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## Note on Atomic Structure

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Atomic structure

The term ‘atom’ is derived from Greek word ‘atomos’ meaning indivisible and it was coined by Democritus in approximately 450 BC. Atom is the fundamental unit of matter. In 1808, John Dalton, an English chemist proposed the fundamental concept of the structure of matter through Dalton’s atomic theory. The main postulates of Dalton’s atomic theory are:

i) Every matter is composed of smallest particle called atoms.

ii) Atom is the indivisible and undestructive unit.

iii. Atom is regarded as a spherical particle which can neither be created nor be destroyed.

iv)Atoms of same elements are identical in all respect.

v) Atoms undergo chemical combination to form compound atom (molecule) in simple whole number ratio.

Dalton’s atomic theory was well accepted till the 19th century. Later on, the numbers of drawbacks were observed. So, this theory was revised, refined and developed by new researchers. The main points to be focused is that whether the atom is divisible or not.

Discovery of element (Discharge tube experiment)

Electron was first discovered by J.J Thompson in 1879 with the help of discharge tube experiment. In this experiment, he filled up gas on a specially designed glass tube (discharge tube) provided with metal electrons.

The discharge is carried out at a high voltage of electricity (10,000V) and low pressure (10­­-3 mmHg).

At this condition, a type of ray starts to travel from cathode to anode; these rays were named as cathode rays. The following properties of the cathode rays were investigated, they are:

i) Cathode rays cast the shadow of an object on their way.

ii) They travel in a straight line.

iii. Cathode rays get deflected towards anode in the presence of electric field, indicating that they carry a negative charge.

iv) They produce the heating effect on the coil.

v) Cathode rays can produce fluorescence in Zinc sulphide screen.

After the investigation of the properties of cathode rays, he concluded that cathode rays carry the negative charge with the certain mass. Later on, these rays were named as electron by Stoney. It is symbolized as e- or simply e.

Discovery of anode rays or discovery of proton

Proton was discovered after the discovery of electron with the assumption that there must be positively charged particle along with negatively charged particle since atom is electrically neutral.

Proton was discovered by E. Goldstein in 1886 with the help of discharge tube experiment with the perforated cathode.

In his experiment, he passed high voltage of electricity (10000V) in a glass tube filled with hydrogen gas and provided with the perforated cathode. The discharge is carried out at low pressure (10-3 mmHg)

At this condition, two types of rays were moving in two opposite direction. Those rays which move towards cathode were named as anode rays. The following properties were investigated, they are:

i) Anode rays cast the shadow of an object on their way.

ii)They travel in a straight line.

iii.) Anode rays get deflected towards cathode in the presence of electric field, indicating that they carry a positive charge.

iv) They produce the heating effect on the coil.

v)The anode can rotate a small paddle placed on their way.

After the investigation of the properties of anode rays, he concluded that anode rays carry the positive charge with the certain mass. These rays were named as the proton. It is symbolized as p+ or simply p.

Discovery of neutron

Neutron was discovered by Sir James Chadwick in 1932. In his experiment, he bombarded α-particle (equivalent to Helium-atom) at Be- target. Another particle was evolved having no charge and mass almost equal to that of the proton.

The ejected particle was named as neutron by Chadwick. It is symbolized as 10n or simply ‘n’.

Subatomic particle

The smaller particles present inside an atom is called sub atomic particles. More than 36 sub atomic particles have been discovered like the electron, proton, neutron, meson, lepton, neutrino, etc. Out of more than 36 sub atomic particles, electron, proton and neutron are called fundamental subatomic particles.

Question: What are the fundamental sub atomic particles? Why are they called so?

Ans:

Electrons, protons, and neutrons are the fundamental sub atomic particles.

