What is Fractional Atomic Mass?

The smallest possible amount of matter which still retains its identity as a chemical element, consisting of a nucleus surrounded by electrons is called an atom. These are the atoms that make up an element. An element is a material with the same number of protons in all of its atoms. Protons, electrons, and neutrons are the three fundamental particles that make up an atom.

The protons (positively charged) and neutrons are found in the nucleus (centre) of the atom (no charge). The electrons are contained in the electron shells, which are the atom’s outermost regions (negatively charged). From then, the notion of atomic mass arose. Protons and neutrons have a mass of around 1.67×10⁻²⁴ grams in common. One atomic mass unit (amu) or one Dalton is how scientists quantify this amount of mass. Protons are positively charged, but neutrons have no charge, despite their identical mass.

Atomic Mass

The average mass of an element’s atoms, measured in atomic mass units, is its atomic mass (amu, also known as Dalton, D). Although kilogram is the SI unit of mass, atomic mass is frequently represented in the non-SI unit Dalton (symbol: Da, or u). Here, 1 Dalton is defined as 1 ⁄ 12 of the mass of a single carbon-12 atom, at rest. The atomic mass of an element is a weighted average of all its isotopes, where the mass of each isotope is multiplied by the abundance of that isotope. 

Example: Atomic mass of Hydrogen is 1, Atomic mass of Helium is 4.00260(Approximately 4)

Element	Atomic Mass
Lithium	6.940
Silicon	28.09
Chlorine	35.457
Carbon	12.01
Polonium	210.00
Bismuth	209.00

In the above table, there are some elements which are having atomic masses as a whole number while there are some elements which are having atomic masses as in decimal values. There are 21 elements that have only one isotope, which means that all of their atoms have the same mass. All other elements have two or more isotopes, resulting in at least two distinct masses for their atoms. When they mix with other elements, however, all elements obey the law of fixed proportions, thus they behave as if they only had one type of atom with a defined mass.

Gram Atomic Mass:  Atomic mass is expressed in grams is known as gram atomic mass.

Formula to calculate atomic mass:

One can identify the atomic mass of an element either by referring to the periodic table or with the help of given formula.

Atomic mass/number)of an element= Mass/number of Proton + Mass/number of Neutron.

Example: Find the element mass number whose atomic number is 18 and the neutron number is 20.

Solution:

Number of proton = 18

Number of Neutrons = 20

Atomic mass Number = Number of protons + number of neutrons

A = 20 + 18

= 38

Reason for fractional atomic mass:

• The atomic masses of most elements are fractional because they exist as a mixture of isotopes of different masses.
• Since the atomic mass of isotopes are different, so average atomic mass is calculated for a single element.
• Avg. mass = total mass of all isotopes/number of isotopes

Overall, we can say that due to multiple numbers isotopes of a single element have fractional atomic mass.

From the above points, it is clear that atomic masses are different for that element that has more than 1 isotope. To address this conundrum, we define atomic mass as the weighted average mass of the element’s naturally occurring isotopes. 

Atomic Mass = [(% abundance of isotope 1)/100] X (mass of isotope 1) + [(% abundance of isotope 2)/100] X (mass of isotope 2) and so on.

Hence, Most of the elements exist in different isotopes i.e., atoms with different masses, e.g. Cl has two isotopes with mass numbers 35 and 37 existing in the ratio 3:1. Hence, the average value is taken.

Example of Lead: Naturally occurring lead is found to consist of four isotopes:

• 1.40%  ²⁰⁴Pb₈₂  whose isotopic mass is 203.973.
• 24.10%  ²⁰⁶Pb₈₂  whose isotopic mass is 205.974
• 22.10%  ²⁰⁷Pb₈₂  whose isotopic mass is 206.976.
• 52.40%  ²⁰⁸Pb₈₂  whose isotopic mass is 207.9

Consider 1 molecule of lead and calculate the average atomic mass of each isotope of lead.

For 1.40 % = (1.40/100) X 203.973= 20.86 g

For 24.10 %= 490.64 g

For 22.10 % = 450.74 g

For  52.40 % = 1080.98 g

Total average atomic mass of lead is = 20.86 + 490.64 + 450.74 + 1080.98 = 207.22 g.

At this point, an essential consequence of the presence of isotopes should be stressed. Atomic weights may vary significantly depending on where a sample of an element was collected when extremely precise findings are obtained. As a result, the International Union of Pure and Applied Chemistry’s Commission on Isotopic Abundance and Atomic Weights has redefined the atomic weights of ten elements with two or more isotopes. The percentages of various isotopes vary widely depending on the element’s source. 

