S.M.Shazzad RahmanLecturer, Textile Engineering Department, NUBCourse Code:CHE1105Course Title: Inorganic and physical chemistry

Atomic Structure

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Rutherford's experimentA stream of alpha particles (much like a stream of tiny bullets) was directed at a thin foil of gold atoms and a detector arranged to surround the sample completely except for a small hole for entry of the particles. The foil was several thousands of atoms thick.

Rutherford scattering apparatus

What was observed?• Most of the alpha particles pass straight through the gold foil without any deflection from their original path.• A few alpha particles are deflected through small angles and few are deflected through large angles.• A very few alpha particles completely rebound on hitting the gold foil and turn back in their path (just as a ball rebounds on hitting a hard wall).

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Explanation• Since most of the alpha particles pass straight through the gold foil without any deflection it shows there is a lot of empty space in an atom.

• Some of the alpha particles are deflected through small and large angles, which shows that there is a 'Centre of positive charge' in an atom, which repels the positively charged alpha particles and deflects them from the original path.

• Very few alpha particles rebound on hitting the gold foil, which shows the nucleus is very dense and hard which does not allow alpha particles to pass through it. The whole mass of the atom is centered at its nucleus.Conclusion• Nucleus of an atom is positively charged• Nucleus is very dense and hard• Nucleus is very small compared to the size of the atom.

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Scattering of alpha particles by the atoms of a gold foil

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A picture of the model as conceived by Rutherford•The atom of an element consists of a small, positively charged nucleus in the Centre, which carries almost the entire mass of the atom.•The electrons are revolving around the nucleus at high speed.•The number of electrons in an atom is equal to the number of protons. Hence it is electrically neutral.•The volume of the nucleus is negligibly small compared to the volume of the atom.•Most of the space in the atom is empty.

Rutherford's nuclear model of the atom

Rutherford compared the structure of an atom to the solar system i.e., just as in the solar system, the Sun is having the maximum mass and planets revolve around it, similarly in an atom, the nucleus forms the main mass of atom and electrons revolve around it.

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Drawback of Rutherford's Atomic ModelRutherford proposed that electrons revolve at high speed in circular orbits around the positively charged nucleus. But according to the electromagnetic theory, if a charged particle were accelerated around another charged particle then there would be a continuous radiation of energy. The loss of energy would slow down the speed of the electron and eventually the electron would fall into the nucleus. But such a collapse does not occur. Rutherford's model was unable to explain it.

Diagram to show how an energy losing electron could fall into the nucleus.

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Neil's Bohr model of an atom

In 1913, Neil's Bohr proposed a model of an atom based on the Planck's quantum theory of radiation. The basic postulates of Bohr's theory are:• An atom consists of a small, heavily positively charged nucleus around which electrons revolve in definite circular paths called orbits.

• These orbits are associated with definite energies called energy shells/energy levels. They are designated as K, L, M, N, …. etc. shells or numbered as 1, 2, 3, 4, …..etc. from the nucleus.

• As long as the electron remains in a particular orbit /energy shell its energy remains constant. This accounts for the stability of an atom.

• Only those orbits are permitted in which angular momentum of the electron is a whole number multiple of (h/2π) where h is Planck's constant. Any moving body taking a circular orbit has an angular momentum equal to the product of its mass (m), velocity of movement (v) and radius of orbit (r). In other words the angular momentum of an electron

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Thus,

This postulate introduces the concept of quantization of angular momentum.• Electrons can either lose or absorb energy abruptly, when they jump from one energy level to another. For instance when an electron moves from the 'normal or ground state - E1' of an atom i.e., the state of lowest energy as required by its 'n' and 'l' values, to a higher level, it causes the atom to be in its 'excited state - E2' i.e., where electrons in an atom occupy energy levels higher than those permitted by its 'n' and 'l' values. The reverse is also true and the change in energy is DE,DE = E2 - E1 = hn

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Limitations and problems

• It could not explain the line spectrum of multi electron atoms.• This model failed to explain the effect of magnetic field on the spectra of atoms (Zeeman effect). The Zeeman effect is the splitting of a spectral line into several components in the presence of a static magnetic field. • The effect of electric field on the spectra could not be explained by Bohr's model (Stark effect). The  Stark effect is the splitting of a spectral line into several components in the presence of an electric field. • The shapes of molecules arising out of directional bonding could not be explained.• The dual nature of electrons (both as wave and particle) and the path of motion of the electron in well defined orbits were not correct.

