Atomic Mass vs Average Atomic Mass vs Relative Isotopic Mass

Atomic Mass, Average Atomic Mass, & Relative Isotopic Mass

Atomic Mass

The atomic mass is the mass of a single atom of an element. The mass of an atom (atomic mass) can be expressed in Kilogram or Gram or a.m.u or u.

The SI unit of mass is the kilogram (kg), but the atomic mass is most often expressed in the non-SI unit a.m.u (atomic mass unit), also known as u (unified mass).

Where 1 a.m.u (or u) is defined as ¹⁄₁₂ absolute mass of a single Carbon¹² atom at rest. This is a standard scale unit to calculate the mass of one atom of any element in a.m.u.

1 a.m.u = Absolute mass of one Carbon atom ÷ 12

The absolute mass of one Carbon¹² atom (in kg) = 1.99264687992 × 10⁻²⁶ kg = 1.99264687992 × 10⁻²³ g. (We will see how it was calculated.)

So, 1 a.m.u = (1.99264687992 × 10⁻²³ g) ÷ (12)
1 a.m.u = 1.66053907 x 10^-24 g = (1 Dalton)
⇒ 1 a.m.u. = 1 u = 1 Da (dalton) = ¹⁄₁₂ x mass of a single Carbon-12 atom = 1.66053907 x 10^-24 g

1.66053907 x 10^-24 gram mass known as Atomic Mass Constant (m_u) and considered as 1 a.m.u. by convention

• When the Mass of an atom is expressed in grams or kilograms, it is called the absolute mass of the atom.
• The mass of the Carbon¹² atom is 12 a.m.u, which is also the mass number (no. of protons + no. of neutrons) of Carbon¹².
• That means 1 a.m.u is the average mass of one proton or one neutron of an element.

Gram to A.M.U. Conversion Factor

1.66053907 x 10^–24 gram mass is considered 1 a.m.u. It is a conventional scale to measure the mass of an atom of various elements.

We know,
1 a.m.u = 1.66053907 x 10^-24 g (Atomic Mass Constant)
So,
1g = (1 a.m.u) ÷ (1.66053907 x 10^-24)
    = 6.02214075 x 10²³ a.m.u.

Now, If we know the mass of an object in Kilogram or Gram then we can easily calculate its mass in a.m.u.

6.02214075 x 10²³ known as Avogadro’s Number (N_A) or 1 mol
So,
1 a.m.u. = (1g) ÷ 6.02214075 x 10²³
1 a.m.u. = (1g) ÷ N_A

Calculate Atomic Masses in A.M.U.

Mass of Proton in a.m.u.

The mass of a Proton = 1.67262779 x 10^-24 g
∵ 1g = 6.02214075 x 10²³ a.m.u.
∴ 1.67262779 x 10^-24 g = (1.67262779 x 10^-24) x (6.02214075 x 10²³ a.m.u.) = 1.00728 a.m.u.

Mass of Neutron in a.m.u.

The mass of a Neutron = 1.67493594 x 10^-24 g
∵ 1g = 6.02214075 x 10²³ a.m.u.
∴ 1.67493594 x 10^-24 g = (1.67493594 x 10^-24) x (6.02214075 x 10²³ a.m.u.) = 1.00867 a.m.u.

Mass of Electron in a.m.u.

The mass of an Electron = 9.1 x 10^-28 g
∵ 1g = 6.02214075 x 10²³ a.m.u.
∴ 9.1 x 10^-28 g = (9.1 x 10^-28) x (6.02214075 x 10²³ a.m.u.) = 0.00055 a.m.u. = 5.5 x 10^-4 a.m.u

Calculate the Atomic Mass of an Element

• The protons and neutrons of the nucleus account for nearly all of the total mass of an atom.
• The electrons make negligible contributions to the mass of the atom.
• Thus, the numeric value of the atomic mass when expressed in a.m.u has nearly the same value as the mass number (Protons + Neutrons).

