Atomic Weight

The atomic weight (also known as relative atomic mass) is a quantity used to express the average weight of an atom. Atoms consist of electrons, protons, and neutrons. Protons and neutrons are mainly responsible for the mass of an atom. For a given element, the proton number (more commonly known as the atomic number) is fixed, but the neutron number can vary. Such elements are called isotopes. Because of this variance in the neutron number, an atom of the same element can have a different atomic mass.

Consider an example of chlorine, which has two naturally-occurring isotopes: ³⁵Cl and ³⁷Cl. The atomic mass of these isotopes is 34.969 u and 36.966 u respectively. The dilemma here is which atomic mass to consider. To solve this problem and have better accuracy in calculations, we average out atomic masses. This average atomic mass is called the atomic weight.

Definition of Atomic Weight

The Atomic weight is defined as the average atomic mass of isotopes of an element in a given sample. It is the weighted average atomic mass calculated using the relative abundance of isotopes of an element. The atomic weight is also known as the relative atomic mass.

Notation

The atomic weight is denoted by the symbol A_r.

Unit

Unlike the atomic mass, the atomic weight does not have any unit. It is a dimensionless quantity.

Formula

The formula of atomic weight can be formulated based on the above definition.

where p_i is the percentage or relative abundance of an isotope i of atomic mass m_i.

The numerator in the above formula gives the average atomic mass, which has a unit of the dalton or the unified atomic mass (u). In order to make the result dimensionless we divide it by 1 u.

1 u is also defined as the one-twelfth atomic mass of carbon-12, 1 u = ¹∕₁₂ m_(¹²C). So, we can also define the atomic weight in terms of carbon-12 as the ratio of the average atomic mass to the one-twelfth atomic mass of carbon-12.

Standard Atomic Weight

When the atomic weight of an element is calculated using the relative abundance based on the Earth, we called it the standard atomic weight A_{r, std} Thus, the standard atomic weight considers naturally occurring isotopes. It is more specific than the atomic weight. The values of the standard atomic weight are published and maintained by the Commission on Isotopic Abundances and Atomic Weights (CIAAW), which is a committee of the IUPAC.

Atomic Weight and Atomic Mass

The atomic weight and the atomic mass are often confused as the same quantity, but they are different. The notion of the atomic weight was discovered prior to the atomic mass. In fact, John Dalton calculated atomic weights of different elements using hydrogen, which is the lightest element, as the reference standard, not atomic masses. The atomic mass came to known with the discovery of isotopes. It was English scientist Francis Aston who accidentally discovered the existence of isotopes. The table below helps to distinguish the differences between both.

Table 1: Comparison between Atomic Weight and Atomic Mass

Atomic Weight	Atomic Mass
The atomic weight is weighted average atomic mass of isotopes.	The atomic mass is the mass of an atom of an element. It does not account isotopes.
It is a dimensionless quantity.	The dalton or the unified mass unit (u) or the atomic mass unit (amu) is the unit used to express the atomic mass.
The atomic weight is more practical and often used by chemists.	It is used when we are dealing with an isotopic atom. It is more likely used by physicists.
The atomic weight is estimated from the atomic mass of isotopes of an element.	It is determined from the atomic number and the mass number. It is the sum of the mass of electrons, protons, and neutrons present in an atom.
The atomic weight depends on the relative abundance of isotopes of an element in a given sample. So, it can vary from sample to sample.	The atomic mass of an isotopic atom is unique. It does not change from sample to sample.
It is usually expressed in fewer decimal figures.	It is mentioned in large significant figures.

When we deal with elements which are mono-isotopic i.e., have only one isotope, the atomic mass and the atomic weight are the same. The difference in the atomic mass and the atomic weight increases when there is a large variance in atomic masses of isotopes. The difference also depends on the relative abundance of isotopes.

Atomic Weight and Atomic Number

Russian chemist Dmitri Mendeleev used the atomic weight to form the raw version of the periodic table. But the atomic weight was found inconsistent to define an element. Later, it was replaced by the atomic number, which uniquely defines an element. Elements in the modern periodic table are arranged with increasing order of the atomic number. The below graph shows the trend of the atomic weight to the atomic number.

As we can see from the above graph, initially for lighter elements, the atomic weight is almost twice the atomic number. For heavier elements, as the atomic number increases, the atomic weight exceeds twice the atomic number. This divergence in the graph is due to an increase in the neutron number. For heavier elements, the number of neutrons in the nucleus is more than the number of protons which increases the mass of an atom. You can extract data from the above graph (atomic weight vs atomic number) using PlotDigitizer.