They are called so because of the following reasons. An element is popularly known by its atomic number. For example Atomic number 14 represents Silicon. The source of the atomic number of an element is the number of protons or the number of electrons present in the atom of the element. In addition to it, the mass of the atom is represented by its atomic mass. For example, Sodium consists of 11 protons and 12 neutrons. So, its atomic mass or the mass number is (11+12) i.e. 23. Chemical reactions that take place involves the loss or gain or share of electrons which can be gained by the compound or molecule. For example: in the chemical reaction, 2Na + Cl2 →2NaCl , Na loses an electron and chlorine gains electron.

Comparative study of electron, proton, and neutron

1) Electron (e- or e)

Discovery: J J Thompson (1879)

- Nobel Prize in 1906

Charge: -1.602 x 10-19 C (-1)

Mass(Rest mass) : 9.11 x 10-28 gm OR 0.00055 amu

Antiparticle: positron (e+)

2) Proton (p+ or p)

Discovery: E. Goldstein (1886)

Charge: +1.602 x 10-19C (+1)

Mass: 1.673 x 10-24 gm or 1.0072 amu

Anti-particle: Antiproton

3) Neutron

- Nobel Prize: 1935

Charge: No charge

Mass: 1.673 x 10-24 gm OR 1.0086amu ( Nearly equal to the mass of an atom of hydrogen)

Anti-particle: Anti neutron ()

Atomic model

Rutherford’s α ray scattering experiment

Ernest Rutherford and his students in 1911 performed an experiment in order to locate the position of electrons and protons inside an atom. This experiment is known as gold foil experiment or Rutherford’s α ray scattering experiment.

In his experiment, a piece of a radioactive substance (Polonium) was placed inside the lead cavity as the source of α-particle (equivalent to doubly ionized Helium nucleus, He2+).

A narrow beam of α-particle was directed by the means of slits and was fired at a thin gold foil. The scattering of α-particle was monitored with the help of movable zinc sulphide screen along with microscope as shown in the figure as zinc sulphide screen produces flash when α-particle strikes in it.

Observation

i) Most of the α-particle (around 99%) passed through gold foil without any deflection.

ii)Some of the α-particles deflected through a small angle.

iii) Only a few α-particle (1 in 10,000) deflected through the large angle and a few of them ( 1 in 20,000) reflected back by suffering an angle of deflection 1800.

Conclusion

i) Most of the α-particle pass through gold foil without deflection concludes that most of the space inside the atom is the vacuum.

ii) Since α-particle is positively charged, the deflection of α-particle concludes that there must be a presence of a heavy positively charged body inside an atom as like charge repel each other. The heavy positively charged body inside an atom was named as a nucleus by Rutherford.

iii. Deflection through the large and back scattering of only a few α-particle concludes that the nucleus occupies very small volume with compared to total volume of an atom.

Rutherford’s atomic model or nuclear model or planetary model

Considering experimental observation and conclusion, Rutherford proposed an atomic model which is known as a nuclear model or planetary model. According to this model, the positively charged nucleus is surrounded by the system of electrons. Electrons are moving around the nucleus with high speed like planetary motion in the solar system. The positively charged nucleus is due to the presence of protons. Electrons and protons are held together by electrostatic force. The effective volume of the nucleus is very small compared with the total volume of an atom.

After the discovery of the neutron in 1932, the position of the neutron was given inside the nucleus of the atom since the mass of the neutron is almost equal to the mass of the proton and the most of the mass of an atom is concentrated at the center of the atom.

Limitations or drawbacks of Rutherford’s atomic model

a) Stability of an atom: The negatively charged proton revolves around the nucleus as suggested by Rutherford but according to the classical theory of electrodynamics, any accelerated charge particle emits radiation and loses energy. The electron is also a charged particle and when it moves, it loses energy in the form of radiation. With the gradual loss of energy, electron comes closer to the nucleus and ultimately falls on it causing the atom to collapse but it never happens with an atom as the atom is a very stable particle. Rutherford could not explain the stability of an atom.

b) Explanation of origin of atomic spectra: When the electron of an atom gains or loses energy, it produces the multi-colored line on the spectrum, which is called atomic spectra. The atomic spectra is a very important feature of an atom. The atomic spectra are of a discontinuous type. Rutherford could not explain the origin of atomic spectra even for a simple hydrogen atom.