Atomic Mass of Oxygen (O¹⁶)

Oxygen (O¹⁶) has 8 protons, 8 neutrons, and 8 electrons
and above we have calculated the mass of one proton, one neutron, and one electron

Therefore,
= (8 x 1.00728 a.m.u) + (8 x 1.00867 a.m.u) + (8 x 0.00055 a.m.u)
= 16.1319886 a.m.u, should be the atomic mass of oxygen (O¹⁶) but

Now, If we first calculate the energy of 1 a.m.u mass, and then if we are given the binding energy of a nucleus, it will be easy to calculate the mass defect for that atomic nucleus.

We know,
1 a.m.u. = 1.66053907 x 10^-27 Kg
1 = 1.66053907 x 10^-27 Kg/a.m.u.
E = MC²
= (1.66053907 x 10^-27 Kg/a.m.u.) x (3 x 10⁸ m/s)²
= (1.66053907 x 10^-27) x (3 x 10⁸)² Joule/a.m.u.
Converting Joule to electron volt (1 J = 1.6 x 10¹⁹ e.v.)
= (1.66053907 x 10^-27) x (3 x 10⁸)² x (1.6 x 10¹⁹) e.v./a.m.u.
Converting electron volt to Mega electron volt (e.v to M.e.v)
= (1.66053907 x 10^-27) x (3 x 10⁸)² x (1.6 x 10¹⁹) x 10^-6
≈ 931.5 M.e.v/a.m.u.

1 a.m.u ≈ 931.5 M.e.v

Actual Atomic Mass of Oxygen (O¹⁶)

Above we have calculated the atomic mass of oxygen = 16.1319886 a.m.u. Still, during the fusion of protons and neutrons, the nucleus of the oxygen atom releases some energy and hence will lose some mass.

Mass defect of Oxygen (O¹⁶)
For Oxygen, the binding energy per nucleon = 8 M.e.v. (Determined experimentally)
Oxygen has 16 nucleons (Protons + Neutrons)
Mass defect = (8 M.e.v x 16) ÷ 931.5 M.e.v/a.m.u. = 0.1374 a.m.u

So the atomic mass of one oxygen atom (O¹⁶) in a.m.u.
= 16.1319886 a.m.u – Mass defect
= 16.1319886 a.m.u – 0.1374 a.m.u = 15.9946 a.m.u

And, the Absolute/Actual Atomic Mass or Mass of one oxygen atom (O¹⁶)
= 15.9946 a.m.u x (Atomic Mass Constant/a.m.u.)
= 15.9946 a.m.u x (1.66053907 x 10^-24 gram/a.m.u)
= 2.655965 x 10^-23 gram
= 2.655965 x 10^-26 Kg

Atomic Mass of Carbon (C¹²)

Mass of carbon atom in a.m.u.
Carbon has 6 protons, 6 neutrons, and 6 electrons
= [(6 × 1.00728 amu) + (6 × 1.00867 amu) + (6 × 0.00055 amu)] – Mass defect
= 12.09900 amu – Mass defect

Mass defect of Carbon¹² atom
For Carbon the binding energy per nucleon = 7.68 M.e.v. (Determined experimentally)
Carbon¹² has 12 nucleons (Protons + Neutrons)
Mass defect = (7.68 M.e.v x 12) ÷ 931.5 M.e.v/a.m.u = 0.0989371981 a.m.u ≈ 0.099 a.m.u

= 12.09900 amu – 0.099 amu
= 12 a.m.u.

And, the Absolute/Actual Atomic Mass or Mass of one Carbon¹² atom
12 a.m.u × (Atomic Mass Constant/a.m.u.)
12 a.m.u. x (1.66053907 x 10^-24 gram/a.m.u.)
= 1.99264688 × 10⁻²³ g

Relative Isotopic Mass

Relative Isotopic Mass simply means HOW MANY TIMES the absolute mass of one atom (in grams or Kilograms) is heavier than the ¹⁄₁₂ absolute mass of one carbon¹² atom.

