Ch.20 - Radioactivity and Nuclear Chemistry

Tro - Chemistry: A Molecular Approach 4th Edition

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Tro 4th Edition

Ch.20 - Radioactivity and Nuclear Chemistry

Problem 68

Chapter 20, Problem 68

Calculate the mass defect and nuclear binding energy per nucleon of each nuclide. a. Li-7 (atomic mass = 7.016003 amu)

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Li-7 consists of 3 protons and 4 neutrons. The atomic mass of a proton is approximately 1.007276 amu, and the atomic mass of a neutron is approximately 1.008665 amu.

Multiply the number of protons by the mass of a proton and the number of neutrons by the mass of a neutron, then sum these values to find the total mass of the nucleons.

Subtract the actual atomic mass of Li-7 (7.016003 amu) from the total mass of the nucleons calculated in Step 2. This difference is the mass defect.

Use Einstein's equation, E=mc^2, where c is the speed of light (approximately 3.00 x 10^8 m/s). Convert the mass defect from amu to kilograms (1 amu = 1.660539 x 10^-27 kg) and then calculate the energy in joules.

Divide the total nuclear binding energy (from Step 4) by the number of nucleons in Li-7 (which is 7) to find the binding energy per nucleon.>

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mass Defect

The mass defect is the difference between the mass of an atomic nucleus and the sum of the individual masses of its protons and neutrons. This discrepancy arises because some mass is converted into energy when nucleons bind together, according to Einstein's equation E=mc². The mass defect is crucial for understanding nuclear stability and energy release in nuclear reactions.

Nuclear Binding Energy

Nuclear binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It is directly related to the mass defect; the greater the mass defect, the higher the binding energy. This energy is a measure of the stability of a nucleus: a higher binding energy indicates a more stable nucleus, while a lower binding energy suggests it is more likely to undergo radioactive decay.

Binding Energy per Nucleon

Binding energy per nucleon is the average energy that binds each nucleon (proton or neutron) in a nucleus. It is calculated by dividing the total binding energy of the nucleus by the number of nucleons. This value is useful for comparing the stability of different nuclei; generally, nuclei with higher binding energy per nucleon are more stable and less likely to undergo fission or fusion.

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Nuclear Binding Energy

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Textbook Question

Calculate the mass defect and nuclear binding energy per nucleon of each nuclide. a. O-16 (atomic mass = 15.994915 amu) b. Ni-58 (atomic mass = 57.935346 amu) c. Xe-129 (atomic mass = 128.904780 amu)

Textbook Question

A typical home uses approximately 1.0⨉10³ kWh of energy per month. If the energy came from a nuclear reaction, what mass would have to be converted to energy per year to meet the energy needs of the home?

Calculate the quantity of energy produced per mole of U-235 (atomic mass = 235.043922 amu) for the neutron-induced fission of U-235 to produce Te-137 (atomic mass = 136.9253 amu) and Zr-97 (atomic mass = 96.910950 amu) (discussed in Problem 58).

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Textbook Question

If 1.0 g of matter is converted to energy, how much energy is formed?

Calculate the quantity of energy produced per gram of U-235 (atomic mass = 235.043922 amu) for the neutron-induced fission of U-235 to form Xe-144 (atomic mass = 143.9385 amu) and Sr-90 (atomic mass = 89.907738 amu) (discussed in Problem 57).

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