UPSC Chemistry Nuclear Chemistry Atoms, Molecules and Nuclear Chemistry

Atoms, Molecules and Nuclear Chemistry

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The combination of different elements to form compounds is governed by some basic rules. These rules, collectively called ‘laws of chemical combination’.



Law of Conservation Mass:

Lavoisier, who is widely regarded as the father of modem chemistry gave the law of conservation of mass. This law states that in any chemical reaction, the mass of the substances that react equals the mass of the products that are formed.


Law of Definite Proportions:

This Jaw was given by Joseph Proust, a French chemist, in 1799. Proust’s law of definite proportions states that different samples of the same compound always contain its constituent elements in the same proportion by mass.


Law of Multiple Proportions:

In 1803 Dalton gave this law. As per this law if two elements combine to form more compounds, the masses of one element combine with a fixed mass of the other element, are in the ratio of small whole numbers.


The Law of Gaseous Volume:

When gases react, the volumes consumed and produced, measured at the same temperature and pressure, are in ratios of small whole numbers. This is also known as Gay-Lussac’s Law.


Dalton’s Atomic Theory

The hypotheses about the nature of matter on which Dalton’s atomic theory is based can be summarized as:

  • Matter consists of indivisible atoms.
  • All the atoms of a given chemical element are identical in mass and in all other properties.
  • Different chemical elements have different kinds of atoms and in particular such atoms have different masses.
  • Atoms are indestructible and retain their identity in chemical reactions.


Laws of Chemical Combination and Dalton’s Theory

  • Dalton’s fourth postulate explains the law of conservation of mass.
  • The fifth postulate is an attempt to explain the law of definite proportions.



Atoms are building blocks of all matter. On the basis of Dalton’s atomic theory, we can define an atom as the basic unit of an element that can enter into chemical combination. The size of an atom is extremely small and not visible to eye. The comparative idea regarding the size of atom can be had from the following:


Relative sizes

Radius (in meter)



Atoms of hydrogen


Grain of sand


Water melon

\[0.2\times {{10}^{-1}}\]

Cricket ball


Atomic Symbols

It was Jon Jacob Berzelius who devised the modern convenient system of using letters of the alphabet to represent elements. The systems of naming the elements are enumerated below:

  • The symbols of the most common elements, mainly non metals, use the first letter of their English name. Examples: H (hydrogen), B (Boron), C (Carbon), N (nitrogen), 0 (Oxygen), F (Flourine), P (Phosphorous), S (Sulphur), I (iodine), etc.
  • If the name of the element has the same initial letter as another element, then the symbol uses the first and second letters of their English name. Examples: He (Helium), Li (Lithium), Be (Beryllium), Ne(Neon), Al (Aluminum)


Atomic Number, Mass Number and Isotopes

The subatomic particles present in atom arc-neutron, proton and electron. All atoms can be identified by the number of protons and neutrons they contain.


Atomic number

The number of protons in the nucleus of an atom decides which element it is. This very important number is called the atomic number (Z). In a neutral atom the number of protons is equal to the number of electrons, so the atomic number also indicates the number of electrons present in the atom. The chemical identity of an atom can be determined solely by its atomic number.


Mass number

The mass number (A) is the total number of neutrons and protons present in the nucleus of an atom of an element.

Mass number = number of protons + number of neutrons

= atomic number + number of neutrons

The number of neutrons in an atom is equal to the difference between the mass number and the atomic number, or (A - Z).



Atoms that have the same atomic number but different mass numbers are called isotopes.



The first isotope of uranium is used in nuclear reactors and atomic bombs, whereas the second isotope lacks the properties necessary for these applications.


Handy Facts

The chemical properties of an element are determined primarily by the protons and electrons in its atoms; neutrons do not take part in chemical changes under normal conditions. Therefore, isotopes of the same element have similar chemistry, forming the same types of compounds and displaying similar relativities.



