Question

What is the nuclear binding energy (in joules) for a 59 Fe nucleus, given that the mass of a proton is 1.673 x 10⁻²⁴ g, the mass of a neutron is 1.675 x 10⁻²⁴ g, and the mass of the nucleus of a 59Fe atom is 9.787 x 10⁻²³ g?

Answer 1

To calculate the nuclear binding energy for a 59Fe nucleus in joules, determine the mass defect by subtracting the mass of the nucleus from the combined mass of its protons and neutrons and then use Einstein's mass-energy equivalence equation (E=mc^2) to convert the mass defect to energy.

Step-by-step explanation:

The student has asked for the nuclear binding energy in joules for a 59Fe nucleus. To calculate this, we need to find the mass defect by subtracting the mass of the nucleus from the total mass of the individual protons and neutrons that comprise the nucleus. The mass defect in grams is converted to energy in joules using Einstein's mass-energy equivalence equation (E=mc2).

First, we calculate the mass of 26 protons and 33 neutrons (since 59Fe has 26 protons and 59-26=33 neutrons): (26 protons × 1.673 x 10-24 g/proton) + (33 neutrons × 1.675 x 10-24 g/neutron) = total mass of nucleons. Next, we find the mass defect: total mass of nucleons - mass of the 59Fe nucleus. The mass defect in grams is then converted to kilograms by multiplying by 10-3 (since 1 g = 10-3 kg).

Finally, we apply the mass-energy equivalence formula with the speed of light (c = 3 x 108 m/s) to find the binding energy in joules: E = (mass defect in kg) × (speed of light in m/s)2.

Since the question is hypothetical and does not provide actual masses of the protons and neutrons within the specific 59Fe nucleus, the precise answer is not provided but can be calculated following the aforementioned steps.