Bohr’s atomic model or quantized shell model

In order to overcome the limitation of Rutherford’s atomic model, in 1913, Neil Bohr proposed quantized shell model. The main postulates of Bohr’s atomic model are:

i) The center of an atom possesses proton within a very small volume and electron revolves around the nucleus in a certain definite circular path called orbit or energy shell.

ii) The orbit of an atom is associated with fixed energy and electron holding capacity. It is denoted by letters K, L, M, etc. or numerals as n=1, n=2, n=3, etc. outwards from the center.

iii) The maximum number of electrons that an orbit can accommodate is given by the 2n2 rule.

iv) The energy of an orbit goes on increasing outwards from the center i.e. E1<E2<E3 and so on. The energy difference between two regular orbits is equal to 1 quantum.

v) In the ground state, the electron neither loses nor gains energy. This explains the stability of an atom.

vi) Absorption or emission of energy by electron promotes it into higher energy level or demotes it into lower energy level during jump respectively. The extent of the jump depends on upon the amount of energy absorbed or released by the electron.

vii) Absorption or emission of energy always occurs in the whole number of quanta. So, no electron can exist in between two orbits. This explains the origin of atomic spectra.

viii) Only energy shell in which the angular momentum of the electron is integral multiple of $$\frac {h}{2Π}$$ is permissible.

i.e. mvr = n$$\frac {h}{2Π}$$

This is known as quantization of angular momentum of the electron in an orbit.

ix) The centrifugal force acting on a moving electron is balanced by the electrostatic force of attraction between electrons and protons

i.e. $$\frac {mv_e^2}{r}$$ =$$\frac {ZK_ee^2}{r^2}$$

Z = Atomic number

Ke = Columbic constant

e = charge of electron

Explanation of line spectra of hydrogen on the basis of Bohr's atomic model

Atom consists of an infinite number of orbits. Each orbit is associated with fixed amount of energy and electron holding capacity. When energy is supplied, electron gets promoted into higher energy level and after the removal of energy, electron returns to lower energy level depending on the amount of energy absorbed or released. During this process of absorption and emission, atomic spectra are resolved.

In the case of hydrogen, the molecular hydrogen is subjected to discharge tube ( at high voltage and low pressure). At first, the molecular hydrogen gets dissociated into atomic hydrogen and later on, the extra energy is used to promote electron in higher energy level. As the excited state is unstable, electrons return to lower energy level by the radiating light of characteristic wavelength. In this way, it gives rise to line spectra of hydrogen. Depending on the wavelength of radiation, line spectra can be divide into five series ; Lyman, Balmer, Paschen, Bracket, and Pfund.

The wavelength of the corresponding series can be calculated by using Balmer's equation:

$$\frac {1}{λ}$$ = $$R_d\:(\frac{1}{n_L^2} - \frac{1}{n_H^2})$$

Rd = Rydberg's constant ( 1.09 x 10-7 m -1)

nL = lower energy level

nH = Higher energy level

Example: Find the wavelength of radiation when electron transmits from 5th orbit to 7th orbit.

Here,

nL = 5

nH = 7

Rd = Rydberg's constant ( 1.09 x 10-5 cm -1)

λ = ?

