Skip to main content
Pearson+ LogoPearson+ Logo
Ch.20 - Nuclear Chemistry
McMurry - Chemistry 8th Edition
McMurry8th EditionChemistryISBN: 9781292336145Not the one you use?Change textbook
All textbooksMcMurry 8th EditionCh.20 - Nuclear ChemistryProblem 7
Chapter 20, Problem 7

Calculate the binding energy a uranium-235 nucleus in units of MeV/nucleon. The mass of an 235U atom is 235.043 929, the mass of a proton is 1.007 28, the mass of a neutron is 1.008 67, and the mass of an electron is 5.486 x 10^-4. (1 MeV = 1.60 x 10^-13 J)(a) 2.84 MeV/nucleon(b) 1.70 x 10^3 MeV/nucleon (c) 11.3 MeV/nucleon (d) 7.62 MeV/nucleon

Verified step by step guidance
1
Calculate the number of protons (Z) and neutrons (N) in the uranium-235 nucleus. Uranium-235 has 92 protons, so the number of neutrons is 235 - 92 = 143.
Calculate the total mass of the protons and neutrons if they were free particles: Total mass = (Z * mass of proton) + (N * mass of neutron).
Calculate the mass defect (Δm) by subtracting the actual mass of the uranium-235 nucleus from the total mass of the protons and neutrons: Δm = (Total mass of protons and neutrons) - (mass of 235U atom).
Convert the mass defect from atomic mass units (amu) to energy using Einstein's equation, E = Δm * c^2, where c is the speed of light. Note that 1 amu = 931.5 MeV/c^2.
Calculate the binding energy per nucleon by dividing the total binding energy by the number of nucleons (A = 235) in the uranium-235 nucleus.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
8m
Was this helpful?

Key Concepts

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

Binding Energy

Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It reflects the stability of the nucleus; a higher binding energy indicates a more stable nucleus. This energy can be calculated using the mass defect, which is the difference between the mass of the individual nucleons and the actual mass of the nucleus.
Recommended video:
Guided course
02:06
Nuclear Binding Energy

Mass Defect

The mass defect is the difference between the total mass of the separate nucleons (protons and neutrons) and the mass of the nucleus itself. This mass loss, due to the conversion of mass into energy according to Einstein's equation E=mc², is crucial for calculating the binding energy. It highlights how energy is released when nucleons bind together to form a nucleus.
Recommended video:
Guided course
00:55
Calculating Mass Defect

Energy Conversion

In nuclear physics, energy is often expressed in different units, such as joules and MeV (mega-electronvolts). To convert the binding energy from joules to MeV, one must use the conversion factor where 1 MeV equals 1.60 x 10^-13 joules. Understanding this conversion is essential for accurately reporting binding energy in the context of nuclear reactions and stability.
Recommended video:
Guided course
01:56
Conversion Factors
Related Practice
Textbook Question
Fluorine-18 undergoes positron emission with a half-life of 1.10 x 10^2 minutes. If a patient is given a 250 mg dose for a PET scan, how long will it take for the amount of fluorine-18 to drop to 75 mg?(a) 56 minutes(b) 96 minutes (c) 132 minutes (d) 191 minutes
783
views
Textbook Question
In a cave in Oregon, archaeologists found bones, plant remains, and fossilized feces. DNA remaining in the feces indi-cates their human origin but not their age. To date the remains, the decay rate was measured and found to be 2.71 disinte-grations/min per gram of carbon. Currently living organisms have a decay rate of 15.3 disintegrations/min per gram of carbon, and the half-life of 14C is 5715 years. How old are the remains? (a) 1460 years(b) 9900 years(c) 14300 years(d) 18600 years
319
views
Textbook Question
Identify the true statement about nuclear power plants and nuclear weapons. (a) Nuclear power plants and nuclear weapons both use uranium enriched to about 90% U-235.(b) Nuclear power plants emit large amounts of CO2 just like coal burning power plants. (c) The United States produces less than 1% of its electrical power from nuclear energy. (d) A nuclear weapon explodes when two pieces of fission-able uranium-235 are pushed together to reach a critical mass.
396
views
Textbook Question
How much energy in kJ/mol is released by the fission of uranium-235 to form barium-140 and krypton-93? The atomic masses are (a) 6.59 x 10^9 kJ/mol (b) 1.66 x 10^10 kJ/mol (c) 1.98 x 10^11 kJ/mol (d) 1.66 x 10^16 kJ/mol
559
views