Thus, elements atoms of different elements having same mass number (A) but different atomic number (z) are termed as isobars. Examples: \[_{7}^{14}N\]and \[_{6}^{14}C\]

                                                    \[_{11}^{24}Na\] and \[_{12}^{24}Mg\]


The atoms of an element which have atomic numbers and mass number both different but the number of neutrons in atomic nuclei are same called isotones.


Atomic Mass

A property closely related to an atom's mass number is its atomic mass. The mass of an atom depends on the number of electrons, protons, and neutrons it contains.

  • A value is assigned to the mass of one atom of a given element so that it can be used as standard. By international agreement, atomic mass (some-times called atomic weight) is the mass of the atom in atomic mass units (amu).
  • One atomic mass unit (also called one Dalton) is defined as a mass exactly equal to one-twelfth the mass of one carbon-12 atom.

Carbon-12 is the carbon isotope that has six protons and six neutrons. Setting the atomic mass of carbon-12 at 12 amu provides the standard for measuring the atomic mass of the other elements.


Amedeo Avogadro, an Italian chemist, first coined the term molecule in 1801 in order to explain the Gay-Lussac’s law.

Molecule may be defined as a combination of two or more than two atoms of the same or different elements in a definite arrangement. These atoms are held together by chemical forces or chemical bonds.


Difference between Atoms and Molecules

  • An atom is the smallest particle of a substance which can-not exist freely whereas molecules can be considered as the smallest particle of an element or of a compound which can exist alone or freely under ordinary conditions.
  • A molecule of a substance shows all chemical properties of that substance.


Representing a Molecule Chemically

The chemical composition of a molecule can be expressed with the help of symbols of elements and formulae.

  • Oxygen molecule is made of two atoms of oxygen and there-fore it is a diatomic molecule (represented by \[{{O}_{2}}\]), hydrogen, nitrogen, fluorine, chlorine, bromine and iodine are other examples of diatomic molecules and are represented as \[{{H}_{2}},{{N}_{2}},{{F}_{2}},C{{I}_{2}},B{{r}_{2}}\],and \[{{I}_{2}}\]respectively.
  • Some other elements exist as more complex molecules. Phosphorus molecule consists of four atoms (denoted by\[{{P}_{4}}\]) whereas sulphur exists as eight atom molecule (\[{{S}_{g}}\]).
  • Normally, molecules consisting of more than three or four atoms are considered under the category of polyatomic molecules.


Handy Facts

Buckminsterfullerene is a soccer ball-shaped molecule.


Molecular Formula

Formulae are combinations of symbols that represent a compound. A formula indicates:

  • The elements involved in the molecule.
  • The number of atoms of each element contained in the molecule. In writing formulae, we use subscripts, coefficients, and parentheses in addition to the symbols of the elements.
  • Subscripts indicate the number of atoms of an element, as in \[{{H}_{2}}\] where two is the subscript meaning two hydrogen atoms. If there is no subscript with a symbol, it is assumed there is only one atom of that element.
  • Coefficients are numbers in front of the formula; indicate the number of molecules of compound, as in 4HCI where four is the coefficient indicating four molecules of HCI.
  • Parentheses are used to separate a radical from the rest of the formula when it would be confusing not to do so.


Steps in Formula Writing

In writing formulae for compounds, there are four steps that should be followed:

  • Determine the symbols for the elements in a compound.
  • Determine the valence of each of the atoms or radicals.
  • Write the positive element's symbol first, followed by that of the negative element.
  • Make the compound electrically neutral by using subscripts.

For example, the formula for calcium chloride may be written as follows:

  • Symbols of Calcium = Ca and Chloride = CI.
  • Ca valence is +2, CI valence is -I.
  • \[C{{a}^{+2}}2C{{I}^{-1}}\]. If we add the charges, we find that this compound is not neutral (+2 - 1 = +1). Therefore, we must proceed to step (4).
  • To have two negative charges to balance the two positive charges, we must have two

\[C{{I}^{-1}}\]ions (\[-1\times 2=-2\]). Thus, the formula would be \[CaC{{I}_{2}}\].


