In this article, we shall study to solve problems based on the calculation of atomic number, atomic mass number, and neutron number

Atomic number (Z) :

The number of protons (positive charge) present in the nucleus of an atom of a particular element is called the atomic number of that element. It is denoted by letter ‘Z’.

Neutron number (N): 

The number of neutrons present in the nucleus of an atom is known as neutron number. It is denoted by ‘N’

Mass number (A): 

The total number of protons and neutrons present in the nucleus of an atom of the element is called mass number. The mass number is denoted as ‘A’.

A  =   Z + N

Example 01:

Calculate the number of electrons, protons, and neutrons in the following atoms.

Atomic Number = Z = 15

Atomic Mass Number = A = 31

Number of protons = atomic number = 15

Number of electrons = atomic number = 15

Neutron number = Number of neutrons = A – Z = 31 – 15 = 16

Number of nucleons = Atomic mass number = 31

Atomic Number = Z = 12

Atomic Mass Number = A = 24

Number of protons = atomic number = 12

Number of electrons = atomic number = 12

Neutron number = Number of neutrons = A – Z = 24 – 12 = 12

Number of nucleons = Atomic mass number = 24

Atomic Number = Z = 17

Atomic Mass Number = A = 37

Number of protons = atomic number = 17

Number of electrons = atomic number = 17

Neutron number = Number of neutrons = A – Z = 37 – 17 = 20

Number of nucleons = Atomic mass number = 37

Atomic Number = Z = 18

Atomic Mass Number = A = 40

Number of protons = atomic number = 18

Number of electrons = atomic number = 18

Neutron number = Number of neutrons = A – Z = 40 – 18 = 22

Number of nucleons = Atomic mass number = 40

Atomic Number = Z = 35

Atomic Mass Number = A = 80

Number of protons = atomic number = 35

Number of electrons = atomic number = 35

Neutron number = Number of neutrons = A – Z = 80 – 35 = 45

Number of nucleons = Atomic mass number = 80

Atomic Number = Z = 20

Atomic Mass Number = A = 40

Number of protons = atomic number = 20

Number of electrons = atomic number = 20

Neutron number = Number of neutrons = A – Z = 40 – 20 = 20

Number of nucleons = Atomic mass number = 40

Atomic Number = Z = 6

Atomic Mass Number = A = 13

Number of protons = atomic number = 6

Number of electrons = atomic number = 6

Neutron number = Number of neutrons = A – Z = 13 – 6 = 7

Number of nucleons = Atomic mass number = 13

Atomic Number = Z = 8

Atomic Mass Number = A = 16

Number of protons = atomic number = 8

Number of electrons = atomic number = 8

Neutron number = Number of neutrons = A – Z = 16 – 8 = 8

Number of nucleons = Atomic mass number = 16

Atomic Number = Z = 26

Atomic Mass Number = A = 56

Number of protons = atomic number = 26

Number of electrons = atomic number = 26

Neutron number = Number of neutrons = A – Z = 56 – 26 = 30

Number of nucleons = Atomic mass number = 56

Atomic Number = Z = 38

Atomic Mass Number = A = 88

Number of protons = atomic number = 38

Number of electrons = atomic number = 38

Neutron number = Number of neutrons = A – Z = 88 – 38 = 50

Number of nucleons = Atomic mass number = 88

Example 02:

Calculate the number of electrons, protons, and neutrons in the following species.

Atomic Number = Z = 15

Atomic Mass Number = A = 31

Number of protons = atomic number = 15

P^3- → P + 3 e^–

Number of electrons = 15 + 3 = 18

Number of neutrons = A – Z = 31 – 15 = 16

Number of nucleons = Atomic mass number = 31

Atomic Number = Z = 35

Atomic Mass Number = A = 80

Number of protons = atomic number = 35

Br^– → Br + e^–

Number of electrons = 35 + 1= 36

Number of neutrons = A – Z = 80 – 35 = 45

Number of nucleons = Atomic mass number = 80

Atomic Number = Z = 20

Atomic Mass Number = A = 40

Number of protons = atomic number = 20

Ca²⁺ → Ca – 2e^–

Number of electrons = 20 – 2= 18

Number of neutrons = A – Z = 40 – 20 = 20

Number of nucleons = Atomic mass number = 40

H₃PO₄

Hydrogen (H):

Atomic Number = Z = 1

Atomic Mass Number = A = 1

Number of protons per atom= atomic number = 1

Number of electrons per atom = Z = 1

Number of neutrons per atom = A – Z = 1 – 1 = 0

There are 3 hydrogen atoms in the molecule

Total number of protons in 3 hydrogens = 1 x 3 = 3

Total number of electrons in 3 hydrogens = 1 x 3 = 3

Total number of neutrons in 3 hydrogens = 0 x 3 = 0

Phosphorous (P):

Atomic Number = Z = 15

Atomic Mass Number = A = 31

Number of protons per atom= atomic number = 15

Number of electrons per atom = Z = 15

Number of neutrons per atom = A – Z = 31 – 15 = 16

There is 1 phosphorous atom in the molecule

Total number of protons in 1 phosphorous = 15 x 1 = 15

Total number of electrons in 1 phosphorous = 15 x 1 = 15

Total number of neutrons in 1 phosphorous = 16 x 1 = 16

Oxygen (O):

Atomic Number = Z = 8

Atomic Mass Number = A = 16

Number of protons per atom= atomic number = 8

Number of electrons per atom = Z = 8

Number of neutrons per atom = A – Z = 16 – 8 = 8

There are 4 oxygen atom in the molecule

Total number of protons in 4 oxygen= 8 x 4 = 32

Total number of electrons in 4 oxygen = 8 x 4 = 32

Total number of neutrons in 4 oxygen = 8 x 4 = 32

Ans:

