An iron isotope of iron,⁵⁶Fe,has a binding energy per nucleon of 8.791 MeV.What is its mass? (The mass of an hydrogen atom is 1.007825 u,the mass of a neutron is 1.008665 u,and the atomic mass unit is 1 u = 931.5 MeV.The number of protons in the iron nucleus is 26.)

Question

Quizplus · Accepted Answer

The mass of the iron isotope can be calculated using Einstein's famous equation E=mc^2, where E is the binding energy of the nucleus and c is the speed of light. Since the binding energy per nucleon is given, we need to multiply it by the number of nucleons in the nucleus (which is the sum of protons and neutrons). The mass of the iron isotope can then be calculated by converting the binding energy from MeV to atomic mass units (u) and dividing by c^2.

Number of nucleons = 26 protons + 30 neutrons = 56
Binding energy = 8.791 MeV
1 u = 931.5 MeV

Mass = (binding energy x number of nucleons)/(c^2)
= (8.791 MeV x 56)/(931.5 MeV/u)^2
= 55.93494 u

Therefore, the best choice is C, 55.93494 u.

An Iron Isotope of Iron,56Fe,has a Binding Energy Per Nucleon

An Iron Isotope of Iron,⁵⁶Fe,has a Binding Energy Per Nucleon