Empirical Formula

The empirical formula of a compound is the simplest formula which expresses its percentage composition. It is the ratio of the different elements present in a chemical compound. Empirical formula does not show the exact number of elements present. For example, molecular formula of Benzene is\[{{C}_{6}}{{H}_{6}}\].

Structural Formula

Structural formula of a molecule represents the structure of the molecule. Structural formula shows how the atoms are bonded to each other.


Molecular Mass

Molecular formula of a compound is normally used for determining the molecular mass of that compound.

  • The molecular mass is the sum of atomic masses of all the atoms present in that molecule.

For example:

The molecular mass of \[C{{O}_{2}}\] is obtained as:

\[C=1\times 12.0\,\,u=12.0\,\,u\]

For two \[O=2\times 16.0\,\,u=32.0\,\,u\]

Mass of \[C{{O}_{2}}=44.0\,\,u\]

Hence, we write molecular mass of\[C{{O}_{2}}=44.0\,\,u\].


Equivalent Mass

The formula to calculate the equivalent mass of an element is given by:

Equivalent mass =\[\frac{Atomic\,\,mass}{Valency}\]


An ion is an atom or a group of atoms that has a net positive or negative charge.

  • The number of positively charged protons in the nucleus of an atom remains the same during ordinary chemical changes (called chemical reactions), but negatively charged electrons may be lost or gained.
  • The loss of one or more electrons from a neutral atom results in a cation, an ion with a net positive charge. For example, a sodium atom (Na) can readily lose an electron to become a sodium cation.
  • On the other hand, an anion is an ion whose net charge is negative due to an increase in the number of electrons. A bromine atom (Br), for instance, can gain an electron to become the bromide ion\[B{{r}^{-}}\].



This law states that equal volumes of gases at the same temperature and pressure contain the same number of molecules regard-less of their chemical nature and physical properties. Avogadro’s number is\[6.022\times {{10}^{23}}\]. It is the number of molecules of any gas present in a volume of 22.4 L and is the same for the lightest gas (hydrogen) as for a heavy gas such as carbon dioxide or bromine. Avogadro’s law provides a method to determine molecular weights of gaseous element.


Avogadro’s number and Molar mass of an element

Chemists measure atoms and molecules (or any particle like ions, radicals, etc.) in moles. Mole is chemist's counting unit and is central to all of quantitative chemistry.

In the SI system the mole (mol.) is the amount of a substance that contains as many elementary entities (atoms, molecules, or other particles) as there are atoms in exactly 12 g (or 0.012 kg) of the carbon-12 isotope. The actual number of atoms in 12 g of carbon-12 is determined experimentally. This number is called Avogadro’s number (\[{{N}_{A}}\]), in honor of Amedeo Avogadro.

The currently accepted value is, \[{{N}_{A}}=6.0221415\times {{10}^{23}}\]Generally, Avogadro’s number is rounded to\[6.022\times {{10}^{23}}\]. This mass of carbon-12 is its molar mass (M), defined as the mass (in grams or kilograms) of 1 mole of units (such as atoms or molecules) of a substance.




Matter is made up of atoms, and therefore an understanding of the structure of atom is very important.

  • In 1879, Sir William Crooks discovered cathode rays. Cathode rays are produced in vacuum tubes equipped with two electrodes.
  • Using a cathode ray tube in 1897, J.J. Thomson determined that all matter, whatever its source, contains particles of the same kind that are much less massive than the atoms of which they form a part.
  • Thomson originally called these as corpuscles which later came to be known as electrons.



Electrons, Protons and neutrons are called fundamental particles. Characteristics of the fundamental particles are given below:



Subatomic particles


\[\downarrow \]

\[\downarrow \]

   \[\downarrow \]

Electrons (Symbol: e)

Proton (Symbol: p)

Neutron (symbol: n)

·                     Discovered by J.J. Thomson in 1897.

·                     Discovered by Ernest Rutherford in 1911

·                     Discovered by James Chadwick in 1932

·                     Negatively charged.