Total number of protons in H₃PO₄ = 3 + 15 + 32 = 50

Total number of electrons in H₃PO₄ = 3 + 15 + 32 = 50

Total number of neutrons in H₃PO₄ = 0 + 16 + 32 = 48

NH₄⁺

Nitrogen (N):

Atomic Number = Z = 7

Atomic Mass Number = A = 14

Number of protons per atom= atomic number = 14

Number of electrons per atom = Z = 14

Number of neutrons per atom = A – Z = 14 – 7 = 7

Hydrogen (H):

Atomic Number = Z = 1

Atomic Mass Number = A = 1

Number of protons per atom= atomic number = 20

Number of electrons per atom = Z = 1

Number of neutrons per atom = A – Z = 1 – 1 = 0

There are 4 hydrogen atoms in the species

Total number of protons in 3 hydrogens = 1 x 4 = 4

Total number of electrons in 3 hydrogens = 1 x 4 = 4

Total number of neutrons in 3 hydrogens = 0 x 4 = 0

Total number of protons in NH₄⁺ = 7 + 4 = 11

NH₄⁺ → NH₄ – e^–

Total number of electrons in NH₄⁺ = 7 + 4 – 1 = 10

Total number of neutrons in NH₄⁺ = 7 + 4 = 11

ClO₃^–

Chlorine (Cl):

Atomic Number = Z = 17

Atomic Mass Number = A = 37

Number of protons per atom= atomic number = 17

Number of electrons per atom = Z = 17

Number of neutrons per atom = A – Z = 37 – 17 = 20

Oxygen (O):

Atomic Number = Z = 8

Atomic Mass Number = A = 16

Number of protons per atom= atomic number = 8

Number of electrons per atom = Z = 8

Number of neutrons per atom = A – Z = 16 – 8 = 8

There are 3 oxygen atom in the species

Total number of protons in 4 oxygen= 8 x 3 = 24

Total number of electrons in 4 oxygen = 8 x 3 = 24

Total number of neutrons in 4 oxygen = 8 x 3 = 24

Total number of protons in ClO₃^– = 17 + 24 = 41

ClO₃^– → ClO₃ + e^–

Total number of electrons in ClO₃^– = 17 + 24 + 1 = 42

Total number of neutrons in ClO₃^– = 20 + 24 = 44

Example 03:

Complete the table

Solution:

Zn

Atomic Number = Z = 30

Atomic Mass Number = A = 64

Number of protons = atomic number = 30

Number of electrons = atomic number = 30

Number of neutrons = A – Z = 64 – 30 = 34

Sr²⁺

Atomic Number = Z = 38

Atomic Mass Number = A = 90

Number of protons = atomic number = 38

Sr²⁺ → Sr – 2e^–

Number of electrons = 38 – 2 = 36

Number of neutrons = A – Z = 90 – 38 = 52

Te

Number of protons = 43

Number of Neutrons = N = 56

Atomic number =Number of protons = Z = 43

Atomic mass number = Z + N = 43 + 56 = 99

Number off electrons = Atomic number = 43

Br^–

Number of neutrons = N = 44

Number of electrons = 36

Br^– → Br + e^–

Number of protons = 36 – 1 = 35

Atomic Number = Number of protons = Z = 35

Atomic mass number = Z + N = 35 + 44 = 79

N

Number of neutrons = N = 7

Number of electrons = 7

Number of protons = 7

Atomic Number = Number of protons = Z = 7

Atomic mass number = Z + N = 7 + 7 = 14

Ca²⁺

Atomic Number = Z = 20

Number of neutrons = N = 20

Atomic Mass Number = Z + N = 20 + 20 = 40

Number of protons = atomic number = 20

Ca²⁺ → Ca – 2e^–

Number of electrons = 20 – 2 = 18

O

Atomic Number = Z = 8

Atomic Mass Number = A = 16

Number of protons = atomic number = 8

Number of electrons = atomic number = 8

Number of neutrons = A – Z = 16 – 8 = 8

The completed table is as follows:

Example 04:

The numbers of electrons, protons, and neutrons in a monoatomic species are equal to 36, 35, and 45 respectively. Assign proper symbol.

Solution:

Number of electrons = 36

Number of protons = Atomic number = Z = 35

Number of neutrons = N = 45

Atomic mass number = A = Z + N = 35 + 45 = 80

Charge on species = Z – Number of electrons = 35 – 36 = -1

The species is

Example 05:

The numbers of electrons, protons, and neutrons in a monoatomic species are equal to 18, 16, and 16 respectively. Assign proper symbol.

Solution:

Number of electrons = 18

Number of protons = Atomic number = Z = 16

Number of neutrons = N = 16

Atomic mass number = A = Z + N = 16 + 16 = 32

Charge on species = Z – Number of electrons = 16 – 18 = -2

The species is

Example 06:

Find the number of electrons in fluorine atom, fluorine molecule, and fluoride ion. The atomic number and mass number of fluorine are 9 and 19 respectively.

Solution:

Atomic number = Z = 9

Atomic mass number A = 19

Fluorine Atom (F):

Number of protons = Atomic number = 9

Number of Protons = Atomic number = 9

Number of electrons = Atomic number = 9

Number of neutrons = a – z = 19 – 9 =10

Fluorine Molecule (F₂):

There are 2 atoms in a molecule of fluorine

Number of protons in fluorine molecule= 9 x 2 = 18

Number of electrons in fluorine molecule= 9 x 2 = 18

Number of neutrons in fluorine molecule= 10 x 2 = 20

Fluoride Ion (F^–):

Number of Protons = Atomic number = 9

F^– → F + e^–

Number of electrons = 9 + 1 = 10

Number of neutrons = a – z = 19 – 9 =10

Example 07:

An isotope of atomic mass 24 had 12 neutrons in its nucleus. What is its atomic number? Represent the isotope in symbolic form.

