Question

The mass of a proton is 1.673×10⁻²⁴g. The mass of a neutron is 1.675×10⁻²⁴g. The mass of the nucleus of a ⁵⁹Fe atom is 9.787×10⁻²³g. What is the nuclear binding energy (in joules) for a ⁵⁹Fe nucleus?

Answer 1

The nuclear binding energy of a ⁵⁹Fe nucleus is approximately 8.8083x10⁻⁸ Joules.

Step-by-step explanation:

The nuclear binding energy of a ⁵⁹Fe nucleus can be calculated using the mass defect and Einstein's equation, E = mc².

The mass defect is the difference between the actual mass of the nucleus and the sum of the masses of its constituent particles.

In this case, the mass defect is given as 9.787×10⁻²³g. To find the nuclear binding energy, we can convert the mass defect to kilograms and multiply it by the square of the speed of light, c, which is approximately 3.00x10⁸ m/s.

Mass defect = 9.787×10⁻²³g = 9.787×10⁻²⁶kg

Nuclear binding energy, E = (mass defect) x (speed of light)²

E = (9.787×10⁻²⁶kg) x (3.00x10⁸ m/s)²

E = 8.8083x10⁻⁸ J

Therefore, the nuclear binding energy of a ⁵⁹Fe nucleus is approximately 8.8083x10⁻⁸ Joules.