Quantum numbers

The discrete collection of real numbers necessary to characterize a physical system is known as “quantum numbers”. To completely describe an electron, there exists 4 quantum numbers. They are Principal quantum number (n), Azimuthal quantum number (l), Magnetic quantum number (m) and Spin quantum number (s).

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Principal Quantum Number (n)

This quantum number determines the main energy shell or energy level in which the electron is present. The principal quantum number gives the average distance of the electron from the nucleus and energy associated with it.It is denoted by the letter 'n' that can take whole number values starting from 1, 2, 3, 4, ….. . The shell with n = 1 is called first shell or 'K' shell. The shell with n = 2 is the 'L' shell and so on. The first shell is closest to the nucleus. As the value of 'n' increases, the distance from the nucleus as well as the energy of the electrons increases.

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Azimuthal or Angular Quantum Number (l)

The Azimuthal quantum number determines the angular momentum of the electron, denoted by the letter 'l'. The value of 'l' gives the sub level or sub shell in a given principal energy shell to which the electron belongs. It can have only positive integral values from zero to (n-1) where 'n' is the principal quantum number. The various sub shell values of l are also designated by the letters s, p, d, f,…… For any main energy level, the energies of the sub shell follow the order s > p > d > f.The different sub shells are represented by first writing the value of 'n' and then the letter designated for the value of 'l'. To illustrate,n = 1 l = 0 one sub shell 1s n = 2 l = 0,1 two sub shells 2s, 2pn = 3 l = 0,1,2 three sub shells 3s, 3p, 3d n =4 l = 0,1,2,3 four sub shells 4s, 4p, 4d, 4fThus for each value of 'n' there are 'n' values of 'l'. The value of azimuthal quantum number gives the shape of the sub shell or orbital. So it is also called as orbital quantum number.

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Magnetic Quantum Number (m)

This quantum number describes the behavior of the electrons in the magnetic field. We know that the movement of electrical charge is always associated with magnetic field.The magnetic quantum number describes the behavior of electron in a magnetic field. In the absence of external magnetic field electrons / orbitals having same values of 'n' and 'l' but different values on 'm' have the same energies. They are called degenerate orbitals. However, in the presence of an external magnetic field the orbitals vary in their energies slightly. This is because the preferred orientation of the orbital in space is a result of interaction of its own magnetic field with that of the external magnetic field.It is denoted by the letter 'm' the values of which depends on 'l'. This quantum number can have all integral values from '-l' to '+l' including 0. Thus for given 'l' value there are (2l + 1) values of 'm'. Two orbitals in the same shell can have identical 'n' and 'l' values but they must have different fixed values of 'm'. The number of orbitals in each sub shell are given below:s sub shell l = 0 m = 0 only one orientation one orbital p sub shell l = 1 m = +1,0, -1 three orientations three orbitalsd sub shell l = 2 m = +2,+1,0,-1,-2 five orientations five orbitals

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Spin Quantum Number (s)

It is observed that the electron is not only revolving around the nucleus but it is also spinning on its own axis. The spin of the electron produces a small magnetic field as a result of which the electron behaves as a 'tiny magnet'. This quantum number describes the spin orientation of the electron. It is designated by s. Since the electron can spin only in two ways: clockwise and anti-clockwise and, therefore, the spin quantum number can take only two values: + ½ or - ½ .

