Md. Imran Nur ManikLecture

Department of PharmacyNorthern University

Bangladesh

Structure of Atom

1. All students-Describe the observations of Rutherford’s α—particle scattering experiment – 5.5

2. A. Even roll

• Define Band spectrum ---4.5

2. B. Odd roll

• Define Line spectrum - 4.5

Quick Quiz-Time 12 minutes

Hydrogen Spectrum (Origin of spectral line)• When an electric discharge is passed through gaseous hydrogen in a discharge tube, the

H2 molecules dissociate and produces hydrogen atoms. The energetically excited hydrogen atoms so produced, emit electromagnetic radiation of discrete frequencies.

• The hydrogen spectrum consists of several series of lines named after their discoverers. In 1885 on the basis of experimental observations Balmer showed that, if spectral lines are

expressed in terms of wavenumber ( ν ), then the visible lines of the hydrogen spectrum obey the following formula :

Where, n is an integer equal to or greater than 3 (i.e., n = 3,4,5,….)The series of lines described by this formula are called the Balmer series. The Balmer series of lines are the only lines in the hydrogen spectrum which appear in the visible region of the electromagnetic spectrum.

Lyman found a series of lines in the ultraviolet region of hydrogen spectrum. Later, three more scientists Paschen, Bracket and Pfund found three more series of lines in the infrared region of hydrogen spectrum which were named after them.

The Swedish spectroscopist, Johannes Rydberg, noted that all series of lines in the hydrogen spectrum could be described by the following expression :

Where, n1 = 1,2…….. n2 = n1 + 1

The value 109,677 cm-1 is called the Rydberg constant for hydrogen and the value of n1 is fixed for a particular series of lines.

The five series of lines that correspond to n1 = 1, 2, 3, 4, 5 are known as Lyman, Balmer, Paschen, Bracket and Pfund series, respectively. Table 2.3 shows these series of transitions in the hydrogen spectrum.

Fig .shows the Lyman, Balmer and Paschen series of transitions for hydrogen atom.

Of all the elements, hydrogen atom has the simplest line spectrum. Line spectrum becomes more and more complex for heavier atom. There are, however, certain features which are common to all line spectra

1. Line spectrum of an element is unique.

2. There is a regularity in the line spectrum of each element i.e. the radiations emitted from an atom have a fixed frequency and wavelength in the spectrum.

ProblemWhat are the frequency and wavelength of a radiation emitted during a transition from n = 5 state to the n = 2 state in the hydrogen atom?

Bohr’s Atomic Model

i) The electron in the hydrogen atom can move around the nucleus in a circular path of fixed radius and energy. These paths are called orbits, stationary states or allowed energy states. These orbits are arranged concentrically around the nucleus.

ii) The energy of an electron in the orbit does not change with time. However, the electron will move from a lower stationary state to a higher stationary state when required amount of energy is absorbed by the electron or energy is emitted when electron moves from higher stationary state to lower stationary state.

Neils Bohr (1913) was the first to explain quantitatively the general features of hydrogen atom structure and its spectrum. Bohr’s model for hydrogen atom is based on the following postulates:

iv) The angular momentum of an electron in a given stationary state can be expressed as in equation-

mevr = n.h/2π ————————————(2)

Thus, an electron can move only in those orbits for which its angular momentum is integral multiple of h/2π. That is why, only certain fixed orbits are allowed.

iii) The frequency of radiation absorbed or emitted when transition occurs between two stationary states that differ in energy by ΔE, is given by :

ΔE = (E2 – E1) = hν   ———————————(1)Where, E1 and E2 are the energies of the lower and higher allowed energy

states respectively. This expression is commonly known as Bohr’s frequency rule.

Reasons for the Failure of the Bohr Model

1. Bohr model can explain only hydrogen atom spectrum but it can’t explain the spectrum of atoms having several electrons.2. An electron is regarded as a charged particle moving in well defined circular orbits around the nucleus. But modern research reveals that electrons may revolve in elliptical orbits also.3. Further, an orbit is a clearly defined path and this path can be completely defined only if both the position and the velocity of the electron are known exactly at the same time. This is not possible according to the Heisenberg’s uncertainty principle. (its position and momentum cannot be precisely pinned down)

4. For the transformation of electrons from one energy level to another, only one line should be obtained in the spectrum. But after analyzing the spectrum, several fine lines are obtained. Bohr’s atomic model can’t explain these features.

Hydrogen energy levels

+1

34

Hydrogen energy levels

+

12

Orbit & OrbitalOrbit and orbital are not synonymous. Orbit : An orbit, as proposed by Bohr, is a circular

path around the nucleus in which an electron moves. Orbital: It is a region of space around the nucleus

where the probability of finding an electron is maximum.