·                     Positively charged

·                     Mass= \[1.674\times {{10}^{-27}}kg\]

·                     Mass = \[9.109389\times {{10}^{-31}}kg\]

·                     Mass = \[1.672\times {{10}^{-27}}kg\]

·                     Charge = 0

·                     Charge = \[-1.602\times {{10}^{-19}}\]coulomb

·                     Charge = \[1.602\times {{10}^{-19}}\] coulomb

·                     Relative charge = 0

·                     Relative charge = -1

·                     Relative charge = +1



·                     1840 times heavier then electron




The discovery of the sub-atomic particles led to the enunciation of different models of the atoms which tried to explain the internal structure of the atom.



Thomson Model

  • J. Thomson proposed that atoms can be considered as a large positively charged body with a number of small negatively charged electrons scattered throughout it. This model was called as Plum pudding model of the atom.
  • The electrons represent the plums in the pudding made of positive charge.
  • Thomson model was discarded because it could not explain certain experimental observations like alpha particle scattering experiment by thin metal foils conducted by Ernest Rutherford.


Rutherford’s Model

In 1909, Rutherford discovered proton in his famous gold foil experiment. In this experiment, Rutherford bombarded a beam of alpha particles on an ultrathin gold foil and then detected the scattered alpha particles in zinc sulfide (ZnS) screen.



  • Most of the particles pass through the foil without any deflection.
  • Some of the alpha particles deflect at small angle.
  • Very few even bounce back (1 in 20,000).



Based on his observations, Rutherford proposed the following structural feature of an atom:

  • Most of the atom's mass and its entire positive charge are confined in a small core, called nucleus. The positively charged particle is called proton.
  • Most of the volume of an atom is empty space.
  • The number of negatively charged electrons dispersed outside the nucleus is same as number of positively charge in the nucleus. It explains the overall electrical neutrality of an atom.


Bohr’s Model

The assumptions of Bohr’s Theory are as follows:

  • Electrons revolve round the nucleus in definite orbits called stationary states.
  • Each stationary state is associated with a definite energy, which is called an energy level.
  • As long as electrons revolve in the stationary states, they don’t lose or gain energy.
  • Electrons may jump from one orbit to another, in which case energy is absorbed or emitted in fixed quantities only (known as ‘quanta’).


Modern Atomic Model

The present accepted model of atom, called quantum mechanical or wave-mechanical concept of atom, is basically mathematical in nature. This was proposed by Erwin Schrodinger- an Austrian physicist in 1926.


Handy Facts

Heisenberg’s Uncertainty Principle

An important consequence of the wave-particle duality of matter and radiation was discovered by Werner Heisenberg in 1927 and is called the Uncertainty Principle. According to this principle, it is not possible to simultaneously measure both the position and momentum (or velocity) of an electron accurately.


The characteristics of each of the quantum numbers are given below:



Quantum numbers

\[\downarrow \]

\[\downarrow \]

\[\downarrow \]

\[\downarrow \]

Principal quantum number (denoted by n)


Azimuthal quantum number (denoted by l)


Magnetic quantum number (denoted by \[{{m}_{l}}\])


The Spin quantum number (denoted by \[{{m}_{s}}\]) describes the spin of the electron, i.e. whether it is clock- wise or anticlockwise. This quantum number was introduced later, it’s not an outcome of the solution of Schrodinger Equation.

• Specifies the energy level (or principal shell) of the electron within the atom and size of the orbital.




• Specifies the shape of an orbital with a particular principal quantum number.





• Describes the direction or orientation of the orbital in space.






• Can take only positive non-zero integral values i.e. 1,2,3,4 etc.







• Divides the shells into smaller groups of orbitals called subshells (sublevels).







• Takes-up any integral value from \[-l\] to \[+l\] (For example, for \[l\]= 1;\[{{m}_{l}}\] can have the values as -1,0 and 1. That means the p-orbital can have three orientation i.e. there are three p orbitals- \[{{p}_{x}},{{p}_{y}}\] and\[{{p}_{z}}\].)