We know,

$$\frac {1}{λ}$$ = $$R_d\:(\frac{1}{n_L^2} - \frac{1}{n_H^2})$$

= $$1.09× 10^{-5}\:(\frac{1}{5^2} - \frac{1}{7^2})$$

= $$1.09× 10^{-5}\:(\frac{1}{25} - \frac{1}{49})$$

= 2.135 x 103

or, λ = $$\frac{1}{2.135×10^3}$$

or, λ = 4.6 x 10-4 cm

Drawbacks of Bohr's atomic model

i) Bohr's atomic model cannot explain the spectra and energy of atom containing more than 1 electron.

ii) This model cannot account the relative brightness of spectral line while some line appears to be bright or faint.

iii) The spectral line is composed of a number of small lines (fine structure) . Bohr's atomic model cannot explain the origin of fine structure.

iv) This model cannot explain the reason why atoms undergo chemical combination to form a compound or why compounds are more stable than their constituent atoms.

v) According to Bohr's atomic model, the electron is assumed to revolve in a fixed circular path with fixed velocity but modern research shows that Bohr's concept of fixed circular path has no more significance.

de-Broglie wave equation (Dual nature of particle)

In 1924, de-Broglie suggested that electron on motion behaves like a particle as well as a wave. He named it to matter wave that differs from mechanical wave like light, sound, electromagnetic radiation.

According to Einstein's mass - energy relationship

E = mc2 --------------(i)

where 'm' is the mass of the particle and 'c' is the velocity of light and according to Plank's photon - energy equation

E = hν--------------(ii)

where 'h' is Plank's constant ( value = 6.6 x 10-34 Js)and v(nu) is the frequency of radiation.

Combining (i) and (ii)

mc2 = hν

or, mc2 = h $$\frac {c}{λ}$$ [Since c = νλ]

or, λ = $$\frac {h}{mc}$$ ----------(iii)

If the velocity of the electron is v, then this equation becomes

or, λ = $$\frac {h}{mv}$$ ----------(iv)

This is called de-Broglie wave equation. The wavelength of an electron is very small. So, its value cannot be determined accurately.

Heisenberg's uncertainty principle

In 1927, Werner Heisenberg put forward uncertainty principle. According to this principle, both position and momentum or velocity of a smaller particle like an electron cannot be determined accurately at the same time i.e. the more precisely the position is determined the less precise the momentum becomes and vice versa.

Let Δx and Δp be the uncertainties in position and momentum respectively, then according to this principle,

Δx.Δp ≥ $$\frac {h}{4Π}$$

From this, it is clear that the increase in uncertainty in position decreases the uncertainty in momentum and vice versa.

Now,

Δp = m Δv

where Δv = uncertainty in velocity

i.e. m Δv . Δx ≥ $$\frac {h}{4Π}$$

i.e. Δv . Δx ≥ $$\frac {h}{4Πm}$$

Therefore, uncertainty is more pronounced for smaller particles.

Orbital or sub shell

Orbital is the three-dimensional space around the nucleus where the probability of finding the electron is maximum. There are four types of orbitals. They are :

i) S - atomic orbital (spherical)

ii) p - atomic orbital (principal)

iii)d - atomic orbital (diffuse)

iv) f - atomic orbital (fundamental)

Each atomic orbital can hold the maximum of 2 electrons. These electrons move in two opposite directions, one moves in the clockwise direction and another moves in anticlockwise directions.

i) s- atomic orbital

All atomic orbital possesses s-atomic orbital. The probability of finding the electron in s- atomic orbital is equal in all directions on the surface of the sphere as it has the spherical geometry. The coefficient of orbital indicates the orbit to which it belongs . For example: '1s' represents that s-atomic orbital belongs to 1st orbit (K) and so on. Each s - atomic orbital can hold the maximum of 2 electrons. The energy of various s-atomic orbital goes on increasing outwards from the center and follows the following order

1s < 2s < 3s and so on

ii) p - atomic orbital

All p-atomic orbital has dumbell shape and starts from 2nd orbit. p- atomic orbital has three orientations Px, Py and Pz along the x-axis, y-axis and z-axis respectively.

Each orientation consists of two lobes at two opposite ends. The probability of finding the electron is maximum at lobes and minimum at nodal planes. p - atomic orbital can hold the maximum of 6 electrons. The energy of p-atomic orbital are equal i.e. EPx = Epy = EPz, p- atomic orbital shows directional properties.

iii) d and f atomic orbital

d and f atomic orbitals have very complicated shape and start from 3rd and 4th orbit respectively. d atomic orbital has high orientation and a maximum number of electrons that it can attain is 10. Similarly, f atomic orbitals have 7 orientations and a maximum number of electrons it can attain is 14.

