what fraction of the total mass of an 56 Fe atom is due to the electrons? The mass of a proton is 1.673 x10-24 g, of a neurton 1.675 x 10-24 g, an of an electron 9.109 x 10-28g.
0.000252565
To determine the fraction of the total mass of an 56 Fe atom that is due to the electrons, we need to calculate the mass contribution of the electrons and compare it to the total mass of the atom.
The atomic mass of 56 Fe is 56 atomic mass units (AMU). Since the atomic mass unit is defined as 1/12th the mass of a carbon-12 atom, 1 AMU is roughly equal to 1.661 x 10-24 grams.
To find the mass contribution of the protons and neutrons in the 56 Fe atom, we need to multiply their masses by their respective quantities:
Mass of protons = 26 protons × (1.673 x 10-24 g/proton) = 43.498 x 10-24 g
Mass of neutrons = 30 neutrons × (1.675 x 10-24 g/neutron) = 50.25 x 10-24 g
The total mass of protons and neutrons in the 56 Fe atom is:
Mass of protons + neutrons = 43.498 x 10-24 g + 50.25 x 10-24 g = 93.748 x 10-24 g
To find the mass contribution of the electrons, we need to multiply the mass of an electron by the number of electrons in the 56 Fe atom. Since an iron atom has 26 electrons:
Mass of electrons = 26 electrons × (9.109 x 10-28 g/electron) = 236.734 x 10-28 g
To compare the mass contribution of the electrons to the total mass of the atom, we need to convert the mass of the electrons to the same units as the total mass of the atom:
236.734 x 10-28 g = 0.236734 x 10-24 g
Now, we can calculate the fraction:
Fraction of the total mass due to electrons = Mass of electrons / (Mass of protons + neutrons + Mass of electrons)
= 0.236734 x 10-24 g / (93.748 x 10-24 g + 0.236734 x 10-24 g)
≈ 0.0025
Therefore, approximately 0.0025 (or 0.25%) of the total mass of a 56 Fe atom is due to the electrons.
To find the fraction of the total mass of an iron-56 (56Fe) atom that is due to the electrons, we need to calculate the mass contributed by the electrons and then compare it to the total mass of the atom.
The mass of an electron is given as 9.109 x 10^-28g.
To calculate the mass contributed by the electrons, we need to know the number of electrons in an iron-56 atom. Since iron-56 (56Fe) has 26 protons, it also has 26 electrons since atoms are electrically neutral.
The total mass of an iron-56 atom can be calculated by summing the masses of its protons and neutrons. However, since the question only provides the mass of protons and neutrons, we'll assume that the mass of a neutron is the same as the mass of a proton.
The mass of a proton (and neutron) is given as 1.673 x 10^-24g.
Now, the total mass of an iron-56 atom is:
Mass of 56Fe = (Number of protons x Mass of a proton) + (Number of neutrons x Mass of a neutron)
Since an iron-56 atom has 26 protons and 30 neutrons:
Mass of 56Fe = (26 x 1.673 x 10^-24g) + (30 x 1.673 x 10^-24g)
To simplify, we can calculate the total mass of the iron-56 atom:
Mass of 56Fe = 56 x 1.673 x 10^-24g
Now, to calculate the mass contributed by the electrons, we multiply the number of electrons by the mass of an electron:
Mass of electrons = Number of electrons x Mass of an electron
Mass of electrons = 26 x 9.109 x 10^-28g
To find the fraction of the total mass of the atom due to electrons, we divide the mass of the electrons by the total mass of the atom:
Fraction = Mass of electrons / Mass of 56Fe
Let's plug the values into the formulas to calculate the fraction:
Mass of 56Fe = 56 x 1.673 x 10^-24g
Mass of electrons = 26 x 9.109 x 10^-28g
Fraction = (26 x 9.109 x 10^-28g) / (56 x 1.673 x 10^-24g)
Calculating the fraction gives us the answer.