Question

Which has the larger binding energy, F-19 or O-17?

Short answer

Answer: F-19 has a larger binding energy compared to O-17.

Step-by-step solution

Determine the nucleon composition of both isotopes

First, determine the number of protons and neutrons in each isotope: - F-19: 9 protons and 10 neutrons (Z = 9, A = 19) - O-17: 8 protons and 9 neutrons (Z = 8, A = 17)

Calculate the mass defect for both isotopes

Next, calculate the mass defect for both isotopes. The mass defect can be calculated as follows: Mass Defect = (Total Mass of Nucleons) - (Mass of the Nucleus) Use the known masses of protons (1.007276 u), neutrons (1.008665 u), and both isotopes (18.998403 u for F-19 and 16.999131 u for O-17) to find the mass defect. For F-19: Mass Defect (F-19) = (9 x 1.007276 u + 10 x 1.008665 u) - (18.998403 u) = 0.138793 u For O-17: Mass Defect (O-17) = (8 x 1.007276 u + 9 x 1.008665 u) - (16.999131 u) = 0.127608 u

Calculate the binding energies for both F-19 and O-17

Now calculate the binding energies for both isotopes using the calculated mass defects and the speed of light (c) constant. Make sure to use the appropriate conversion factors for units. We will use the following binding energy formula: Binding Energy = (Mass Defect) x c^2 For this exercise, let's use the conversion factor 931.5 MeV/c^2 per atomic mass unit (u) and binding energy formula: Binding Energy = (Mass Defect) × 931.5 MeV/c^2/u For F-19: Binding Energy (F-19) = 0.138793 u × 931.5 MeV/c^2/u = 129.331 MeV For O-17: Binding Energy (O-17) = 0.127608 u × 931.5 MeV/c^2/u = 118.884 MeV

Compare the binding energies and determine the isotope with the larger binding energy

Now compare the binding energies for F-19 and O-17 that we have calculated: Binding Energy (F-19) = 129.331 MeV Binding Energy (O-17) = 118.884 MeV Since the binding energy for F-19 is greater than the binding energy for O-17, we can conclude that F-19 has the larger binding energy.

Key concepts

Nuclear Chemistry

Nuclear chemistry is the branch of chemistry that deals with changes in the nucleus of atoms. Unlike regular chemical reactions that involve the exchange or sharing of electrons, nuclear reactions involve the change of an atom's nucleus, resulting in different elements or isotopes. This field is essential for understanding processes such as radioactive decay, nuclear fission, and nuclear fusion.

At its core, nuclear chemistry looks at how and why these changes occur, and the energy associated with these changes. Binding energy, for instance, is a key concept that represents the energy required to split a nucleus into its component protons and neutrons. The stronger the forces that hold the nucleus together, the higher the binding energy is, which is an indication of the nucleus's stability.

Atomic Mass Unit

An atomic mass unit (amu) is a small unit of mass used to express atomic and molecular weights. It is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 at rest and in its ground state. This unit is particularly important in nuclear chemistry because it allows scientists to compare the masses of different atoms and isotopes on a scale suitable for the very small particles involved.

In our example involving F-19 and O-17, atomic mass units help us calculate the mass defect, which is directly related to the binding energy – the focus of our comparison of these two isotopes.

Mass Defect Calculation

The mass defect is the difference between the sum of the individual masses of nucleons (protons and neutrons) and the actual mass of an atomic nucleus. The mass defect arises because some mass is 'lost' and converted into binding energy that holds the nucleus together, according to the mass-energy equivalence principle represented by Einstein’s equation, E=mc^2. Therefore, a larger mass defect signifies a higher binding energy and consequently a more stable nucleus.

In our exercise, the mass defects for F-19 and O-17 were calculated using the actual masses of the isotopes and the known masses of protons and neutrons. We found that F-19 had a greater mass defect, suggesting more mass was converted into binding energy.

Nuclear Stability

Nuclear stability is a concept that explains why some atomic nuclei are stable while others decay. This stability is influenced by a balance between the attractive nuclear forces and the repulsive electromagnetic forces among protons. The neutron-to-proton ratio plays a vital role in nuclear stability; too many or too few neutrons can lead to nuclear instability and radioactive decay.

Binding energy per nucleon is one indicator of nuclear stability, with higher values indicating a more stable nucleus. A stable nucleus will generally have enough binding energy to hold it together against the natural repulsive forces between the protons. From our calculations, since F-19 has a larger binding energy compared to O-17, it is inferred to be more stable.