• The shells or energy levels are designated as K, L, M, N etc. depending on the values of n i.e. 1,2,3,4 etc. respectively.



• \[l\] may be zero or a positive integer-less than or equal to (n-1) (n is the principal quantum number), i.e. =0, 1, 2, 3... (n - 1).




• The number of electrons that can be accommodated in one shell is \[2{{n}^{2}}\].

• Different values correspond to different types of subshells and each subshell contains orbitals of a given shape as  shown below:

1 = 0 (s orbital): Spherical      1=1 (p-orbital): Dumb-bell

1= 4 (d-orbital): cloverleaf





Each electron in an atom is described by four different quantum numbers. The first three (\[n,l,{{m}_{l}}\]) specify the particular orbital of interest, and the fourth (\[{{m}_{s}}\]) specifies how many electrons can occupy that orbital.


Table of Allowed Quantum Numbers





Number of orbitals

Orbital Name

Number of electrons





1 s






2 s




-1, 0, + 1


2 p






3 s




-1, 0, + 1


3 P




-2, -1, 0, +1,+2


3 d






4 s






4 p




-2, -1, 0, +1,+2


4 d




-3, -2, -1, 0,+1,+2,


4 f



  • The Pauli Exclusion Principle (Wolfgang Pauli, Nobel Prize in 1945) states that no two electrons in the same atom can have identical values for all four of their quantum numbers.
  • The distribution of electrons among the orbitals of an atom is called the electronic configuration. The electrons are filled in according to a scheme known as the Aufbau principle (“building-up”), which corresponds to increasing energy of the subshells as below:

1s \[\to \]2s\[\to \] 2p\[\to \]3s\[\to \]3p\[\to \]4s\[\to \]3d\[\to \] 4p \[\to \] 5s \[\to \] 6s \[\to \] 4f\[\to \] 5d, 6p \[\to \] 7s \[\to \] 5s



Handy Facts

Because an electron spins, it creates a magnetic field, which can be oriented in one of two directions. For two electrons in the same orbital, the spins must be opposite to each other; the spins are said to be paired. These substances are not attracted to magnets and are said to be diamagnetic. Atoms with more electrons that spin in one direction than another contain unpaired electrons. These substances are weakly attracted to magnets and are said to be paramagnetic.



In 1896, a French physicist named Henri Baequeral discovered that uranium-containing crystals emitted rays that could expose and fog photographic plates. He called these rays-uranic rays. Marie curie, later discovered two other elements-polonium and radium emitting uranic rays. She renamed uranic rays as radioactivity (or radioactive decay).

Radioactivity may be defined as disintegration or decay of unstable atoms accompanied by emission of radiation

Radioactivity can be of two types-Natural and artificial or induced radioactivity.


Nature of Radiations

The invisible radioactive radiations are of three types:

  • Alpha (\[\alpha \]) particle: a helium nucleus (\[_{2}^{4}\alpha \]or \[_{2}^{4}He\]) without electrons. These are positively charged and largest particle emitted by radioactive nuclei. Also has the highest charge.
  • Beta (\[\beta \]) particle: a beta particle (\[{{^{0}}_{-1}}\beta \]or\[{{_{-1}}^{0}}e\]) is an electron emitted from an atomic nucleus.
  • Positron: the antiparticle of an electron/beta particle, \[{{^{0}}_{1}}\beta \] or\[{{^{0}}_{1}}e\]. The same size as an electron but with a positive charge.
  • Gamma (\[\gamma \]) rays: high-energy rays (like X-rays).


Comparison of the Properties of Alpha, Beta, and Gamma Rays



\[\alpha \] ray

\[\beta \] ray

\[\gamma \] ray


Helium nuclei, \[_{2}^{4}\]He

Fast electrons

Electro-magnetic radiation


One-tenth of the velocity of light

Velocity of light

Velocity of light

Penetrating power




Stopped by

Paper of 0.01 mm thick

1 cm of aluminum

Several cm thick lead/concrete layer


Nuclear Reactions

A nuclear reaction is that which proceeds with a change in the composition of the nucleus resulting in the formation of an atom of a new element.

