Question

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; na = 6.0221367 × 1023 /mol; c = 2.99792458 × 108 m/s]

Answer 1

To solve this, we use Einstein's famous equation: E=mc^2, where c is the speed of light (300 million m/s). E is the nuclear binding energy and m is the mass defect. To compute for m, we find the difference of potassium's atomic mass and the mass of its subparticles.

Potassium has an atomic number of 19, meaning it has 19 protons. The mass number is 40. Then, the amount of neutrons = 40 - 19 =21. Lastly, for a neutral atom, it has equal number of protons and electrons. So, electrons = 19. Solving for the mass of its subparticles:

[19(1.672623 × 10–24 g) + 19(9.109387 × 10–28 g) + 21(1.674928 × 10–24 g)](6.022 x 10^23 amu/ 1 g) = 40.32979519

Therefore, mass defect = 40.32979519 - 39.9632591 = 0.367 amu or g/mol

Substituting the equation:
E = (0.367 g/mol)(1 mol/6.022 x 10^23 nucleons)(1 kg/1000 g)(3 x 10^8 m/s)^2
E = 3.3 x10^13 J/nucleon