Nuclear stability and are fundamental concepts in understanding atomic nuclei. They explain why some nuclei are stable while others undergo radioactive decay. , the force holding nucleons together, is key to nuclear stability.
Calculations of reveal patterns across the periodic table. This knowledge is crucial for understanding nuclear reactions like and , which power stars and nuclear plants. The plays a central role in these processes.
Nuclear Stability and Binding Energy
Concept of binding energy
Energy required to disassemble a into its constituent protons and neutrons
Measure of the strength of the nuclear force holding the nucleus together
Nuclear stability determined by the binding energy per
Higher binding energy per nucleon indicates more stable nuclei ()
Lower binding energy per nucleon indicates less stable nuclei more likely to undergo radioactive decay ()
is the difference between the mass of a nucleus and the sum of the masses of its individual protons and neutrons
Mass defect related to binding energy through 's equation E=mc2
Binding energy calculated from mass defect using equation Eb=(Δm)c2
Eb is binding energy
Δm is mass defect
c is speed of light
Strong nuclear force is responsible for holding nucleons together within the nucleus
Calculation of binding energy
Binding energy per nucleon is total binding energy divided by number of nucleons (protons and neutrons) in nucleus
Measure of average energy required to remove a single nucleon from nucleus
Steps to calculate binding energy per nucleon:
Determine mass defect (Δm) by subtracting actual mass of nucleus from sum of masses of individual protons and neutrons
Calculate total binding energy using equation Eb=(Δm)c2
Divide total binding energy by total number of nucleons (A) to obtain binding energy per nucleon Eb/A