We can also notice from the above graph the atomic weight does not always increases with rise in the atomic number. In between there are small dips in the atomic weight. Examples are ₁₈Ar, 39.948 and ₁₉K, 39.098; ₂₇Co, 58.933 and ₂₈Ni, 58.693; ₅₂Te, 127.6 and ₅₃I, 126.904.

Uncertainties in Atomic Weight

There are always uncertainties in the values reported by the CIAAW. They are discussed below.

• Measurement Limits: The measurement limits are always present in experimental results. There is a limit to which we measure the atomic mass of an isotope. This results in uncertainty in the atomic mass itself. For example, the atomic mass of sodium-23 is 22.989 769 282 0(19), where “(19)” represents uncertainty in the atomic mass. It can also be represented as 22.989 769 282 0 ± 000 000 001 9.
• Sampling Error: The sampling error results when a given sample may not represent the original source. This may be due to negligence from the human side.
• Unequal Distribution: The relative abundance of an isotope can vary from the source. Since the Earth is a huge giant, the distribution of an isotope can differ in air, ocean, soil, crust, volcanoes. For example, the presence of lighter isotopes of thallium is more in igneous rocks compare to sedimentary rocks.

Formats of Atomic Weight

The atomic weight is reported in many formats based on the requirement. The below mentions some of the common formats.

1. Abridged: The abridged format published by the CIAAW. It mentions the atomic weight in five significant figures. For example, A_{r, abridged} of ₁₀Ne is 20.180.
2. Interval: When the average atomic mass of an element vary significantly from different sources, we preferably use interval to mention the atomic weight. For example, A_r of ₅B is [10.806, 10.821].
3. Conventional: The conventional format is commonly used format. The values are approximated to fewer decimal points. For example, A_{r, conv} of ₅B is 10.81.
4. Standard: The standard format is more precise with mentioning of uncertainty. For example, A_{r, std} of ₂He is 4.002 602(2).

Molecular Weight

The molecular weight is the weight of a molecule. It can be calculated by adding the atomic weights of each element in the molecule. The molecular weight of any molecule can be determined by knowing its molecular formula and atomic weights of its elements. It is synonymous with the relative molar mass. Consider an example of methane, which has the molecular formula CH₄. So, we can calculate the molecular weight of methane as:

To Calculate Atomic Weight

The atomic weight of any element can be calculated by knowing the individual atomic mass and the relative abundance of isotopes.

Example 1: To Calculate Atomic Weight of Hydrogen

Hydrogen has three naturally occurring isotopes. The data of the isotopes is mentioned in the below table.

Table 2: Isotopes of Hydrogen with Relative Abundance

Isotope	Atomic Mass (u)	Relative Abundance (%)
Hydrogen (1H)	1.007 825	99.98
Deuterium (2H)	2.014 102	0.02
Tritium (3H)	3.016 049	trace

Since tritium presence in very small, we can simply ignore it. Thus, the atomic weight accurate up to three decimal figures is calculates as follows:

Example 2: To Calculate Atomic Weight of Carbon

Carbon has around 15 known isotopes of which only two are stable. The data of these two isotopes is mentioned in the below table.

Table 3: Isotopes of Carbon with Relative Abundance

Isotope	Atomic Mass (u)	Relative Abundance (%)
Carbon-12 (12C)	12	98.9
Carbon-13 (13C)	13.003 355	1.1

The atomic mass of carbon-12 is exactly 12 u. The atomic weight accurate up to three decimal figures is calculates as follows:

Example 3: To Calculate Atomic Weight of Oxygen

Oxygen has three naturally-occurring isotopes. The data of the isotopes is mentioned in the below table.

Table 4: Isotopes of Oxygen with Relative Abundance

Isotope	Atomic Mass (u)	Relative Abundance (%)
Oxygen-16 (16O)	15.994 915	99.76
Oxygen-17 (17O)	16.999 132	0.04
Oxygen-18 (18O)	17.999 159	0.20

Since tritium presence in very small, we can simply ignore it. Thus, the atomic weight accurate up to three decimal figures is calculates as follows:

Example 4: To Calculate Atomic Weight of Zinc

Zinc has five stable isotopes. The data of the isotopes is mentioned in the below table.

Table 5: Isotopes of Zinc with Relative Abundance

Isotope	Atomic Mass (u)	Relative Abundance (%)
Zinc-64 (16Zn)	63.929 142	49.17
Zinc-66 (17Zn)	65.926 033	27.73
Zinc-67 (18Zn)	66.927 127	4.04
Zinc-68 (18Zn)	67.924 844	18.45
Zinc-70 (18Zn)	69.925 319	0.61

Since tritium presence in very small, we can simply ignore it. Thus, the atomic weight accurate up to three decimal figures is calculates as follows:

List of Elements by Atomic Weight

The table below lists the atomic weights of all 118 elements with their atomic numbers.

