5 moles of nitrogen-14 nuclei are formed, emphasizing the importance of precision in scientific calculations.

Takeaways
  • πŸ“š The video explains how to calculate the mass defect of an isotope and the nuclear binding energy per nucleon.
  • πŸ” Mass defect is defined as the difference between the mass of the nucleus and the mass of individual particles that constitute the nucleus.
  • πŸŒ€ Carbon-12 is used as an example, with a mass number of 12 and an atomic number of 6, containing six protons and six neutrons.
  • βš–οΈ The atomic mass unit (amu) is used to convert mass to kilograms, with 1 amu equal to 1.66054 Γ— 10^-27 kilograms.
  • 🧬 The mass of the carbon-12 nucleus is calculated by subtracting the mass of six electrons from the mass of the carbon atom.
  • πŸ’₯ The mass of individual protons and neutrons is summed to find the total mass of the particles that make up the nucleus.
  • βœ‚οΈ The mass defect of carbon-12 is calculated by subtracting the summed mass of protons and neutrons from the mass of the carbon nucleus.
  • ⚑ The nuclear binding energy per nucleon is found using Einstein's mass-energy equivalence formula, E=mc^2.
  • πŸ”„ A negative energy value indicates that energy is released when the nucleus is formed, as mass is converted to energy.
  • πŸ”’ The binding energy per nucleon is calculated by dividing the total binding energy by the number of nucleons in the nucleus.
  • πŸ“‰ The video also covers a problem involving the formation of nitrogen-14 nuclei from protons and neutrons, including the calculation of energy released.
Q & A

  • What is the mass defect of carbon-12?

    -The mass defect of carbon-12 is the difference between the mass of the carbon-12 nucleus and the combined mass of its individual protons and neutrons. It is calculated to be approximately -1.643 Γ— 10^-28 kilograms.

  • How many protons and neutrons does carbon-12 have?

    -Carbon-12 has six protons and six neutrons, as the atomic number (number of protons) is six and the mass number is 12.

  • What is the significance of the mass of electrons in calculating the mass of the carbon nucleus?

    -The mass of electrons is relatively insignificant compared to the mass of the nucleus. It can be neglected for a rough estimate, but for an exact calculation, the mass of the electrons should be subtracted from the mass of the carbon atom.

  • What is the conversion factor from atomic mass units (amu) to kilograms?

    -One atomic mass unit (amu) is equal to 1.66054 Γ— 10^-27 kilograms.

  • How is the nuclear binding energy per nucleon calculated?

    -The nuclear binding energy per nucleon is calculated using the equation Ξ”E = Ξ”m * c^2, where Ξ”m is the mass defect and c is the speed of light. The result is then divided by the number of nucleons (protons and neutrons) to get the energy per nucleon.

  • What is the nuclear binding energy per nucleon of carbon-12 in joules and mega electron volts?

    -The nuclear binding energy per nucleon of carbon-12 is approximately 1.232 Γ— 10^-12 joules per nucleon. When converted to mega electron volts per nucleon, it is about 7.7 MeV/nucleon.

  • What is the relationship between mass defect and energy release during nuclear reactions?

    -The mass defect represents the mass lost when particles come together to form a nucleus. This lost mass is converted into energy, which is released during the process. Hence, a negative energy value indicates energy release.

  • How many nucleons are there in a nitrogen-14 nucleus?

    -A nitrogen-14 nucleus has 14 nucleons, which includes seven protons and seven neutrons.

  • What is the mass defect when 5 moles of nitrogen-14 nuclei are formed from protons and neutrons?

    -The mass defect for the formation of 5 moles of nitrogen-14 nuclei from protons and neutrons is approximately -5.055 Γ— 10^13 joules.

  • How is the energy released when 5 moles of nitrogen-14 nuclei are formed expressed in mega electron volts?

    -The energy released when 5 moles of nitrogen-14 nuclei are formed is approximately 3.16 Γ— 10^26 mega electron volts.

  • What is the importance of the negative sign in the calculation of energy changes in nuclear reactions?

    -The negative sign in the calculation of energy changes indicates that energy is released during the process, such as when particles combine to form a nucleus. A positive value would indicate energy input, such as when a nucleus is broken apart.