Solution:

Atomic mass number = A = 24

Number of neutrons = N = 12

Number of protons = A – Z = 24 – 12= 12

Atomic number = Number of protons = Z = 12

The element is

Isotopes, Isotones, and Isobars

• Different atoms of the same element having the same atomic number but having different mass numbers are known as isotopes.
• Atoms of the different elements having a different atomic number but having the same mass numbers are known as isobars.
• Atoms of the different elements having the different atomic number, different mass number but having the same neutron number are known as isotones.

Example 08:

Write the complete symbol for the atom with the given atomic number (Z) and atomic mass (A):

• Z = 17 and A = 35

• Z = 92, A = 233

• Z = 4, A = 9

Example 09:

Give an isobar, an isotone, and an isotope of

Isobar
Isotone
Isotope

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In this article, we shall study the concept of quantum numbers and the model of an atom based on the quantum numbers.

Concept of Quantum Numbers:

In 1926, Erwin Schrodinger put forward a theory of atom called as a quantum mechanical theory. Quantum mechanical theory is based on two principles. a) Wave-particle duality of subatomic particles and b) Uncertainty principle.

Wave-particle duality principle of subatomic particles was put forward by L. DeBroglie it states that “All the subatomic particles electrons, protons, and neutrons possess both particle and wave properties”.

Uncertainty principle was put forward by W. Heisenberg it states that “It is impossible to determine the position and momentum of a particle simultaneously”. It means that if the position of the electron in an atom is known then there is uncertainty about its momentum and when the momentum of an electron in an atom is known there is uncertainty about the position of the electron.

According to this theory, Each electron shell of an atom is composed of several subshells. To specify the position of the electron in an atom each electron is assigned four quantum numbers and these numbers give location and energy of the electron.

The numbers which assign the position and energy to an electron are called quantum numbers. There is a set of four quantum numbers associated with each electron of an atom. The four quantum numbers are a) Principal quantum number ‘n’  b) Azimuthal quantum number ‘l’ c) Magnetic quantum number ‘m’  d) Spin quantum number ‘s’

Principal Quantum Number (n):

This quantum number was introduced by Neil Bohr. It is denoted by the letter ‘n’. It gives the main energy level (shell) to which the electron belongs. It defines the distance of the electron from the nucleus and energy level. These energy levels are also designated by letters as follows:

Azimuthal Quantum Number (l):

It was introduced by Somerfield.  This quantum number refers to the energy sub-level (subshell).  It is denoted by the letter ‘l’. It can have any integral value from 0 to (n – 1). This quantum number indicates the subshell in which the electron is present and the number of subshells present in a principal shell.

It is also responsible for the particular shape of the particular shell because it defines the spatial distribution of the electron cloud around the nucleus. Thus the subshell (Orbital) with l = 0 is called ‘s’ orbital. The subshell (Orbital) with l = 1 is called ‘p’ orbital. The subshell (Orbital) with l = 2 is called ‘d’ orbital. The subshell (Orbital) with l = 3  is called ‘f’ orbital

It is used to calculate angular momentum of an electron in particular shell using the formula

Each subshell contains maximum 2 (2l +1) electrons. It also decides the number of nodal planes of the orbital. For s orbital l = 0, hence s orbital there is no nodal plane. For p orbital l = 1, hence p orbital there is one nodal plane. For d orbital l = 2, hence d orbital there are two nodal planes.

Notes:

For the first orbit:

n = 1, then  l = 0 to (1 – 1) = 0 to 0,  then  l = 0. Thus in the first main energy level, there is only one subshell i.e. ‘s’ orbital.

For the second orbit:

n = 2 then  l = 0 to (2 – 1) = 0 to 1, then l = 0, 1. Thus in the second main energy level, there are two subshells i.e. ‘s’ orbital and ‘p’ orbital.For the Third orbit n = 3 Then  = 0 to (3 – 1) = 0 to 2 then             = 0, 1, 2. Thus in the third main energy level there

For the Third orbit:

n = 3 then  l = 0 to (3 – 1) = 0 to 2 then l = 0, 1, 2. Thus in the third main energy level, there are three subshells i.e. ‘s’ orbital, ‘p’ orbital and ‘d’ orbital.

For the fourth orbit:

n = 4 Then l = 0 to (4 – 1) = 0 to 3 then l  = 0, 1, 2, 3. Thus in the fourth main energy level, there are four subshells i.e. ‘s’ orbital, ‘p’ orbital, ‘d’ orbital, and ‘f’ orbital.

Magnetic Quantum Number (m):

This quqntum number is denoted by letter ‘m’. This number was introduced to explain the splitting of atomic spectra in a magnetic field (Zeeman effect).

For Azimuthal number ‘l’ possible values of magnetic quantum numbers are – l  to + l   through 0. i.e. m =  , …., -3, -2, -1, 0, 1, 2, 3, ….., . This quantum number gives the possible orientation of the orbital in the space. For a given value of l, there are (2l +1) values of m.

This number is also known as the orientation quantum number because it gives the distribution of electron clouds in space around the nucleus.

