ATOMIC STRUCTURE
Dalton’s Theory of Atom
John Dalton developed his atomic theory. According to this theory the Atom is considered to be hard, dense and smallest particle of matter, which is indivisible, the atoms belonging to a particular element, is unique. The properties of elements differ because of the uniqueness of the atoms belonging to particular elements. This theory provides a satisfactory basis for the laws of chemical combination. The atom can neither be created nor be destroyed i.e., it is indestructible.
Drawbacks: It fails to explain why atoms of different kinds should differ in mass and valency etc.
Sub-Atomic Particles: The discovery of various sub-atomic particles like electrons, protons etc. during late 19^{th} century led to the ideal that the atom was no longer an indivisible and the smallest particle of the matter.
Characteristics of the three fundamental particles are:
| Electron | Proton | Neutron |
Symbol | e or e^{–1} | P | n |
Approximate relative mass | 1/1836 | 1 | 1 |
Approximate relative charge | –1 | +1 | No charge |
Mass in kg | 9.109 × 10^{–31} | 1.673 × 10^{–27} | 1.675 × 10^{–27} |
Mass in amu | 5.485 × 10^{–4} | 1.007 | 1.008 |
Actual charge (coulomb) | 1.602 × 10^{–19} | 1.602 × 10^{–19} | 0 |
Actual charge (e.s.u.) | 4.8 × 10^{–10} | 4.8 × 10^{–10} | 0 |
The atomic mass unit (amu) is 1/12 of the mass of an individual atom of _{6}C^{12}, i.e., 1.660 × 10h – 27 kg. The neutron and proton have approximately equal masses of 1 amu and the electron is about 1836 times lighter. Its mass can sometimes be neglected as an approximation.
The electron and proton have equal, but opposite, electric charge while the neutron is not charged.
Models of Atom
Thomson’s Model: Putting together all the facts known at that time, Thomson assumed that an atom is a sphere of positive charges uniformly distributed, with the electrons scattered as points throughout the sphere. This was known as plum-pudding model at that time. However this ideal was dropped due to the success of a-particle scattering experiments studied by Rutherford and Mardson.
Rutherford’s Model: a-particle emitted by radioactive substance were shown to be dipositive Helium ions (He^{++}) having a mass of 4 units and 2 units of positive charge.
Rutherford allowed a narrow beam of α-particles to fall on a very thin gold foil of thickness of the order of 4 × 10^{–4} cm and determined the subsequent path of these particles with the help of a zinc sulphide fluorescent screen. This zinc sulphide screen gives off a visible flash of light when struck by an α-particle, as ZnS has the remarkable property of converting kinetic energy of particle into visible light.
Observation:
Conclusion:
Drawbacks of Rutherford’s Atomic Model
It was calculated that electron should fall into the nucleus in less than 10^{–8} sec. But it is known that electrons keep moving outsided the nucleus.
To solve this problem Neils Bohr proposed an improved form of Rutherford’s atomic model.
Before going into the details of Neils Bohr model we would like to inctroduce you some important atomic terms.
Atomic Structure:
If the atom gains energy the electron passes from a lower energy level to a higher energy level, energy is absorbed that means a specific wave length is absorbed. Consequently, a dark line will appear in the spectrum. This dark line constitutes the absorption spectrum.
Hydrogen atom: If an electric discharge is passed through hydrogen gas taken in a discharge tube under low pressure, and the emitted radiation is analyzed with the help of spectrograph, it is found to consist of a series of sharp lines in the UV, visible and Ir regions. This series of lines is knows as line or atomic spectrum of hydrogen. The lines in the visible region can be directly seen on the photographic film.
Each line of the spectrum corresponds to a light of definite wavelength. The entire spectrum consists of six series of lines each, known after their discoverer as the Balmer, Paschen, Lyman, Brackett, Pfund and Humphrey series. The wavelength of all these series can be expressed by a single formula.
= wave number
l = wave length
R = Rydberg constant (109678 cm^{–1})
n_{1} and n_{2} have integral values as follows
Series | n_{1} | n_{2} | Main spectral lines |
Lyman | 1 | 2, 3, 4, etc. | Ultra-vio |
Balmer | 2 | 3, 4, 5, etc. | Visible |
Paschen | 3 | 4, 5, 6, etc. | Infra-red |
Brackett | 4 | 5, 6, 7, etc. | Infra-red |
Pfund | 5 | 6, 7, 8, etc. | Infra-red |
Types of emission spectra
Planck’s Quantum Theory
When a black body is heated, it emits thermal radiations of different radiations of different wavelengths or frequency. To explain these radiations, Max Planck put forward a theory known as Planck’s theory. The main points of quantum theory are:
Bohr’s Atomic Model
Bohr developed a model for hydrogen and hydrogen like atoms one-electron species (hydrogenic species). He applied quantum theory in considering the energy of an electron bond to the nucleus.