Outlines
00:00
πŸ”¬ Calculating Mass Defect and Nuclear Binding Energy of Carbon-12

This paragraph introduces the concept of mass defect and nuclear binding energy, focusing on carbon-12 as an example. It explains that mass defect is the difference between the mass of the nucleus and the sum of the individual masses of protons and neutrons. The atomic mass of carbon is given as 12 amu, which converts to 1.99265 x 10^-26 kg. The mass of the carbon nucleus is calculated by subtracting the mass of six electrons from the atomic mass. The masses of protons and neutrons are also provided, and their sum is used to find the mass defect. The nuclear binding energy per nucleon is then calculated using Einstein's mass-energy equivalence formula, E=mc^2, where the mass defect is multiplied by the speed of light squared to find the energy released when the nucleus forms.

05:03
πŸ“š Understanding Nuclear Binding Energy and Mass Defect Calculations

This paragraph delves deeper into the calculation of mass defect and nuclear binding energy, using the example of carbon-12. It provides the numerical values for the mass of the carbon nucleus and the individual protons and neutrons, leading to the calculation of the mass defect as -1.643 x 10^-28 kg. The nuclear binding energy is then calculated using the mass defect and the speed of light, resulting in -1.47 x 10^-11 J per nucleus. The paragraph clarifies the significance of a negative value, indicating energy release during the formation of the nucleus. It also explains how to calculate the binding energy per nucleon, which for carbon-12 is 1.232 x 10^-12 J per nucleon, and how to convert this to mega electron volts per nucleon.

10:04
πŸ§ͺ Energy Release in Nitrogen-14 Nucleus Formation

The third paragraph discusses the process of calculating the mass defect and energy release when nitrogen-14 nuclei are formed from protons and neutrons. It begins by explaining the concept of mass defect in the context of forming a nitrogen nucleus and the expectation of energy release. The atomic mass of nitrogen is given, and the mass of the nitrogen atom is calculated by subtracting the mass of seven electrons. The masses of protons and neutrons are used to find the total mass of the subatomic particles in the nitrogen nucleus. The mass defect is calculated, and the energy released during the formation of one nitrogen nucleus is determined. The paragraph concludes with the calculation of the total energy released if five moles of nitrogen nuclei were formed.

15:30
πŸ”‹ Total Energy Release in Nitrogen-14 Nucleus Formation Over Five Moles

This final paragraph focuses on the calculation of the total energy released when five moles of nitrogen-14 nuclei are formed. It presents the mass defect and the energy released per nucleus, then scales this up to five moles using Avogadro's number. The energy change is calculated in joules and then converted to mega electron volts, correcting a previous mistake regarding the conversion factor. The final answer is given as 3.16 x 10^26 mega electron volts, emphasizing the importance of accuracy in calculations.