The magnetic quantum number tells to which orbital the electron belongs. It also tells the number of orbitals which corresponds to a particular shell. For example: s subshell l = 0 therefore m = 0. This means that s subshell contains only one orbital.

p subshell l = 1 therefore m = -1, 0, +1. This means that p subshell contains three orbitals. They are designated as Px, Py and Pz,  along the x-axis, along the y-axis and along the z-axis respectively. Thus p orbitals have three orientations in space along co-ordinate axes. In absence of magnetic field, these orbitals are equivalent in energy and are said to have three fold degenerate.

d subshell l = 2 therefore m = -2, -1, 0, +1, +2. This means that d subshell contains five orbitals. They are designated as dxy, dyz, dzx, dx2-y2, and dz2.   Thus d orbitals have five orientations in space. In absence of magnetic field, these orbitals are equivalent in energy and are said to have five fold degenerate.

f subshell l = 3 therefore m = -3, -2, -1, 0, +1, +2, +3. This means that f subshell contains seven orbitals and have seven orientations in space. In absence of magnetic field, these orbitals are equivalent in energy and are said to have seven fold degenerate.

Spin Quantum Number (s):

It is denoted by letter ‘s’. The electron in orbital motion can spin clockwise or anticlockwise about its own axis, hence two values of quantum number are possible.  These values are taken as + 1/2 and – 1/2.

Opposite spins are called antiparallel spins. The same spin is called the parallel spin. The spin quantum number indicates a magnetic moment associated with the electron.

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In this article, we shall study the concept of quantum numbers and different types of orbitals and their shapes.

Difference Between Shell, Subshell, and Orbital:

• All electrons that have the same value for n (the principal quantum number) are in the same shell.Within a shell (same n), all electrons that share the same  (the angular momentum quantum number, or orbital shape) are in the same subshell. The electrons in subshell have same principal quantum number, same azimuthal quantum number and  differ  in magnetic and spin quantum number
• When electrons share the same n, l, and m, we say they are in the same orbital (they have the same energy level, shape, and orientation). The electrons in orbital differ only in spin quantum number.

Shapes of Orbitals:

• Node: There is a region where the probability of finding the electron is zero. It is called a node.
• Nodal Plane: A plane passing through the nucleus on which the probability of finding an electron is zero is called the nodal plane. The number of nodal planes in an orbital is equal to the azimuthal quantum number.
• Spherical or Radial Node: A spherical surface within an orbital on which the probability of finding the electron is zero is called a spherical or radial node.

Types of Orbitals:

s – orbital:

• For s orbital Azimuthal quantum number  = 0 and the magnetic quantum number m = 0 hence s orbitals have unique orientation in space. Thus s orbital corresponds to spherical shape with the atomic nucleus at its centre.
• For every value of ‘n’, there is one ‘s’ orbital i.e. s orbitals are present in all principal energy levels.  Its radius depends on the value of n. As the value of n increases the size of the s orbital also increases.
• It has no nodal plane.

p – orbital:

• For p orbital Azimuthal quantum number l = 1 and the magnetic quantum number  m = -1, 0, +1. Hence p orbitals have three orientations in space.
• Thus p orbital corresponds to dumb-belled shape with the atomic nucleus at its center.
• p orbitals have two lobes directed on opposite sides of the nucleus. P-orbitals are orientated in three different directions along X, Y and Z axis of the usual coordinate system.  These orbitals are designated as P_x, P_y & P_z orbitals.
• p-orbital have one nodal plane.

d – orbital:

• For d orbital Azimuthal quantum number l = 2 and the magnetic quantum number  m = -2, -1, 0, +1, +2. Hence d orbitals have five orientations in space.
• Thus d orbital corresponds to 4 double dumb-belled shapes (d_xy, d_yz, d_zx, d_x²_y²) with the atomic nucleus at its centre and one dumb belled with dough nut shaped (d_z²).
• d orbital has two nodal planes.

f – orbital:

• For f orbital Azimuthal quantum number l = 3 and the magnetic quantum number m = -3. -2, -1, 0, +1, +2, +3. Hence f orbitals have seven orientations in space.
• f orbital has complex shapes with the atomic nucleus at its centre.
• f orbital has three nodal planes.

Quantum Numbers of Electrons in First Three Shells (Orbits)

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The distribution of electrons in various shells and orbitals of an atom is known as electronic configuration. Generally electronic configuration is given by nl^x. Where n is shell number, l is subshell and x are the number of electrons.

Aufbau Principle:

The arrangement of the electrons in an atom is called the electronic configuration of an atom. The method of filling up or building up a sequence of energy levels for electrons in an atom is based on Aufbau principle. In German, the word aufbau means building up.

According to this principle, orbitals are filled in the order of increasing energy. The lowest energy level is filled first. The higher energy levels are then filled up one after another. This gives the atom the maximum stability and the atom is said to be in ground state or the normal state.

The order of increasing energy levels is 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p < 6f Diagrammatically it is represented as follows

Pauli’s Exclusion Principle:

“No two electrons. in an atom can have the same values for all four quantum numbers”. i.e. to exist in the same atom the two electrons can have three quantum numbers identical but fourth must be different.

Example: Let us consider electrons in the first orbit of helium atom

Here we can see that the three values of quantum number are the same but fourth value is different. Thus Pauli’s exclusion principle helps in calculating the maximum number of electrons present in any energy level (Orbit).

Hund’s Rule of Maximum Multiplicity:

In a given subshell, electrons occupy all the available orbitals singly, before they pair up in any orbital.

Example 1:

Consider electronic configuration of phosphorous. The atomic number of phosphorous is 15. Its basic electronic configuration is  2, 8, 5. The detailed electronic configuration is 1s², 2s² 2p⁶, 3s² 3p³. The box diagram for final orbit configuration for P is as below

Here we can see that the electrons in p orbitals occupy the position singly till all orbitals are singly filled.