Home work :Differentiate between orbit and orbital

Quantum Numbers A large number of orbitals are possible in an atom. Qualitatively these orbitals can be distinguished by their size, shape and orientation. An orbital of smaller size means there is more chance of finding the electron near the nucleus. Atomic orbitals are precisely distinguished by what are known as quantum numbers. Each orbital is designated by three quantum numbers labeled as n, l and m. Thus, the numbers which express the size, shapes, direction of the orbital from the nucleus and the spins of the electron on their own axis are called quantum numbers.

There are four types of quantum numbers.1. Principal quantum number2. Subsidiary quantum number or Azimuthal quantum number3. Magnetic quantum number4. Spin quantum number

1. Principle Quantum Number:This number expresses the orbits or principal energy levels in which the electron revolves round the nucleus. It is denoted by n ( n =1, 2, 3 etc). The value of ‘n’ represents the shells or energy levels. For the first shell, n =1, for the second shell, n = 2 and so on. Thus, with the increase in the value of ‘n’, the number of allowed orbit increases. Different values of n are represented by capital letters K, L, M, N, etc.

Principal quantum number n = 1 2 3 4 ………… Letter designation of Shell = K L M N …………

Principal quantum number represents any particular orbit. The value of n gives roughly the binding force and the distance between the nucleus & the electron and also the energy it possesses. The first energy level is the one nearest the nucleus. Consequently, it is strongly bound with nucleus and possesses the lowest energy.Size of a shell increases with increase of principal quantum number ‘n’. In other words, the electron will be located away from the nucleus with increase of principal quantum number . Maximum possible number of electrons in a shell is 2n2.

2. Azimuthal or Subsidiary Quantum Number:The main energy levels (or shells) of electron may be considered as being made up of one or more sub-levels (sub-shells). The quantum number which represents the existence of an electron in an sub-shell is called the subsidiary or Azimuthal quantum number. It is designated by the letter ‘l’.

It defines the three dimensional shape of the sub-shell. For a given value of n, l can have values ranging from 0 to (n – 1), that is, for a given value of n, the possible values of l are : l = 0, 1, 2, ………. (n-1)

For example, when n = 1, value of l is only 0. For n = 2, the possible values of l are 0 and 1. For n = 3, the possible values of l are 0, 1 and 2.

The number of sub-shells in a principal shell is equal to the value of n. For example in the first shell (n = 1), there is only one sub-shell which corresponds to l = 0.

For (n = 2), there are two sub-shells (l = 0, 1) in the second shell; for (n = 3) three (l = 0, 1, 2) in third shell and so on.

Sub-shells corresponding to different values of l are represented by the following symbols.Value for l : 0 1 2 3 ………… Notation for sub-shell : s p d f …………

Maximum number of electrons in a sub-shell is 2(2l+1). Where, l = 0,1,2,3…..etc. Example :If n = 7, what are the possible values of l?

Basic concept(read only)For example, for principal quantum number n = 1, the only possible value for

l is 0 i.e., there is only one possible subshell i.e. s-subshell (n = 1, l = 0). For n = 2, there are two possible values of l, l = 0 and l = 2 – 1 = 1. This means that there are two subshells in the second energy shell with n = 2. These subshells are designated as 2s and 2p. Similarly, when n = 3, l can have three values i.e. 0, 1 and 2. Thus there are three subshells in third energy shell with designations 3s, 3p and 3d respectively. For n = 4, there are four possible values of azimuthal quantum number l (= 0, 1, 2, and 3) each representing a different sublevel. In other words, the fourth energy level consists of four subshells which are designated as 4s, 4p, 4d and 4f. Thus for different values of principal quantum numbers we have

3s 3p 3d2s 2p

A Cross Section of an Atom

1s

n0

p+

The first ionization energy level has only one sublevel (1s). The second energy level has two sublevels (2s and 2p).The third energy level has three sublevels (3s, 3p, and 3d).

Although the diagram suggests that electrons travel in circular orbits, this is a simplification and is not actually the case.

Rings of Saturn

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The following table shows the permissible values of ‘l’ for a given principal quantum number and the corresponding sub-shell notation.

n l Sub-shell notation1 0 1s

2 0 2s

2 1 2p

3 0 3s

3 1 3p

3 2 3d

4 0 4s

4 1 4p

4 2 4d

4 3 4f

read onlyIt has seen that when an excited atom which gives a line emission spectrum is placed in a strong magnetic field, its spectral lines are further resolved into still thinner (i.e. closely spaced) lines. This type of splitting of spectral lines into a number of closely spaced lines has been explained by Linde who assumes that under the influence of magnetic field each sub-shell is further sub-divided into sub-shells, called orbitals which give the thinner lines in the spectrum. In order to represent these orbitals the first two quantum numbers viz, principal quantum number (a) and azimuthal quantum number (1) are not sufficient. Rather, a third quantum number which is called magnetic quantum number (m) is used to represent the orbitals of which a given sub-shell is composed.

