what fraction of the total mass of an 56 Fe atom is due to the electrons? The mass of a proton is 1.673 x 10-24 g, of a neutron 1.675 x 10-24 g, an of an electron 9.109 x 10-28g.
To determine the fraction of the total mass of an iron-56 (56 Fe) atom that is due to the electrons, we need to calculate the total mass of the electrons and compare it to the overall mass of the atom.
Step 1: Determine the number of protons, neutrons, and electrons in an iron-56 atom.
An iron-56 atom has 26 protons and 30 neutrons. Since the atomic number of iron is 26, it indicates the number of protons, which is equal to the number of electrons in a neutral atom.
Step 2: Calculate the total mass of the protons and neutrons.
The mass of a proton is given as 1.673 x 10^(-24) g, and the mass of a neutron is given as 1.675 x 10^(-24) g. To calculate the total mass of the protons and neutrons in an iron-56 atom, multiply the mass of a proton by the number of protons, and multiply the mass of a neutron by the number of neutrons:
Total mass of protons = (mass of a proton) x (number of protons)
Total mass of protons = (1.673 x 10^(-24) g) x (26)
Total mass of protons = 4.345 x 10^(-23) g
Total mass of neutrons = (mass of a neutron) x (number of neutrons)
Total mass of neutrons = (1.675 x 10^(-24) g) x (30)
Total mass of neutrons = 5.025 x 10^(-23) g
Step 3: Calculate the total mass of the electrons.
The mass of an electron is given as 9.109 x 10^(-28) g. Since the number of electrons in an iron-56 atom is the same as the number of protons (26), we can calculate the total mass of the electrons by multiplying the mass of an electron by the number of electrons:
Total mass of electrons = (mass of an electron) x (number of electrons)
Total mass of electrons = (9.109 x 10^(-28) g) x (26)
Total mass of electrons = 2.370 x 10^(-26) g
Step 4: Calculate the total mass of the iron-56 atom.
The total mass of the iron-56 atom is the sum of the masses of the protons and neutrons:
Total mass of iron-56 atom = Total mass of protons + Total mass of neutrons
Total mass of iron-56 atom = 4.345 x 10^(-23) g + 5.025 x 10^(-23) g
Total mass of iron-56 atom = 9.370 x 10^(-23) g
Step 5: Calculate the fraction of the total mass due to the electrons.
To find the fraction of the total mass of the iron-56 atom that is due to the electrons, divide the total mass of the electrons by the total mass of the iron-56 atom:
Fraction = Total mass of electrons / Total mass of iron-56 atom
Fraction = (2.370 x 10^(-26) g) / (9.370 x 10^(-23) g)
Fraction = 2.528 x 10^(-4)
Therefore, the fraction of the total mass of an iron-56 atom that is due to the electrons is approximately 2.528 x 10^(-4).