Find the nuclear binding energy of potassium-40 (atomic mass = 39.9632591 amu) in units of joules per nucleon. [Data: neutron mass = 1.674928 * 10^-24 g; proton mass = 1.672623 * 10^-24g; electron mass = 9.109387 * 10^-28 g; N_A = 6.0221367 * 10²³ /mol; c = 2.99792458 * 10⁸ m/s]

Question

Quizplus · Accepted Answer

The nuclear binding energy is calculated by finding the difference between the mass of the unbound nucleons and the actual mass of the nucleus, then converting this mass defect into energy using Einstein's equation $E=mc^2$. For potassium-40, with 19 protons and 21 neutrons, the mass of the unbound nucleons (using the given masses for protons and neutrons) is higher than the actual atomic mass. The difference, when converted to energy and divided by the number of nucleons (40), gives the binding energy per nucleon. The calculation involves converting atomic mass units (amu) to kilograms, using the speed of light in meters per second, and dividing by Avogadro's number to find the energy per nucleon. The correct answer, based on the calculation, is closest to the value given in option A.

Find the Nuclear Binding Energy of Potassium-40 (Atomic Mass =