Therefore, the process in which the artificial transmutation of a stable nuclide leads to the formation of radioactive isotope is called artificial radioactivity or induced radioactivity.



Following are some of the important points, given in table, which differentiate a nuclear reaction from ordinary chemical reaction.


Nuclear Fusion

Nuclear fusion refers to a nuclear reaction in which two light nuclei fuse together to form heavy nucleus with release of large amount of energy.


Nuclear Fission

Nuclear fission is a nuclear reaction in which a heavy atomic nucleus (such as that of uranium) disintegrates into two nearly equal fragments with release of large amount of energy.


Application of Nuclear Fusion For The Benefit Of Mankind (Nuclear Reactor)

It has been possible control fission of U-235 so that energy is released slowly at a usable rate. Controlled fission is carried out in a specially designed plant called a nuclear power reactor or simply nuclear reactor. The chief components of a nuclear reactor are:


  • U-235 fuel rods constitute the ‘fuel core’. The fission of U-23 5 produces heat energy and neutrons that start the chain reaction.
  • Moderator slows down or moderates the neutrons. The most commonly used moderator is ordinary water. Graphite rods are sometimes used. Neutrons slow down by losing energy due to collisions with atoms/molecules of the moderator.
  • Control rods control the rate of fission of U-23 5. These are made of boron-10 or cadmium that absorbs some of the slowed neutrons. Thus the chain reaction is prevented from going too fast.
  • Coolant cools the fuel core by removing heat produced by fission. Water used in tine reactor serves both as moderator and coolant Heavy water (\[{{D}_{2}}O\]) is even more efficient than light water.
  • Concrete shield which protects the operating personnel and environment from destruction in case of leakage of radiation.


Nuclear power is a major source of energy for electrical generation worldwide.


Hydrogen Bomb or H-Bomb

This destructive device makes use of the nuclear fusion of the isotopes of hydrogen. It consists of a small plutonium fission bomb with a container of isotopes of hydrogen.



Uses for Radioactive Substances and Radiation

Radioactive substance and radiation have been used for the benefit of people also.



Radionuclides are used to directly treat illnesses. For example radioactive iodine is used, which is taken up almost exclusively by the thyroid, to treat cancer or hyperthyroidism. Radioactive tracers and dyes are also used to accurately map a specific area or system, such as in a cardiac stress test, which may use a radioactive isotope like Technetium-99 to identify areas of the heart and surrounding arteries with diminished blood flow. Cobalt-60 is also used to treat cancer patients. In Positron emission tomography (PET), a computer imaging diagnostic technique, radioactivity of some substances is utilized.


Smoke Detectors

Some smoke detectors also use radioactive elements as part of their detection mechanism, usually americium-241. The ionizing radiation of the alpha particles is used to cause and then measure changes in the ionization of the air immediately around the detector. A change due to smoke in the air will cause the alarm to sound.



Essentially high-powered versions of the types of X-Ray machines used in medicine, industrial radiography cameras use X-rays or even gamma sources (such as Iridium-192, Cobalt-60 or Cesium-137) to examine hard to reach or hard to see places This is frequently used to examine welds for defects or irregularities, or examining other materials to locate structural anomalies or internal components.


Food Safety

Food irradiation is the process of using radioactive sources to sterilize foodstuffs. The radiation works by killing bacteria and viruses, or eliminating their ability to reproduce by severely damaging their DNA or RNA.



One important contribution that nuclear science has made in this area is the ability to determine the age of ancient artifacts. There are several techniques for doing this, but the most common process for dating objects of up to about 50,000 years is called radiocarbon dating.



Unstable nuclei have also been used as radioactive tracers in scientific research. A tracer is a radioactive element whose pathway through a chemical reaction can be followed. For example, scientists have used carbon-14 to study many aspects of photosynthesis. Likewise, phosphorus-32 atoms can be used to trace phosphorus-containing chemicals as they move from the soil into plants.

Notes - Atoms, Molecules and Nuclear Chemistry

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