Mindmap
Keywords
πŸ’‘Mass Defect
Mass defect refers to the difference in mass between the nucleus of an atom and the sum of the masses of its individual protons and neutrons. It is a key concept in the video, as it is used to calculate the nuclear binding energy, which is a measure of the stability of an atomic nucleus. In the script, the mass defect of carbon-12 is calculated by subtracting the mass of the carbon nucleus from the combined mass of its six protons and six neutrons.
πŸ’‘Nuclear Binding Energy
Nuclear binding energy is the energy released when nucleons (protons and neutrons) bind together to form an atomic nucleus. It is a measure of the stability of a nucleus, with higher binding energies indicating more stable nuclei. The video explains how to calculate the nuclear binding energy per nucleon using the mass defect and the famous equation E=mc^2, where E is energy, m is mass defect, and c is the speed of light.
πŸ’‘Carbon-12
Carbon-12 is an isotope of carbon with six protons and six neutrons, giving it a mass number of 12. It is used as a reference standard for atomic mass units. In the video, carbon-12 is used as an example to demonstrate the calculation of mass defect and nuclear binding energy, highlighting its importance in understanding nuclear physics.
πŸ’‘Atomic Number
The atomic number of an element is a unique identifier that represents the number of protons in the nucleus of an atom. It determines the element's identity on the periodic table. In the script, the atomic number is used to determine the number of protons in carbon-12 and nitrogen-14, which is essential for calculating the mass defect and nuclear binding energy.
πŸ’‘Neutrons
Neutrons are subatomic particles found in the nucleus of an atom, alongside protons. They have no electric charge and contribute to the mass of the atom. The script discusses the number of neutrons in carbon-12 and nitrogen-14 and how their mass, along with that of protons, is used in the mass defect calculation.
πŸ’‘Protons
Protons are positively charged subatomic particles found in the nucleus of an atom. The number of protons defines the element and its atomic number. The video script uses the mass of protons as part of the calculation for the mass defect of carbon-12 and nitrogen-14, emphasizing their role in atomic structure and nuclear reactions.
πŸ’‘Electrons
Electrons are negatively charged subatomic particles that orbit the nucleus of an atom. They are essential for maintaining electrical neutrality in atoms. In the script, the mass of electrons is considered when calculating the mass of the carbon nucleus, although it is noted to be relatively insignificant compared to the mass of protons and neutrons.
πŸ’‘Atomic Mass Unit (amu)
An atomic mass unit (amu) is a unit of mass used to express the mass of atoms and molecules. One amu is defined as one twelfth of the mass of a carbon-12 atom. The video script uses amu to convert the mass of carbon and nitrogen atoms into kilograms for the purpose of calculating the mass defect and nuclear binding energy.
πŸ’‘Speed of Light (c)
The speed of light (c) is a fundamental physical constant, approximately 3 x 10^8 meters per second, and is used in various equations in physics, including Einstein's famous E=mc^2. In the context of the video, the speed of light is squared and multiplied by the mass defect to calculate the nuclear binding energy.
πŸ’‘Mega Electron Volt (MeV)
A mega electron volt (MeV) is a unit of energy commonly used in nuclear physics and particle physics. It is used to express the energy changes that occur during nuclear reactions. The video script includes a conversion from joules to MeV to express the nuclear binding energy per nucleon of carbon-12 in a unit more familiar to those in the field.
πŸ’‘Nitrogen-14
Nitrogen-14 is an isotope of nitrogen with seven protons and seven neutrons, giving it a mass number of 14. In the video, nitrogen-14 is used as another example to illustrate the calculation of mass defect and the release of energy when its nucleus is formed from protons and neutrons.
Highlights

The video explains how to calculate the mass defect of an isotope and the nuclear binding energy per nucleon.

Mass defect is the difference between the mass of the nucleus and the mass of individual particles that constitute the nucleus.

Carbon-12 has six protons and six neutrons, with the mass number being the sum of protons and neutrons.

The atomic mass unit (amu) is converted to kilograms using the conversion factor 1.66054 x 10^-27 kg.

The mass of the carbon nucleus is calculated by subtracting the mass of six electrons from the mass of the carbon atom.

The mass of the carbon atom is 1.99265 x 10^-26 kg, and the mass of its nucleus is approximately 1.99210 x 10^-26 kg.

The mass of six protons and six neutrons that make up carbon-12 is 2.00853 x 10^-26 kg.

The mass defect of carbon-12 is calculated to be -1.643 x 10^-28 kg.

Nuclear binding energy per nucleon is calculated using the equation Ξ”E = Ξ”m * c^2, where c is the speed of light.

The change in energy for carbon-12 is -1.47 x 10^-11 joules per individual nucleus, indicating energy release during nucleus formation.

The binding energy per nucleon for carbon-12 is 1.232 x 10^-12 joules per nucleon, or 7.7 mega electron volts per nucleon.

For nitrogen-14, the mass defect is calculated similarly by comparing the mass of the nucleus to the mass of individual protons and neutrons.

The mass of the nitrogen atom is 2.32527 x 10^-26 kg, and the mass of its nucleus is 2.32463 x 10^-26 kg.

The mass defect for nitrogen-14 formation from protons and neutrons is -1.8655 x 10^-28 kg.

The energy released during the formation of one nitrogen-14 nucleus is -1.679 x 10^-11 joules.

For the formation of 5 moles of nitrogen-14 nuclei, the total energy released is 5.055 x 10^13 joules or 3.16 x 10^26 mega electron volts.

The video emphasizes the importance of correctly applying the negative sign in calculations to avoid significant errors.

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Mass DefectNuclear BindingCarbon-12IsotopesElectronsProtonsNeutronsEnergy ReleasePhysics CalculationEducational ContentScience Tutorial