Table 6: List of Elements by Atomic Weight

Atomic Number	Element	Symbol	Atomic Weight
1	Hydrogen	H	1.008
2	Helium	He	4.002 602
3	Lithium	Li	6.94
4	Beryllium	Be	9.012 183 1
5	Boron	B	10.81
6	Carbon	C	12.011
7	Nitrogen	N	14.007
8	Oxygen	O	15.999
9	Fluorine	F	18.998 403 16
10	Neon	Ne	20.179 7
11	Sodium	Na	22.989 769 28
12	Magnesium	Mg	24.305
13	Aluminium	Al	26.981 538 4
14	Silicon	Si	28.085
15	Phosphorus	P	30.973 762
16	Sulphur	S	32.06
17	Chlorine	Cl	35.45
18	Argon	Ar	39.948
19	Potassium	K	39.098 3
20	Calcium	Ca	40.078
21	Scandium	Sc	44.955 908
22	Titanium	Ti	47.867
23	Vanadium	V	50.941 5
24	Chromium	Cr	51.996 1
25	Manganese	Mn	54.938 043
26	Iron	Fe	55.845
27	Cobalt	Co	58.933 194
28	Nickel	Ni	58.693 4
29	Copper	Cu	63.546
30	Zinc	Zn	65.38
31	Gallium	Ga	69.723
32	Germanium	Ge	72.63
33	Arsenic	As	74.921 595
34	Selenium	Se	78.971
35	Bromine	Br	79.904
36	Krypton	Kr	83.798
37	Rubidium	Rb	85.467 8
38	Strontium	Sr	87.62
39	Yttrium	Y	88.905 84
40	Zirconium	Zr	91.224
41	Niobium	Nb	92.906 37
42	Molybdenum	Mo	95.95
43	Technetium	Tc	98
44	Ruthenium	Ru	101.07
45	Rhodium	Rh	102.905 49
46	Palladium	Pd	106.42
47	Silver	Ag	107.868 2
48	Cadmium	Cd	112.414
49	Indium	In	114.818
50	Tin	Sn	118.71
51	Antimony	Sb	121.76
52	Tellurium	Te	127.6
53	Iodine	I	126.904 47
54	Xenon	Xe	131.293
55	Caesium	Cs	132.905 452
56	Barium	Ba	137.327
57	Lanthanum	La	138.905 47
58	Cerium	Ce	140.116
59	Praseodymium	Pr	140.907 66
60	Neodymium	Nd	144.242
61	Promethium	Pm	145
62	Samarium	Sm	150.36
63	Europium	Eu	151.964
64	Gadolinium	Gd	157.25
65	Terbium	Tb	158.925 354
66	Dysprosium	Dy	162.5
67	Holmium	Ho	164.930 328
68	Erbium	Er	167.259
69	Thulium	Tm	168.934 218
70	Ytterbium	Yb	173.045
71	Lutetium	Lu	174.966 8
72	Hafnium	Hf	178.49
73	Tantalum	Ta	180.947 88
74	Tungsten	W	183.84
75	Rhenium	Re	186.207
76	Osmium	Os	190.23
77	Iridium	Ir	192.217
78	Platinum	Pt	195.084
79	Gold	Au	196.966 57
80	Mercury	Hg	200.592
81	Thallium	Tl	204.38
82	Lead	Pb	207.2
83	Bismuth	Bi	208.980 4
84	Polonium	Po	209
85	Astatine	At	210
86	Radon	Rn	222
87	Francium	Fr	223
88	Radium	Ra	226
89	Actinium	Ac	227
90	Thorium	Th	232.037 7
91	Protactinium	Pa	231.035 88
92	Uranium	U	238.028 91
93	Neptunium	Np	237
94	Plutonium	Pu	244
95	Americium	Am	243
96	Curium	Cm	247
97	Berkelium	Bk	247
98	Californium	Cf	251
99	Einsteinium	Es	252
100	Fermium	Fm	257
101	Mendelevium	Md	258
102	Nobelium	No	259
103	Lawrencium	Lr	266
104	Rutherfordium	Rf	267
105	Dubnium	Db	268
106	Seaborgium	Sg	269
107	Bohrium	Bh	270
108	Hassium	Hs	270
109	Meitnerium	Mt	278
110	Darmstadtium	Ds	281
111	Roentgenium	Rg	282
112	Copernicium	Cn	285
113	Nihonium	Nh	286
114	Flerovium	Fl	289
115	Moscovium	Mc	290
116	Livermorium	Lv	293
117	Tennessine	Ts	294
118	Oganesson	Og	294
[Data Source: Royal Society of Chemistry]

Associated Articles

• Atomic number
• Atomic mass
• Atomic mass unit