Example – 2:

Consider electronic configuration of sulphur. The atomic number of sulphur is 16. Its basic electronic configuration is 2, 8, 6. The detailed electronic configuration is 1s², 2s² 2p⁶, 3s² 3p⁴. The box diagram for final orbit configuration for S is as below

Here we can see that the electrons in p orbital occupy the position singly till all orbitals are singly filled and then the pairing starts.

Stability of Completely Filled and Half Filled Subshells:

The ground state electronic configuration of the atom of an element always corresponds to the state of the lowest total electronic energy.

The electronic configurations of most of the atoms follow the basic rules viz. Aufbau principle, Pauli’s exclusion principle, and Hund’s rule. However, in certain elements such as Cu, or Cr, where the two subshells (4s and 3d) differ slightly in their energies, an electron shifts from a subshell of lower energy (4s) to a subshell of higher energy (3d), provided such a shift results in all orbitals of the subshell of higher energy getting either completely filled or exactly half filled.

The valence electronic configurations of Cr and Cu, therefore, are 3d⁵ 4s¹ and 3d¹⁰ 4s¹ respectively and not 3d⁴ 4s² and 3d⁹ 4s². It has been found that there is extra stability associated with these electronic configurations.

Electronic Configuration of copper (Z = 29):

Expected configuration: 1s², 2s² 2p⁶, 3s² 3p⁶, 4s² 3d⁹.

Actual configuration: 1s², 2s² 2p⁶, 3s² 3p⁶, 4s¹ 3d¹⁰.

Electronic Configuration of chromium (Z = 24):

Expected configuration:  1s², 2s² 2p⁶, 3s² 3p⁶, 4s² 3d⁴.

Actual configuration:  1s², 2s² 2p⁶, 3s² 3p⁶, 4s¹ 3d⁵.

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In this article, we shall study Thomson’s model of an atom and its deficiencies and Rutherford’s atomic model and its deficiencies.

Thomson’s Model of an Atom:

J. J. Thomson, in 1898, proposed that an atom possesses a spherical shape (radius approximately 10^–10 m) in which the positive charge is uniformly distributed. The electrons are embedded into it in such a manner as to give the most stable electrostatic arrangement. Many different names are given to this model, for example, plum pudding, raisin pudding, or watermelon. It can be visualized as a positive charge with plums or seeds (electrons) embedded into it (watermelon). An important feature of this model is that the mass of the atom is assumed to be uniformly distributed over the atom.

Although this model was able to explain the overall neutrality of the atom but was not consistent with the results of later experiments.

Basis of Rutherford’s Atomic Model:

Alpha particles from a radioactive substance were made incident on the thin foil of gold of thickness 10^-7 m. After passing through the foil, the alpha particles were detected at various places on the ZnS screen or photographic plate. The following four types of particles were detected.

• Most of the alpha particles just passed through without any deviation as if there is empty space.
• A few alpha particles were deflected through smaller angles.
• A few alpha particles deviated through larger angles.
• Very few rebounded back This larger deflection is possible only if α-particles collide with heavy and positively charged particles inside the atom because like charges only repel each other.  This massive +ve charge is at centre of an atom and called nucleus.
• Very few alpha particles were rebounded i.e. they deviated through 180°. This concludes that the nucleus is very small as compared to the volume of the atom.

Conclusions :

• Based on the experiment Rutherford concluded that most of the alpha particles having positive charge went through the foil undeflected. Hence there must be empty space in the atom.
• Some of the particles were deflected.  It is due to the positive charge present in a very small space within the atom. He called this centrally cored and positively charged region of an atom as a nucleus. The rest of the portion of the atom should be empty.

Rutherford’s Atomic Model:

From the observations of his experiment, Rutherford put forward the concept of his atomic model.

The atom consists of the centrally located positively charged nucleus. The whole mass of an atom is concentrated in the nucleus. Around the nucleus, there is empty space in which the negatively charged electrons revolve in different orbits. Rutherford’s model of an atom is also called as a planetary model of an atom.

Limitations Of Rutherford’s Atomic Model:

• The negatively charged electrons revolve around the nucleus in a circular orbit, hence they possess centripetal acceleration. According to the classical theory of electromagnetism, accelerated charge radiates energy continuously. Therefore, the
  electron should radiate energy while going round the nucleus losing its energy continuously. therefore, it should approach nearer the nucleus while going round emitting radiations of increasing frequency and finally falling in the nucleus. Thus it should move in a spiral path and should emit continuous spectrum and thus structure atom is not stable. Actually, the spectrum observed is line spectrum of definite frequency, and hence a modification of Rutherford’s atom model was necessary.

• This model of an atom fails to explain the distribution of electrons in different orbit around the nucleus.
• According to Rutherford’s model of an atom, the atomic spectrum should be continuous. But atomic spectrum is found to be discontinuous. Rutherford model fails to explain the discontinuity of the atomic spectrum.
• This model also fails to explain the line spectra of atoms, which show discrete lines, each line corresponds to a fixed frequency.

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In last article, we have discussed, the discovery of electron and characteristics of electron. In this article, we shall discuss the discovery of proton and neutron and their characteristics.

Discovery of Proton:

Proton was discovered by E. Goldstein in 1886. He performed the same experiment as performed by J.J. Thomson but used perforated cathode. He found that on passing an electric discharge through a gas under reduced pressure, rays containing positive particles move towards the cathode.  As they appear to arise from the anode they are called anode rays or canal rays. They are found to contain positively charged particles called protons.

Origin of Positive Rays:

When an electric discharge is passed through gas at very low pressure in the discharge tube cathode rays are produced. The cathode rays consist of a stream of high-speed electrons. When these fast-moving electrons strike the atoms or molecules of the gas present in the discharge tube, they remove one or more electrons from the neutral atoms or molecules. Thus positive ions of gas are formed. These ions which move towards the perforated cathode kept midway in the tube and constitute the positive rays coming through the perforated cathode.

