18.2-18.3: Stability of Nuclei and Energetics of Nuclear Reactions

When a nucleus forms, some of the mass of the separate nucleons is converted into energy (_________). The difference in mass between the separate nucleons and the combined nucleus is called the _________.

binding energy , mass defect

The greater the binding energy per nucleon, the ________ stable the nucleus is. Binding energy ________ as the nuclear mass _________.

more , increases , increases

State the equation used for calculating binding energy (E). How is it calculated?

∆E = (∆m)c²

• Calculated by converting into energy units the mass difference (i.e. mass defect) between the sum of the masses of the free nucleons and the actual mass of the nucleus

The ∆H_rxn for nuclear reactions is called the __________. The equation for calculating it is __________ and then converting it to energy units (8.987 × 10¹⁰ kJ = 1 mol amu). A positive __________ indicates an __________ reaction while a negative __________ indicates an ___________.

Q-value , Q = ∑masses_products - ∑masses_reactants , Q-value , endergonic , Q-value , exergonic

The ratio of neutrons : protons (N/Z) is an important measure of _________ of the nucleus. If the N/Z ratio is too high, neutrons are converted to _________ via _________. If the N/Z ratio is too low, protons are converted to __________ via _________ or ________ (or α decay, but not as efficient).

stability , protons , ß decay , neutrons , positron emission , electron capture

Most stable nuclei have _________ numbers of protons and neutrons. Only a few don’t. If the __________ adds to a “magic number,” the nucleus is more stable.

even , total number of nucleons

The nucleus is most stable when N or Z = __________.

2, 8, 20, 28, 50, 82; or N = 126

What is the “band of stability”?

Area on a graph comprised of the stable nuclides of each element. Typically plotted with the number of neutrons on the y-axis and the number of protons on the x-axis; bordered by unstable neutron-rich and neutron-poor nuclides that undergo radioactive decay

List the stable N/Z value for each range of Z: 1-20, 20-40, 40-80, and Z > 83.

N/Z = 1, N/Z = 1.25, N/Z = 1.5, there are no stable nuclei

What are the steps for predicting radioactive decay?

1. Determine the Z and N values present for the given nuclide.

2. Divide N by Z and compare this value to the stable N/Z value for the element.

   1. Could also compare the atomic mass (A) for the given isotope and the average atomic mass of that element in the periodic table

3. If the N/Z ratio is too high, neutrons will convert protons through Beta emission/decay.

4. If the N/Z ratio is too low, protons will convert to neutrons through positron emission or electron capture

What is a “decay series”? How do we determine the stable nuclide at the end?

All of the radioactive nuclides that are produced one after the other until a stable nuclides is made

Steps to determining the stable nuclide formed:

1. Count the number of α and ß decays

2. From the mass no. subtract 4 for each α decay

3. From the atomic no. subtract 2 for each α and ß decay and add 1 for each ß