3.Magnetic Quantum Number: The magnetic quantum number was introduced to explain the orientation of

orbitals in space particularly under the influence of an applied magnetic field. This is designated by ‘m’.

The magnetic quantum number  ‘m’ determines the number of orbitals and their orientation within a subshell. The permitted values of m are dependent upon l. For any sub-shell (defined by ‘l’ value), 2l+1 values of m are possible and they are from –l to +l including 0.

Thus, for l = 0, the only permitted value of m = 0, [2(0)+1 = 1, one s orbital]. For l = 1, m can be -1, 0 and +1 [2(1)+1 = 3, three p orbitals; the value of 2l+1

will be three and there will be three different orbitals. ]. For l = 2, m = -2, -1, 0, +1 and +2, [2(2)+1 = 5, five d orbitals]. Each orbital in an atom, therefore, is defined by a set of values for n, l and m.

An orbital described by the quantum numbers n = 2, l = 1, m = 0 is an orbital in the p sub-shell of the second shell.

The following chart gives the relation between the sub-shell and the number of orbitals associated with it.

Values of l 0 1 2 3 4 5

Sub-Shell Notation s p d f g h

Number of orbitals 1 3 5 7 9 11

Basic concept (read only)

We have seen that for s sub-shell l= 0. Now when I = 0, m = 0 (only one value). One value of m (= 0) for l= 0 (s sub-shell) implies that s sub-shell of any energy level has only one space orientation and hence can be arranged in space only in one way along x, y or z-axis. This means that for each value of principal quantum number ‘n’, there is only one orientation for l = 0 (s orbital) or there is only one s orbital.

Now when I = 1, m = 0, ±1 (Three values). Three values of m (= 0, ±1) for l= 1 (p subshell) imply that p sub-shell of any energy level (p sub-shell starts from 2nd energy level with n = 2) has three space orientations and hence can be arranged in space in three different ways along x, y and z axes Consequently p sub-shell is sub-divided into three orbitals which, on the basis of the orientation of their lobes of maximum electron density with respect to x, y and z axes, are designated as px (m = 0), py, (m = +1) and pz (m= —1).

read only• The two lobes of a p-orbital can be separated by a plane

which contains the nucleus and is perpendicular to the orbital axis. (See Fig. 2.13). The electron density (i.e. probability of finding the electron) at the nucleus as well as on the plane is zero. The nucleus at which the electron density is zero is called node and the plane passing through the orbital-axis (at this plane as well) the electron density is zero is called nodal plane.

4. Spin Quantum Number:

In 1925, George Uhlenbeck and Samuel Goudsmit proposed the presence of the fourth quantum number known as the spin quantum number (ms).

In other words, an electron has, besides charge and mass, intrinsic spin angular momentum. Spin angular momentum of the electron, a vector quantity, can have two orientations relative to the chosen axis. These two orientations are distinguished by the spin quantum numbers ms which can take the values of + or -. These are called the two spin states of the electron and are normally represented by two arrows, ↑ (spin up) and ↓ (spin down). Two electrons that have different ms values (one +1/2 and the other -1/2) are said to have opposite spins. An orbital cannot hold more than two electrons and these two electrons should have opposite spins.

The three quantum numbers are used to define its size/energy, shape and orientation. But all these quantum numbers are not enough to explain the line spectra observed in the case of multi-electron atoms, that is, some of the lines actually occur in doublets (two lines closely spaced), triplets (three lines, closely spaced) etc. This suggests the presence of a few more energy levels than predicted by the three quantum numbers.

Summary of Quantum NumbersTo sum up, the four quantum numbers provide the following information :1) ‘n’ defines the shell, determines the size of the orbital and also to a large

extent the energy of the orbital. There are n subshells in the nth shell. 2) ‘l’ identifies the subshell and determines the shape of the orbital. There

are (2l+1) orbitals of each type in a subshell, that is, one s orbital (l = 0), three p orbitals (l = 1) and five d orbitals (l = 2) per subshell. To some extent l also determines the energy of the orbital in a multi-electron atom.

3) ‘m’ designates the orientation of the orbital. For a given value of l, m has (2l+1) values, the same as the number of orbitals per subshell. It means that the number of orbitals is equal to the number of ways in which they are oriented.

4) ms refers to orientation of the spin of the electron.

Principal Quantum

number (n)

Subsidiary Quantum number (l)

l=o to n-1

Sub-levels Magnetic Quantum number (m)M=+l to –l including 0

Orbital number

1(K) 0 1s 0 1

2(L) 01

2s2p

0+1, 0, -1

13

3(M) 012

3s3p3d

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

135

4(N) 0123

4s4p4d4f

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

1357

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symmetry under 360 degree, 180 degree, and 120 degree rotations (m=1, 2, 3, respectively).