Pauli's Exclusion Principle

According to this principle, an orbital can accommodate maximum of two electrons and these two must have opposite spins. This means that an orbital can have 0, 1 or 2 electrons. Moreover, if an orbital has two electrons, they must be of opposite spins.

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Aufbau Principle

The Aufbau principle states that in the ground state of an atom, an electron enters the orbital of lowest energy first, and then the subsequent electrons are fed in the order of increasing energies into the orbitals. The relative energies of various orbitals are given in fig.1.6. From the figure, the following sequence is observed for orbitals in the increasing energy:1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s.

1s 2s 3s 4s 5s 6s 7s

2p 3p 4p 5p 6p 7p

3d 4d 5d 6d 7d

4f 5f 6f 7f

Aufbau PrincipleThe Aufbau principle states that in the ground state of an atom, an electron enters the orbital of lowest energy first, and then the subsequent electrons are fed in the order of increasing energies into the orbitals. The relative energies of various orbitals are given in fig.1.6. From the figure, the following sequence is observed for orbitals in the increasing energy:1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s.

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Heisenberg Uncertainty Principle

Werner Heisenberg, in 1927, pointed out that we can never measure accurately both the position and velocity (or momentum) of a microscopic particle as small as an electron. Consequently, it is not possible to talk of the trajectory of an electron. On this basis, Heisenberg put forward a principle known as uncertainty principle. According to Heisenberg's uncertainty principle, it is not possible to measure simultaneously both the position and velocity (or momentum) of a microscopic particle with absolute accuracy or certainty.

The more accurately you know the position (i.e., the smaller Dx is) , the less accurately you know the momentum (i.e., the larger Dp is); and vice versa

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Implications

It is impossible to know both the position and momentum exactly, i.e., Δx=0 and Δp=0

These uncertainties are inherent in the physical world and have nothing to do with the skill of the observer

Because h is so small, these uncertainties are not observable in normal everyday situations

Heisenberg’s Uncertainty Principle involving energy and time

The more accurately we know the energy of a body, the less accurately we know how long it possessed that energy

The energy can be known with perfect precision (ΔE = 0), only if the measurement is made over an infinite period of time (Δt = ∞)

7N 1s2 2s2 2px1 2py

1

2pz1

6C 1s2 2s2 2px1

2py1

No pairing of electrons is possible unless all orbital's in the same sub shell have one electron each.

Hund’s Rule of Maximum Multiplicity

8O 1s2 2s2 2px2 2py

1 2pz1

9F 1s2 2s2 2px2 2py

2 2pz1

10Ne 1s2 2s2 2px2 2py

2

2pz2

11Na 1s2 2s2 2px2 2py

2 2pz2

2s1 12Mg 1s2 2s2 2px

2 2py2 2pz

2

3s2

13Al 1s2 2s2 2px2 2py

2 2pz2 3s2 3px

1

14Si 1s2 2s2 2px2 2py

2 2pz2 3s2 3px

1

3py1

15P 1s2 2s2 2px2 2py

2 2pz2 3s2 3px

1

3py13pz

1

Hund’s Rule of Maximum Multiplicity

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Shapes S of orbital's s orbital's are non-directional and spherically symmetrical, This means that the probability of finding the electron is same in all directions at a particular distance from the nucleus, The 1s orbital is shown in the figure

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Shape of p orbitalsFor p-orbitals (l=1), there are three possible orientations corresponding to m = -1, 0, +1 values. This means that there are three p - orbitals in each p-subshell. These are designated as px, py and pz; For e.g., 2px, 2py and 2pz.

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For d-orbital (l = 2), there are five possible orientations corresponding to m = - 2, -1, 0, + 1, +2. This means that there are five orbitals in each d-subshell. For 3d subshell, these are designated as 3dxy, 3dyz, 3dxz, 3dx2- y2 and 3dz2. These five orbitals are equal in energy but differ in their orientations. The shapes of 3d orbitals are shown in the figure

Shape of d orbitals

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Shape of f orbital's