Sales Toll Free No: 1-855-666-7446

# Atomic Mass Unit

Top
 Sub Topics The mass of an atom or its constituents is expressed in the unit of unified atomic mass constant (u), which was previously known as atomic mass unit(amu).The atomic mass is a number assigned to each chemical element, which specifies the average mass of the atom. The atomic weight scale is chosen so that the mass of a carbon atom of isotope 12C is exactly 12. This unit called relative nuclidic mass is defined as 1/12 of the mass of carbon 12. It was introduced in 1960 by an international agreement and this unit is denoted by u based on the atomic mass 12C = 12.

## Atomic Mass Unit Definition

Definition of Atomic Mass Unit
To define atomic mass unit of an element is "a number which indicates how many times heavier is average atom of that element as compared with 1/12th of the mass of C-12."

Atomic mass of an element is the average mass of all existing isotopes of an element.

Atomic mass = $\frac{Average\ mass\ of\ atoms\ of\ an\ element}{1/12 \times Mass\ of\ an\ atom\ of\ C-12}$

The average mass of an atom = $\frac{RA_{(1)} \times M + RA_{(2)} \times M}{RA_{(1)} + RA_{(2)}}$

Here RA = Relative abundance
M = Mass number of isotopes of an element.

## Standard for the Atomic Mass Unit

To establish a uniform mass scale for atoms it is necessary to select a standard against which the relative masses can be compared. Currently the agreed upon reference is the most abundant isotope of carbon, called carbon-12 and symbolized 12C. One atom of this isotope is assigned exactly 12 units of mass, which is called atomic mass units.

Some prefer to use the symbol amu for the atomic mass unit. The internationally accepted symbol is u. By assigning 12u to the mass of one atom of 12C, the size of the atomic mass unit is established to be 1/12 of the mass of a single carbon-12 atom.

1 atom of 12C has a mass of 12u (exactly)
1 u equals 1/12 the mass of 1 atom of 12C (exactly)

## Unified Atomic Mass Unit

The unified atomic mass unit u also called the Dalton (Da) is related to the macroscopic SI base unit of mass, the kilogram (kg), through the Avogadro number NA, defined as the number of atoms (6.0221 $\times$ 1023) at rest and in their ground state contained in exactly 12g (12 $\times$ 10-3kg) of carbon-12. Since 12g of carbon-12 is also defined as a mole (mol) of carbon -12 we can state that NA = 6.0221 $\times$ 1023 mol-1.

We conclude that the mass of one carbon-12 atom equals to (12g)/NA and that the relationship between the unified atomic mass unit u and the SI mass unit kilogram is 1 u = 1.6605 $\times$ 10-27kg.

Unit for atomic mass - An atomic mass unit is equal to 1.66053 $\times$ 10-24g.

## Atomic Mass Unit Conversion

It is more convenient to write the mass of a nucleus in atomic mass units instead of kg. The modern symbol for the atomic made unit is "u"; in older literature it is often written "amu". The atomic mass unit is defined as exactly 1/12 the mass of a neutral 12C atom. the conversion factor between u and kg is

1 u = 1.6605 $\times$ 10-27 kg

## Average Atomic Mass

1. The average atomic mass of an element depends on both the mass and the relative abundance of each of the elements isotopes.
2. The percentage of each isotope in the naturally occurring element on earth is nearly always the same no matter where the element is found.
3. The percentage at which each of an element's isotopes occurs in nature is taken into account when calculating the elements average atomic mass.
4. Average atomic mass is weighed average of the atomic masses of the naturally occurring isotopes of an element.

## Average Atomic Mass Formula

The average atomic mass for an aggregate of atoms of the same kind can be determined by taking a weighted average of the stable isotopes of that atom. The formula for average atomic mass is given by

Average atomic mass = $\frac{Average\ mass\ of\ atoms\ of\ an\ element}{1/12 \times Mass\ of\ an\ atom\ of\ C-12}$

For example, the atomic mass of helium is 4.00260 amu; thus the average mass of a helium atom is about one third of the mass of a 12C atom. The atomic mass of titanium is 47.90 amu; thus the average mass of a titanium atom is about four times the mass of a 12C atom.