Important postulates: An atom consists of a dense nucleus situated at the center with the electron revolving around it in circular orbitals without emitting any energy. The force of attraction between the nucleus and an electron is equal to the centrifugal force of the moving electron.
Of the finite number of circular orbits possible around the nucleus, the electron can revolve only in those orbits whose angular momentum (mvr) is an integral multiple of factor h/2p.
Where, m = mass of the electron
v = velocity of the electron
n = orbit number on which electron is present
r = radius of the orbit
As long as an electron is revolving in a orbit it neither loses nor gains energy. Hence these orbits are called stationary states. Each stationary state is associated with a definite amount of energy and it is also known as energy levels. The greater the distance of the energy level form the nucleus, the more is the energy associated with it. The different energy levels are numbered as 1, 2, 3, 4 (from nucleus onwards) or K, L, M, N etc.
Ordinarily an electron continues to move in a particular stationary state without losing energy. Such a stable state of the atom is called as ground state or normal state.
If energy is supplied to an electron, it may jump (excite) instantaneously from lower energy (say 1) to higher energy level (say 2, 3, 4, etc) by absorbing one quantum of energy. This new state of electron is called as excited state. The quantum of energy absorbed is equal to the difference in energies of the two concerned levels. Since the excited state is less stable, atom will lose it’s energy and come back to the ground state.
Energy absorbed or released in an electron jump, (ΔE) is given by
ΔE = E_{2} – E_{1} = hv
Where E_{2} and E_{1} are the energies of the electron in the first and second energy levels, and v is the frequency of radiation absorbed or emitted.
Merits of Bohr’s theory:
Limitations of Bohr’s Theory
By Bohr’s theory
Coulombic force =
(where ε_{0} is permittivity of free space)
K = 9 × 10^{9} Nm^{2}C^{–2}
In C.G.S units, value of K = 1 dyne cm^{2} (esu)^{–2}
The centrifugal force acting on the electron is
Since the electrostatic force balance the centrifugal force, for the stable electron orbit.
...............(i)
...............(ii)
According to Bohr’s postulate of angular momentum quantization, we have
............ (iii)
Equating (ii) and (iii)
Solving for r we get r =
Where n = 1, 2, 3, ………….∞
Hence only certain orbits whose radii are given by the above equation are available for the electron. The greater the value of n, i.e., farther the level from the nucleus the greater is the radius.
The radius of the smallest orbit (n = 1) for hydrogen atom (Z = 1) is
r_{0} = 0.529 Å
Radius of nth orbit for an atom with atomic number Z is simply written as
Illustration: Calculate the ratio of the radius of Li^{+2} ion in 3^{rd} energy level to that of He^{+} ion in 2^{nd} energy level:
Solution:
n_{1} = 3
n_{2} = 3
z_{1} = 3 (for Li^{2+})
z_{2} = 2 (for He^{+})
From equation (1) we known that
Substituting this in equation (4)
Total energy (e)
Substituting for r, gives us
E where n 1, 2, 3.........
This expression shows that only certain energies are allowed to the electron. Sin e this energy expression consists so many fundamental constant, we are giving you the following, simplified expressions.
E = erg per Atom
(1 eV = 3.83 × 10^{–23} Kcal)
(1 eV = 1.602 × 10^{–12} erg)
(1 eV = 1.602 × 10^{–19} J)
kcal/mole (1cal = 4.18 J)
The energies are negative since the energy of the electron in the atom is less than the energy of a free electron (i.e., the electron is at infinite distance from the nucleus) which is taken as zero. The lowest energy level of the atom corresponds to n = 1, and as the quantum number increases, E become less negative.
When n = ∞, E = 0 which corresponds to an ionized atom i.e., the electron and nucleus are infinitely separated.
We know that, mvr =
By substituting for r we are getting
Where excepting n and z all are constant, v =
Further application of Bohr’s work was made, to other one electron species (Hydrogenic ion) such as He^{+} and Li^{2+}. In each case of this kind, Bohr’s prediction of the spectrum was correct.