Characteristics of Canal Rays:

• They travel in a straight line in the opposite direction to that of cathode rays.
• Canal rays produce fluorescence when incident on zinc sulphide screen.
• Unlike cathode rays, the positively charged particles depend upon the nature of gas present in the cathode ray tube.
• These are simply the positively charged gaseous ions.
• The charge to mass ratio of the particles is found to depend on the gas from which these originate.
• Some of the positively charged particles carry a multiple of the fundamental unit of electrical charge.
• The behaviour of these particles in the magnetic or electrical field is opposite to that observed for electron or cathode rays.

Characteristics of Protons:

• Protons are positively charged.
• Protons are located in the nucleus.
• Protons have mass 0f 1.0078 a.m.u. (1.672 ×  10^-27  Kg.). This mass of a proton is considered as unit mass ( 1 a.m.u. ).
• Mass of one proton is almost equal to the mass of one hydrogen atom.
• The proton carries a positive charge of  1.6 ×  10^-19  C. This charge carried by the roton is considered to be the unit positive charge.
• Proton is denoted by   1 H 1  or 1 P 1. I.e. it has unit positive charge and unit mass.
• All atoms contain proton.

Discovery of Neutron:

In 1920 Rutherford proposed existence of the third neutral particle in an atom. Neutron was discovered by Sir James Chadwick in 1932. He observed that when Beryllium (Be) is bombarded by α -particles; particles having no charge and mass equal to that at proton were produced (ejected).  He called them as neutrons.

Characteristics of Neutrons:

• Neutrons have no charge i.e. they are electrically neutral.
• They are located in the nucleus of an atom.
• Mass of neutron is of 1.008665 a.m.u  (1.675 ×  10^-27  Kg ). For practical purpose, this mass is assumed as unit mass.
• Mass of neutron is nearly as that of the proton.
• Neutron is denoted as 0 n 1.

Other Subatomic Particles:

Mesons, positrons, neutrinos, antiprotons are other subatomic particles. Other subatomic particles discovered recently are quarks, antiquarks, pions, gluons, boson and god particle.

Discovery of X-rays:

X-Rays were discovered by Wilhelm Roentgen in 1895. He discovered that when cathode rays strike metal with a high atomic number, radiation of very short wavelength was emitted. He was unable to explain the nature of the emitted rays hence he called these rays as X-rays.

Characteristics of X-Rays:

• These rays are capable of penetrating through wood, paper, and flesh but are stopped by bones and metallic substance.
• X-Rays are electromagnetic waves.
• They are chargeless.
• X-rays produce fluorescence in many substances. The fluorescence in different substances has different characteristics.
• X-ray kill some form of animal tissues.
• X-ray affect photographic plates.
• X-rays travel by velocity of light (3 x 10⁸ m/s) in air or vacuum.
• They are not deflected by electric or magnetic fields.
• They ionize air or gas through which they pass.

Moseley’s Contribution:

Moseley in 1913 found that each element when bombarded by high-velocity electrons, emit X-rays of different frequency.  Thus the atomic number of many elements was determined accurately by the following relationship.

Atomic number α square root of the frequency of X-rays. He gave relation Where a and k are constant. Z is an atomic number and υ is the frequency of X-ray. Thus he stated that frequency of radiation from elements depends upon the number and arrangement of unit particles in their atoms. Hence atomic number (z) is a fundamental property of all elements.

Important Terms and Concepts:

Atomic number (Z) :

The number of protons (positive charge) present in the nucleus of an atom of a particular element is called the atomic number of that element. It is denoted by letter ‘Z’.

Neutron number (N): 

The number of neutrons present in the nucleus of an atom is known as neutron number. It is denoted by ‘N’

Mass number (A): 

The total number of protons and neutrons present in the nucleus of an atom of the element is called mass number. The mass number is denoted as ‘A’.

A  =   Z + N

Representation of Atom in Symbolic Form: 

Generally, every atom X is represented as

Concept of Isotopes, Isobars, and Isotones:

Isotopes: 

Different atoms of the same element having the same atomic number but having different mass numbers are known as isotopes.

Examples :

Characteristics of Isotopes:

• Different Atoms of the same element having the same atomic number but having different mass numbers are known as isotopes.
• Isotopes are the atoms of the same element.
• They have the same atomic number but different mass numbers.
• They have the same number of protons but the different number of neutrons.
• Since they have the same atomic number they show the same chemical properties.
• They occupy the same positions in the periodic table.

Isobars: 

Atoms of the different elements having a different atomic number but having same mass numbers are known as isobars.

Examples :

Characteristics of Isobars:

• Atoms of the different elements having the different atomic numbers but having the same mass numbers are known as isobars.
• Isobars are the atoms of different elements.
• They have the same mass number but different atomic numbers.
• They have a different number of protons and neutrons.
• Since they have different atomic number they show different chemical properties.
• They occupy different positions in the periodic table.

Isotones: 

Atoms of the different elements having the different atomic number, different mass number but having same neutron number are known as isotones.

Examples:

Characteristics of Isotones:

• Atoms of the different elements having the different atomic number, different mass number but having same neutron number are known as isotones.
• Isotones are the atoms of different elements.
• They have the different mass numbers and different atomic numbers.
• They have the same number of neutrons.
• Since they have a different atomic number they show different chemical properties.
• They occupy different positions in the periodic table.

Science > Chemistry > Atomic Structure > Discovery of Proton and Neutron

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In this article, we shall study earlier concepts of an atom, discovery of electron, and its characteristics.