Quantum number

Quantum number is the set of 4 numbers that describes the energy of the electron ( the main energy level, the shape of the orbital, the orientation of orbital in space and rotation of electron about its own axis). There are 4 quantum numbers.and they are

i) Principal quantum number (n)

ii) Azimuthal/Angular momentum quantum number (l)

iii) Magnetic quantum number(m)

iv) Spin quantum number (s)

i) Principal quantum number (n)

The quantum number that describes the energy of an electron on the main energy level in which electron is present is known as the principal quantum number. It is denoted by n. It can have any integer value from 1 to ∞. The principal quantum number gives the idea about the location and energy of an electron.

i.e. n = 1 (K), n =2 (L), n =3 (M), etc.

The permissible energy of orbit for hydrogen, Ex = $$\frac {-13.6}{n^2}$$ (ev)

i.e. E3 > E2 > E1

ii) Azimuthal quantum number

The quantum number that describes the shape of orbital in which electron resides is known as the .

azimuthal quantum number. It is denoted by 'l'.

It can have only +ve integer value from 0 to ( n - 1) where 'n' is the principle quantum number .

Table no. 1: Designation of subshell

 Value of l Designation of Subshell Spectroscopic term 0 s sharp 1 p principal 2 d diffuse 3 f fundamental

Table number 2: Relation of n and l

 Value of n Value of l ( 0 to n-1 ) Number of subshell Designation 1 0 (s) 1 1s 2 0,1 (s,p) 2 2s and 2p 3 0,1,2(s,p,d) 3 3s and 3p 4 0,1,2,3(s,p,d,f) 4 4s,4p,4d and 4f

iii) Magnetic quantum number

The quantum number that describes the orientation of orbital in space is called magnetic quantum number. It is represented by 'm'. It can have any integer value from -l to +l through 0, where 'l' is the azimuthal quantum number. For the given value of l, there will be (2l + 1) values of m.

Table no.3 : Relation between l and m

 Value of l The number of values of m(2l + 1) Values of m( -l to +l through0) Designation 0(s) 1 0 s 1(p) 3 -1, 0, +1 Px, Py Pz 2(d) 5 -2,-1,0,+1,+2 dxy, dxz, dyz,dx2- y2, dz2 3(f) 7 -3,-2,-1,0,+1,+2,+3 -

iv) Spin quantum number

The quantum number that describes the rotation of electron about its own axis is said to be the spin quantum number. It is represented by 's' or 'Ms'. It can have only two values $$\frac{-1}{2}$$ and $$\frac {+1}{2}$$

Example: Find the value of n, l, m and s for 3rd orbit

Solution, For 3rd orbit

n = 3

For n = 3, l = 0 to ( 3 - 1) = 0 to 2 = 0, 1, 2 i.e. s,p,d

For l =0 , m= 0 (-l to +l through 0)

For l = 1, m = -1, 0 ,+1(-l to +l through 0)

For l =2 , m = -2, -1, 0 ,+1,+2 (-l to +l through 0)

s = $$\frac{-1}{2}$$ or $$\frac {+1}{2}$$

Example" Allocate the position of electron having following quantum number

n = 4, l = 1, m = -1 and s = $$\frac {+1}{2}$$

Solution:

n = 4 ( 4tth orbit)

l = 1 ( p -orbital)

m = -1(Px)

s = $$\frac {+1}{2}$$ (clockwise)

i.e. the required position = 4Px1

An electron is present in Px orbital of 4th orbit with clockwise spin.

Example: Assign all four quantum numbers for electrons of Mg- atom.

