Contents
The laws of Physics Topics are used to explain everything from the smallest subatomic particles to the largest galaxies.
How do you Find the Nuclear Mass of an Element? What is Atomic Number and Atomic Mass of Elements?
Unified atomic mass unit: The mass of an atom is so small that it is not expressed in kilogram or gram. Instead a special unit called unified atomic mass unit has been designed for this and is expressed as u. This unit is often called dalton or Da. Earlier the atomic mass were represented by amu or atomic mass unit. It was expressed in terms of the mass of hydrogen or oxygen atom. Presently, carbon is taken as the standard as C12 atoms can be obtained free from its isotopes, in nature.
Definition: \(\frac{1}{12}\)th of the mass of a C12 atom is called 1 atomic mass unit (u).
1 mol of carbon-12 has a mass 12 g and contains 6.023 × 1023(Avogadro’s number) of atoms.
Hence, mass of 1 atom of C12 = \(\frac{12}{6.023 \times 10^{23}} \mathrm{~g}\)
∴ As per definition,
1 u = \(\frac{1}{12}\) × \(\frac{12}{6.023 \times 10^{23}}\)g
= 1.66 × 10-24g
= 1.66 × 10-27kg
Equivalent energy of the unified atomic mass: According to E = mc2, equivalent energy of
1 u of mass = 1.66 × 10-24 × (2.998 × 1010)2 erg
= 1.66 × 10-24 × (2.998 × 1010)2 eV
= \(\frac{1.66 \times 10^{-24} \times\left(2.998 \times 10^{10}\right)^2}{1.6022 \times 10^{-12}}\)eV
= 931.2 × 106eV = 931.2 MeV
It is important to remember the value 931.2 MeV for several mathematical calculations, in nuclear physics.
Atomic mass : Relative atomic mass: Atomic mass of an element is the mass of an isotope of that element (discussed later).
Depending upon the abundance of isotopes of an element present on the earth’s surface or in the atmosphere, an average mass of the atom of element is calculated. This average atomic mass is called the relative atomic mass of that element. It is sometimes referred to as atomic weight though it actually expresses the mass and not the weight.
It has been possible to measure precisely the atomic mass or relative atomic mass of elements using mass spectroscopes. Table-2 represents the values in u of a few elements. Data sources are http ://wwv.chemqmu1.ac.uk/iupac/AtWt and www.nndc.bnl.gov/masses.
Table-2
Nuclear mass: Nuclear mass = atomic mass – mass of electrons in the atom of the element. Mass of one electron me is taken as 0.00055 u. Except for very precise measurement, mass of a nucleus and the atomic mass are taken to be the same.
Mass number:
Definition: The whole number nearest to the atomic mass of an element expressed in atomic mass unit, is the mass number of the element. Mass number is equal to the number of protons and neutrons in the nucleus of that atom.
Example: Mass number of hydrogen (H1) is 1 and that of uranium (U238) is 238.
Mass number is simply a number and has no unit. It is usually expressed by the letter A.
The number of protons present in the nucleus of an element is called the atomic number of the element and represented by Z. The difference (A – Z) represents the number of neutrons in the nucleus. Mass number, atomic number, and neutron number of some elements are listed in Table-3.
Table – 3
Notation for mass number: To denote or express the mass number (A) of any element the symbol of the element is used then the mass number is written as a superscript either to the left or to the right side of the symbol.
Example: H1, C12, N14, or, 1H, 4He, 12C, 14N, ……. .
Isotopes: Atoms having the same atomic number but different mass numbers are called isotopes.
Isotopes have identical chemical properties because they are basically the same element, but differ in physical properties because they differ in mass. All the isotopes of an element should in principle occupy the same place as the parent element in the periodic table. The name has originated from this property. Isotopes are formed due to the difference in number of neutrons in the nucleus of an element. Table-4 lists some important isotopes of a few elements.
Table – 4
Carbon has three isotopes C12, C13 and C14. Therefore, when defining relative atomic mass one should write carbon-12 atom and not carbon atom.
Heavy Water: The isotope of hydrogen having mass number 2 is called deuterium. Its symbol is H2. Often it is also expressed as D. Deuterium has one proton and one neutron in its nucleus.
In water (H2O) hydrogen chemically combines with oxygen. Deutenum too, can form similar molecule, D2O in combination with oxygen and is called deuterium oxide or heavy water. Natural water and heavy water have same chemical properties but they differ in physical properties as shown-
In any sample of common water the abundance of heavy water is 1 in 5000 parts.
Heavy water is used in nuclear reactors as ‘moderators’ that slow down the fast moving neutrons formed.
Isobars: The atoms having the same mass number are called isobars. However, isobars differ in their neutron and proton numbers.
Example: C14 and N14 are isobars but neutron number and proton number in C14 are 8 and 6 while those in N14 are 7 and 7 respectively.
Isotones: Atoms having the same number of neutrons in their nucleus are isotones. They differ in mass number and in proton number.
Example: C14 and O16 are mutual isotones. In C14, neutron number = 8, proton number = 6, mass number = 14. In O16 the corresponding numbers are 8, 8 and 16 respectively.
Atomic number:
Importance of atomic number in an atom: The number of protons in the nucleus of an atom of an element determines the characteristics of that element. For instance, if there are 6 protons it is definitely a carbon atom, if there are 8 protons it is an oxygen atom. Neutrons inside the nucleus and electrons outside the nucleus cannot be used to identify the element.
If the number of neutrons in an atom changes an isotope is formed and when there is a change in the number of electrons an ion is formed. Interestingly, if the proton number is altered, the element itself changes into another element. For example, all atoms of oxygen invariably have 8 protons in their nucleus. While proton number remains constant, the electron and neutron numbers may vary in an atom.
We know, elements are arranged in the periodic table according to the change in their chemical properties, taking hydrogen as the first element. In the periodic table we observe that change in chemical property results in a corresponding change in its atomic number (or number of protons). In fact, this observation led to the definition of atomic number.
Definition: Taking hydrogen as the first element, the serial number of an element, arranged according to gradual change in chemical property in the periodic table is called atomic number of that element.
Modern definition of atomic number is as follows:
Definition: Atomic number or proton number (Z) of an element is the number of protons present in the nucleus of an atom of that element.
From the position of the element in the periodic table its atomic number can be determined.
Since, an atom is electrically neutral and the number of electrons is equal to the number of protons so, the number of electrons in a neutral atom can also be taken as the atomic number of that element.
Representation of atomic number: Atomic number of an element is represented by Z. Electric charge in the nucleus of an atom is + Ze where e is the magnitude of charge of an electron. Similar to the method of denoting the mass number of an atom, we can express the atomic number of an element. In this case we write the symbol of the element and then either on the left or on the right side of the symbol we write the atomic number as a subscript. When writing the symbol of an element it is not necessary that we write the atomic number. But the mass number needs to be mentioned. For example, we can write H1