Oxygen in Antarctic precipitation has an atomic weight of 15.99903, but oxygen in marine N₂O has an atomic mass of 15.9997. The isotopes’ “fractionation” is produced by tiny variations in their masses causing slightly varying rates of chemical and physical reactions. When an isotope is produced from nuclear reactors, the difference can be even more significant. 

Sample Questions

Question 1: The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1: 4. What is the ratio of the number of their molecules?

Answer:

Given ratio of masses of oxygen and nitrogen = 1:4, Let mass of O₂ = w

Mass of N₂ = 4w

Molecules of O₂ = w ⁄ (32 × N_A)

Molecules of N₂ = 4w ⁄ (28 × N_A)

Ratio of number of molecules = w ⁄ (32 × N_A) ÷ 4w ⁄ (28 × N_A)

= 7 ⁄ 32

Hence, the ratio is 7 : 32.

Question 2: Find the ratio of a number of oxygen atoms (O) in 16.0 g Ozone (O₃), 28.0 g Carbon Monoxide (CO) and 32.0 g Oxygen (O₂). (Atomic mass : C =12, O =16 and Avogadro’s constant N_A = 6.0 × 10²³ mol⁻¹)

Answer:

Molar mass of O₃ = 48 g

Given: Mass of O₃ = 16 g

Number of moles of O₃ = 16 ⁄ 48 = 1 ⁄ 3

1 mole = 3N_A Oxygen atoms

1 ⁄ 3 mole = N_A Oxygen atoms

• So, Number of atoms = N_A (Oxygen atoms)

Molar mass of CO = 28 g

Given: Mass of CO = 28 g

Number of moles = 28 ⁄ 28 = 1

1 mole = N_A Oxygen atoms

• So, Number of atoms =  N_A (Oxygen atoms)

Molar mass of O₂ = 32 g

Given: Mass of O₂ = 32 g

Number of moles = 32 ⁄ 32 = 1

1 mole = N_A Oxygen atoms

• So, Number of atoms =  N_A (Oxygen atoms)

Hence,  the ratio is 1 : 1 : 1.

Question 3: Determine the number of protons, neutrons, and electrons in the following isotopes that are used in medical diagnoses:

(a) atomic number 9, mass number 18, the charge of 1−

(b) atomic number 43, mass number 99, the charge of 7+

Answer:

a) p: 9; n: 9; e: 10

b) p: 43; n: 56; e: 36

Question 4: An element has the following natural abundances and isotopic masses: 90.92% abundance with 19.99 amu, 0.26% abundance with 20.99 amu, and 8.82% abundance with 21.99 amu. Calculate the average atomic mass of this element.

Answer:

Naturally occurring element is found to consist of three isotopes:

90.92% whose isotopic mass is 19.99 amu.

0.26% whose isotopic mass is 20.99 amu.

8.82% whose isotopic mass is 21.99 amu.

Considering 1 Mole of element, lets calculate average atomic mass of each isotope of lead.

For 90.92% = (90.92 ⁄ 100) × 19.99 = 18.17 g .

For 0.26% atomic mass = 0.05 g

For 8.82% atomic mass = 1.94 g.

Average atomic mass of the given element = 18.17 + 0.05 + 1.94 = 20.16 g

Hence, the average atomic mass of the given element is 20.16 g.

Question 5: Atomic mass of most of the elements is fractional. What is the possible reason for this?

Answer:

On macroscopic level, most of the elements exist as a mixture of isotopes which though may be radioactive, affect the mass of the atom. We know that the atomic mass of an atom depends upon the atomic mass of each of its isotopes. Due to this mixture of the isotopes, the atomic mass is fractional.

Question 6: What is fractional atomic mass?

Answer:

It is observed that atomic masses are not whole numbers. The reason is that most natural elements are a mixture of constant composition containing two or more isotopes. The relative atomic mass of any element is the weighted average of the relative atomic masses of its natural isotopes. For example, Chlorine consists of a mixture of two isotopes of masses 35 and 37 in the ratio of 3:1.

Average relative atomic mass of chlorine = (35 × 3 + 37 × 1) ⁄ 4 = 35.5 g

Hence, the fractional atomic mass is 35.5 g.

Question 7:  Calculate The Average Atomic Mass Of Bromine Atom

Answer:

The atomic mass of an element is the mass of one atom of that element. Average atomic mass takes into account the isotopic abundance.

Isotope of bromine with atomic mass 79 u = 49.7%

Therefore, Contribution of ³⁵Br₇₉ to atomic mass = (79 × 49.7) ⁄ 100 = 39.26 u

Isotope of bromine with atomic mass 81 u = 50.3%

Contribution of ³⁵Br₈₁ to the atomic mass of bromine = (81 × 50.3) ⁄ 100 = 40.64 u

Average atomic mass of the bromine atom = 39.26 + 40.64 u = 79.9 u

Hence, the average atomic mass of the bromine atom is 79.9 u.