what fraction of the total mass of an 56Fe atom is due to the electrons?
To determine the fraction of the total mass of a 56Fe atom that is due to electrons, we need to consider the atomic composition and relative masses of the particles involved.
1. Find the atomic composition of iron (Fe):
The atomic number of iron is 26, so it has 26 protons in its nucleus. Since the atom is neutral overall, it also has 26 electrons surrounding the nucleus.
2. Determine the mass of the iron nucleus:
The atomic mass of 56Fe is approximately 56 atomic mass units (AMU), and since protons and neutrons contribute to the atomic mass, we can assume that the majority of the mass is concentrated in the nucleus.
3. Calculate the mass of the electrons:
Electrons have a very small mass compared to protons and neutrons. Each electron has a mass of approximately 0.00055 AMU (or 9.11 x 10^-28 grams).
4. Find the total mass of the iron atom:
To calculate the total mass, we add the mass of the iron nucleus to the combined mass of all the electrons.
Mass of iron nucleus = 56 AMU
Mass of electrons = 26 electrons × 0.00055 AMU/electron
5. Calculate the fraction of the total mass due to electrons:
Divide the mass of the electrons by the total mass of the atom and express it as a fraction or percentage.
Now, let's do the calculations:
Mass of iron nucleus = 56 AMU
Mass of electrons = 26 electrons × 0.00055 AMU/electron = 0.0143 AMU
Total mass of the iron atom = Mass of iron nucleus + Mass of electrons = 56 AMU + 0.0143 AMU = 56.0143 AMU
Fraction of the total mass due to electrons = Mass of electrons / Total mass of the iron atom
= 0.0143 AMU / 56.0143 AMU
So, the fraction of the total mass of a 56Fe atom that is due to electrons is approximately 0.000255, or 0.0255%.