600 B.C. Indian saint and philosopher Maharshi Kanad proposed that matter is made up of the smallest individual particles. He called these particles ‘paramanu’. Around 400 B.C. The Greek Philosopher Democritus suggested that all the matter is composed of tiny, discrete, indivisible particles. He called these particles ‘atoms’. Both the ideas are of conceptual nature and didn’t have any experimental evidence.

Assumptions of Dalton’s atomic theory:

The first concept was given by John Dalton. The postulates of his theory are:

• Every element is made up of extremely small particles called an atom.
• The atoms are indivisible and they can neither be created nor be destroyed. Atoms of the same element resemble each other in all respects but differ from the atoms of other elements.
• When chemical compounds are formed they do so by the combination of atoms of different elements in a simple proportion of whole numbers.
• Atoms of different elements may combine in more than one proportion to form different compounds.

Evidence of Electrical Nature of Matter:

When a glass is rubbed with silk or ebonite is rubbed with fur, electricity is generated. Electricity gets transferred from one point to another point through certain substances. This phenomenon indicated that the matter has electrical nature.

Michael Faraday in 1832 passed electricity through the solution and he called the phenomenon as electrolysis. He observed that charged particles migrate towards oppositely charged electrodes. During this process, they accumulate on the electrode or escape out as a gas at the electrode. On the basis of his experiments, he proposed the laws of electrolysis. These laws of electrolysis given by Michael Faraday provide a relation between matter and electricity. These laws assumed the discrete nature of electricity. These discrete particles are called electrons by Loney.

Fundamental particles of an atom:

Protons, neutrons, and electrons that make up an atom are known as the fundamental subatomic particles. Protons and neutrons are present in the nucleus of an atom, they are called intranuclear particles or nucleons. Electrons revolve around the nucleus in a circular orbit. They are called extra-nuclear particles.

Discovery of Electrons:

Electrons were the first of sub-atomic particles to be discovered, by J.J. Thomson in 1859. J.J. Thomson made a detailed study of the discharge of electricity through gases under very low pressure. This experiment was performed using a cathode ray tube (Crooke’s tube).  It consists of a glass tube connected to two metal electrodes at two ends.  There is a side tube connected to a vacuum pump to reduce pressure.

When a gas is subjected to a high potential (5000 to 10000 V) at low pressure, the glass wall of tube glows with fluorescent light.  This glow is because of the bombardment of glass by rays emitted from the cathode.  As the rays arise from the cathode, they are called cathode rays. These rays were found to consist of negatively charged particles with a negligible but definite mass.

Cathode rays produce heat energy when they collide with the matter. It is due to the kinetic energy possessed by the cathode rays. Cathode rays also rotate the paddle wheel in their path. They move from the negative electrode to the positive electrode. Which clearly indicate that the cathode ray consists of a negatively charged particle. Thomson called these particles as negatrons. Stoney changed this name to electrons.

Thomson also showed that the electrons are present in atoms of all elements. Thus electrons are the fundamental particles of an atom.

Charge to Mass Ratio of Electron:

J. J. Thomson measured the ratio of electrical charge (e) to mass (m) of cathode ray particles using specially designed cathode ray tube.

Construction of Apparatus:

The apparatus consists of a discharge tube containing gas at a very low pressure about 0.01 mm of mercury. The discharge tube has cathode C at one end and fluorescent screen S at the other. Anode A consists of a cylinder with a fine bore.

The electric field can be applied between the plates P1 and P2. Plate P1 is positive and plate P2 is negative

The magnetic field can be applied perpendicular to the electric field and perpendicular to the plane of the diagram and into the plane.

Working:

Cathode emits electrons and they are collimated by cylindrical fine bore anode. The velocity of electrons depends on the potential difference between the cathode and the anode. When no field is applied. The electrons move in a straight line and forms spot at O at the centre of the screen.

When cathode rays are passed through an electric field created by applying a potential across the plates P₁ and P₂ only. It is found that the cathode rays particles get deflected towards the positive plate.

When cathode rays are passed through the magnetic field created by applying a strong magnetic field only, it is found that the cathode rays particles get deflected in a circular path.

Thomson applied both the fields simultaneously and adjusted its value such that the spot remains at the centre of the screen at O. Knowing values of V, B and d and using following formula the e/m ratio can be determined.

Where E = V/x. The value of e/m is 1.758820 x 10¹¹ C kg^-16.

Thomson repeated the experiment for different materials of the cathode and found that the e/m ratio is always the same. From this, he concluded that the particles present in cathode rays (electrons) are fundamental particles of any atom of all matter.

Equation of Path of Parabolic path of Electron:

The path of an electron in the electric field is parabolic whose equation is given by

Where y = deflection of the path of the electron in the y-direction

x = Distance between the parallel plates

e = Charge on electron

E = Intensity of the electric field

m = Mass of electron

v = velocity of electron

Radius of Circular Orbit of Electron:

The radius of the circular orbit of an electron in the magnetic field is given by

Where r = radius of the circular path of an electron in magnetic fields

e = Charge on electron

B = Magnetic induction

m = Mass of electron

v = velocity of electron

Alternate Equation for e/m Ratio:

Millikan’s Oil Drop Experiment:

In the first step, the oil drops are allowed to fall between the plates in the absence of an electric field. Due to gravity, they accelerate first, but gradually velocity decreases up to certain minimum value due to air resistance. Then the drops start moving downward with a constant velocity called terminal velocity (v₁). The terminal velocity of the drop is measured. As the velocity is constant, the air resistance and weight of the drop are equal in magnitude. Thus the net force acting on the drop is zero.