Solution

12Mg = 1s2 2s2 2p63s2

 Electrons n l m ms 1s2 1 1 0 0 0 0 +$$\frac{1}{2}$$ -$$\frac{1}{2}$$ 2s2 2 2 0 0 0 0 +$$\frac{1}{2}$$ -$$\frac{1}{2}$$ 2p6 2 2 2 2 2 2 1 1 1 1 1 1 -1 -1 0 0 +1 +1 +$$\frac{1}{2}$$ -$$\frac{1}{2}$$ +$$\frac{1}{2}$$ -$$\frac{1}{2}$$ +$$\frac{1}{2}$$ -$$\frac{1}{2}$$ 3s2 3 3 0 0 0 0 +$$\frac{1}{2}$$ -$$\frac{1}{2}$$

Aufbau principle ( The rule of filling electrons in diffuse orbital) or (n + l) rule

Aufbau principle states that electrons are filled in different orbitals on the basis of their increasing energy. According to this principle, orbital with lower energy is filled first followed by orbital with higher energy. The energy of orbital depends on the principal quantum number (n) and azimuthal quantum number (l) . So, this can be generalised as an (n + l) rule.

Rules:

1. The orbital with lower value of (n + l) is filled first. For excample: 3s is filled before 3p becaues.

for 3s, n + l = 3 + 0 = 3

for 3p, n + l = 3 + 1 = 4

2. If more than one orbital with the same value of ( n + l) is present, the orbital with the lower value of 'n' is filled first.

For example, 2p is filled before 3s.

Exceptions

The electronic configuration of some elements does not follow Aufbau principle in the form of half filled and completely filled orbital. It is due to extra stability gained by half filled and completely filled orbitals.

24Cr = 1s22s22p63s23p64s23d4 ( Expected electronic configuration)

= 1s22s22p63s23p64s13d5( Actual electronic configuration, half filled)

29Cu = 1s22s22p63s23p64s23d9( Expected electronic configuration)

= 1s22s22p63s23p64s13d10( Actual electronic configuration, fully filled)

Pauli's exclusion principle

Wolfgang Pauli put forward a principle for filling electron in an orbital. According to the principle, no any two electrons of an atom can have the idental value of all four quantum numbers.

Illustration: In the case of Neon,

10Ne = 1s2 2s2 2p6

 Electrons n l m ms 1s2 1 1 0 0 0 0 +$$\frac{1}{2}$$ -$$\frac{1}{2}$$ 2s2 2 2 0 0 0 0 +$$\frac{1}{2}$$ -$$\frac{1}{2}$$ 2p6 2 2 2 2 2 2 1 1 1 1 1 1 -1 -1 0 0 +1 +1 +$$\frac{1}{2}$$ -$$\frac{1}{2}$$ +$$\frac{1}{2}$$ -$$\frac{1}{2}$$ +$$\frac{1}{2}$$ -$$\frac{1}{2}$$

Conclusion

i) Each orbital can hold the maximum of 2 electrons with opposite spin.

2) The maximum number of electrons present in an orbit is equal to the twice of the square of a number of orbital present in that orbit. ( 2n2)

Degenerate orbitals

In the absence of the external magnetic field, all orbitals having the identical value of 'n' and 'l' and different values of 'm' must have equal energy. These orbitals are called degenerate orbitals.

In the presence of the external magnetic field, the degenerate orbitals have slightly different energy.

Hund's rule of maximum multiplicity ( The rule of filling electrons in degenerate orbitals)

When more than one orbital having equal energy ( degenerate orbital) are available, electrons are filled in these orbitals separately with parallel spin. The pairing of electrons will start only after these orbitals are singly occupied. This rule is called Hund's rule of maximum multiplicity.

For example: 8O = 1s2 2s22p4

• Atom is the fundamental unit of matter. In 1808, John Dalton
• )Atoms of same elements are identical in all respect.
•  Atom is the indivisible and undestructive unit.
• The ejected particle was named as neutron by Chadwick. It is symbolized as 10n or simply ‘n’.
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