Relative Isotopic Mass of Carbon¹²

To determine the Relative Isotopic Mass of Carbon¹², we divide the mass of one C¹² atom by the ¹⁄₁₂ mass of C¹² (Atomic Mass Constant).

Relative Isotopic Mass of Carbon¹²
= (Actual Mass of C¹² isotope) ÷ (Atomic mass constant)
= (1.99264688 × 10⁻²³ g) ÷ (1.66053907 x 10^-24 g)
= 12

So, the Atomic Mass of Carbon¹² is 12 a.m.u but the Relative Isotopic Mass of one Carbon¹² atom is simply 12 with no dimensions.

• Relative Isotopic Mass represents HOW MANY TIMES the absolute mass of one atom of an element is heavier than 1⁄12 mass of one Carbon12 atom.
• Relative Isotopic Mass is obtained by dividing the Atomic Mass (m_a)of an isotope by the Atomic Mass Constant (m_u) yielding a dimensionless value.
• The word “relative” in the term “relative isotopic mass” refers to the scaling relative to ¹⁄₁₂ mass of one Carbon¹² atom.

Relative Isotopic Mass of Oxygen¹⁶

Relative Isotopic Mass of Oxygen¹⁶
= (Mass of O¹⁶ isotope) ÷ (Atomic mass constant)
= (2.655965 x 10^-23 gram) ÷ (1.66053907 x 10^-24 gram)
= 15.9946

The Atomic Mass and the Relative Isotopic Mass refer to a certain specific isotope of an element. Because substances are usually not isotopically pure, it is convenient to use the Standard Elemental Atomic Mass

_Standard Relative Atomic Mass (A_r, _standard(E))

The Standard Relative Atomic Mass is the elemental atomic mass which is the average (mean) relative isotopic mass of an element, weighted by the abundance of its isotopes on earth.

On the Periodic Table, the atomic mass of carbon is reported as 12.011. This is the Standard Relative Atomic Mass (Standard Average Relative Atomic Mass or Standard Atomic Weight or Standard Average Atomic Mass/Weight) of carbon.

No single carbon atom has a relative mass of 12.011, but a handful of Carbon atoms (including their isotopes: C¹², C¹³, & C¹⁴) have an average mass of 12.011.

Calculate the Relative Atomic Mass

Ar, _standard = [Relative isotopic mass x (% abundance / 100)] + [Relative isotopic mass x (% abundance / 100)] + ……

Standard Relative Atomic Mass of Chlorin

isotope ³⁵Cl constitutes 75.77% of the copper on Earth and the rest 24.23% being ³⁷Cl, so
A_r, _standard(Cl) = [³⁵Cl relative isotopic mass x (% abundance / 100)] + [³⁷Cl relative isotopic mass x (% abundance / 100)]
A_r, _standard(Cl) = [34.96885269 x (75.77 / 100)] + [36.96590258 x (24.23 / 100)]
A_r, _standard(Cl) = [34.96885269 x 0.7577] + [36.96590258 x 0.2423]
A_r, _standard(Cl) = 35.4527379 ≈ 35.5

Because relative isotopic masses are dimensionless quantities, this weighted mean is also dimensionless. It can be converted into a measure of mass by multiplying it with the atomic mass constant.

Relative Atomic Mass (A_r)

Relative Atomic Mass or Atomic Weight or Average Atomic Weight or Average Atomic Mass: It is the same as Standard Relative Atomic Mass, this term is used for a single specific given sample from a particular location.

The relative atomic mass of a given element sample is the weighted arithmetic mean of the masses of the individual atoms (including their isotopes) that are present in the sample.

This quantity can vary substantially between samples because the sample’s origin may have produced unique combinations of isotopic abundances.

Standard Relative Atomic Mass is a standardized value obtained with the various element samples being taken from Earth and is a more common, and more specific quantity.