## Calculating Average Atomic Mass

The average atomic mass can be calculated by multiplying the atomic mass of each isotope by its relative abundance and adding the results. Calculating average atomic mass of isotopes are shown by taking an example of chlorine shown below.

Calculate the average atomic mass of chlorine?

To determine the average atomic mass of chlorine two isotopes are considered, Cl-35 and Cl-37. The natural abundance and the atomic mass of each isotopes are given.

 The isotopes of chlorine Isotopes Natural abundance Atomic mass Cl-35 75.771% 34.969amu Cl-37 24.229% 36.966amu

Convert the percent natural abundance of each isotope into a decimal number by dividing each by 100%.
75.771% becomes 0.75771 and 24.229% becomes 0.24229

Multiply the atomic mass of each isotope by the decimal equivalent of its natural abundance.
Cl-35 0.75771 $\times$ 34.969amu = 26.496 amu
Cl-37 0.24229 $\times$ 36.966amu = 8.956 amu

The atomic mass of chlorine is the sum of the contributions from the two isotopes.
Atomic weight of Cl = 26.496amu + 8.956amu = 35.453amu

## Subatomic Particles

What is a subatomic particle?

Subatomic particles are the tiny pieces that come together to make up a single atom.

Subatomic particles definition

Subatomic particles of an atom are particles that are smaller than atoms. Historically subatomic particles were considered to be electrons, protons and neutrons. How ever, the definition of subatomic particles has now been expanded to include elementary particles, which are so small that they do not appear to be made of anything more minute.

Negatively charged subatomic particles

Protons are positively charged subatomic particles found in the nucleus. Neutrons are neutral subatomic particles also found in the nucleus. Electrons are negatively charged subatomic particles that surround the nucleus. Electrons are negatively charged, an atom that has more electrons than protons is a negatively charged ion.

The subatomic particles chart is given below.

 Particle Location Charge Mass Electron Outside nucleus -1 $\frac{1}{1840}$ Neutron In nucleus Zero $\frac{1856}{1840}$ Proton In nucleus +1 $\frac{1853}{1840}$

## Atomic Mass Number

Atomic Mass Number Definition

The atomic mass number is the sum of the number of protons and neutrons in the nucleus of an atom and is usually denoted by the symbol A.

The atomic mass number of an atom is equal to the atomic number (that is the number of protons) plus the number of neutrons. Therefore, the equation for atomic mass is

A = Z + N

Mass Number vs Atomic Mass

The mass number of an element is the sum of the number of protons and neutron present in the nucleus of the atom. The mass number of an element is nearly equal to the atomic mass of that element. However, the main difference between the two is that mass number is always a whole number whereas atomic mass is usually not a whole number.

Periodic table with mass number and atomic number

## Relative Atomic Mass

Relative Atomic Mass Definition

The definition for relative atomic mass is given by relative atomic mass formula mentioned below.

Relative Atomic Mass = $\frac{Mass\ of\ one\ atom\ of\ an\ element}{1/12\ mass\ of\ one\ atom\ of\ carbon-12}$

Relative atomic mass is also defined by

Relative Atomic Mass of Element = Weighted average of relative isotopic masses of the element.

## Gram Atomic Mass

Gram Atomic Mass Definition

The quantity of an element equal to the relative atomic mass in gram is termed as the gram atomic mass or gram atomic weight of the element. The mass of 1 mole of atoms of an element is equal to its relative atomic mass in grams.

Therefore we can say that gram atomic mass or gram atom is the mass of one Avogadro number of atoms expressed in grams.

1 gram atomic mass = 1 gram atom = Mass of 6.023 $\times$ 1023 atoms of the substance

## Finding Atomic Mass

Atomic mass of a molecule is calculated by considering an example of naturally occurring copper which consists of 69.17% copper 63 which has an atomic mass of 62.919598 amu, and 30.83% coppe-65, which has an atomic mass of 64.927793 amu.

Therefore

Atomic mass = 0.6917 $\times$ 62.929599 amu + 0.3083 $\times$ 64.927793 amu = 63.55 amu

So the calculated atomic mass of naturally occurring copper is 63.55 amu.