In the second step, an electric field is produced in the chamber. A likely looking drop is selected and kept in the middle of the field of view by adjusting the voltage. So that the drop is moving down with constant velocity called terminal velocity (v₂). Thus net force acting on it is zero. Thus the electric force is balancing the downward forces.

The charge on an electron is given by

Where η = Coefficient of the viscosity of gaseous medium (air)

v₁ = Terminal velocity of the oil drop when an electric field is not applied

v₂ = Terminal velocity of the oil drop when an electric field is applied

E = Intensity of the electric field between plates

f = Density of oil

σ = density of the gas (air)

g = acceleration due to gravity

Millikan repeated the experiment by varying the strength of x-rays used for ionization of air no. of times. Due to which the no. of electrons attaching to the oil drop varied. Then he obtained various values for the charge and is found to be an integral multiple of 1.6 x 10^-19 C.

In 1923, Millikan won the Nobel Prize in Physics in part because of this experiment.

The charge on an Electron:

Scientist R. A. Millikan in his oil-drop experiment determined the charge on the electron and he found that the charge on an electron is 1.6022 x 10^-19 C.

Mass of an Electron:

Using e/m ratio and charge on the electron, the mass of an electron is found to be 9.1094 x 10^-31 kg.

Characteristics of Electrons:

• Electrons are negatively charged.
• They are revolving in circular orbits around the nucleus.
• They have mass 0f 0.00055 a.m.u.  (9.11 × 10 ^-31 Kg.). This mass of an electron is negligible compared to other particles. Hence it is taken as zero.
• Its mass is 1/1837 times that of the proton.
• Electrons carry a negative charge of 1.6 × 10 ^-19 C. This charge carried by the electron is considered to be a unit negative charge.

Science > Chemistry > Atomic Structure > Discovery of Electron

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Radioactivity was discovered by French physicist Antoine Becquerel in 1896. The phenomenon of spontaneous and continuous and uncontrollable disintegration of an unstable nucleus accompanied by the emission of active radiations is called natural radioactivity. The substance which exhibits radioactivity is called a radioactive substance. e.g. Uranium, thorium, radium, etc. The radiations emitted by the radioactive substance are alpha particles, beta particles, and gamma radiations.

Characteristics of Natural Radioactivity:

• These characteristics are also called as Rutherford-Soddy’s radioactive disintegration theory
• Radioactivity is a purely nuclear phenomenon.  The nucleus of a radioactive substance is unstable and such unstable nucleus undergoes spontaneous breakdown (disintegration). The process continues till a stable nucleus is obtained.
• As radioactivity is the nuclear phenomenon it is unaffected by chemical combination. i.e. the element will exhibit radioactivity in free as well as a combined state.
• Radioactivity is a spontaneous process. It is independent of external factors like temperature, pressure, and the state of existence of substance or catalytic action. Hence the process of radioactive disintegration is uncontrollable using these factors.
• The nucleus of radioactive element emit alpha  (α), beta(β) and gamma (γ)  radiations and gets converted into the nucleus of another element.
• The elements undergoing disintegration is called parent element and a new element formed is called a daughter element. Daughter element has different chemical and physical properties as compared with that of its parent element.
• During disintegration, besides emission of alpha  (α), beta(β) and gamma (γ) radiation, a large amount of energy is liberated in form of γ rays. When γ rays are given out no new element is formed.
• The time taken, by a radioactive substance to disintegrate half of its initial quantity is called as half-life period.  Half-life period is a characteristic property of every radio element.
• When radioactive substance emits one α -particle mass number of daughter element reduces by 4 units and atomic number reduces by 2 units. When a radioactive substance emits one β – particle, the atomic number of daughter element increases by one unit but the mass number remain unchanged.
• The rate of disintegration at any instant is directly proportional to the radioactive nuclei present at that instant.
• Thus the rate of disintegration depends on nature and the original amount of the radioactive substance. It is an exponential process and practically never gets completed.

Characteristics of α – particles:

• These are positively charged particles.  So α-rays are called α – particles rather than α -rays.
• Actually, α particles are helium nuclei having 4 unit mass and 2 unit of positive charge.
• They are deflected towards a negative plate of the electric field.
• They have greater ionizing power.
• They have least penetration power.
• They can affect a photographic plate.
• They travel in straight line.
• They have a velocity which is about    1/10 th that of light.
• When radioactive substance emits one α -particle, the mass number of daughter element formed is 4 units less and the atomic number is 2 units less.

Characteristics of β-particles:

• β- Rays are negatively charged particles. So they are called β – particles rather than β – rays.
• β- particles are nothing but high-velocity electrons having unit negative charge and negligible mass.
• These rays are deflected towards + ve plate of the electric field.
• They have less ionizing power as compared with that of α- rays5.   They have greater penetration power than that of α – rays
• They affect a photographic plate to the much higher extent than the α- particles.
• They do not travel in straight line.
• They have a greater velocity than that of the α- rays very close to that of light.
• When a radioactive substance emits one β -particle, the atomic number of daughter element formed is one unit higher but the mass number remains unchanged.

Characteristics of γ – rays:

• γ-rays are nonmaterial
• They are electromagnetic radiations.
• They are chargeless, hence remain undeflected due to the electric or magnetic field.
• They have very low ionizing power.
• They have high penetration power.
• They have a very little effect on a photographic plate.
• They travel in straight line.
• They have a velocity equal to that of the light.
• When radioactive substance emits γ rays there is no change in atomic number and mass number.

Distinguishing between α particles and β particles:

Distinguishing between α particles and γ rays:

Distinguishing between β particles and γ rays :

Science > Chemistry > Atomic Structure > Radioactivity

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