Top 3 Atomic Models | Engineering

Various atomic models proposed by scientists over the 1st few decades are: 1. Thomson’s Plum Pudding Model (1911) 2. Rutherford’s Nuclear Model 3. Bohr’s Model.

1. Thomson’s Plum Pudding Model (1911):

Thomson visualised all of the positive charge of an atom as being spread out uniformly throughout a sphere about 10^-10 m in diameter, with the electrons as smaller particles distributed in shells. While the net force exerted by the positively charged sphere on each electron is toward the centre of the sphere, the electrons mutually repel each other and form shells. This atomic model was given up after sometime since it could not account for some observed phenomena.

This model could not explain the correlation of emission of frequencies of electrons in Thomson atom with the observed frequencies of light emitted by different substances. Also it could not explain the spectral series. Hence it ran into difficulties and rejected. Take the case of hydrogen with a single electron in its structure.

According to Thomson’s view regarding emission of light, hydrogen can provide only a single spectral line. This is contrary to the observed facts which indicate that in the hydrogen spectrum, there are several series with each series consisting of several discrete spectral lines. Although Thomson model represented a considerable progress towards the truth yet the experimental evidence failed to substantiate it.

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Further, it was completely given up, when it could not provide any satisfactory mechanism for explaining the large deflection suffered by Rutherford’s α-particles, scattering experiments. It was, therefore, abandoned and replaced by Rutherford’s Nuclear Atomic Model.

2. Rutherford’s Nuclear Model (1911):

This model was proposed by Rutherford in 1911. According to this an atom of a matter consists of a central positively charged nucleus of radius 10^-12 cm. It practically carries the whole mass of the atom. It is surrounded by ‘Planetary’ electrons of radius 10^-13cm at distances relatively greater as compared to the diameter of the electrons. The radius of the atom is 10^-8 cm. Thus the atom like the solar system is an exceedingly open structure and this is why it can be penetrated by high speed particles of various kinds.

This model has the following deficiencies:

Rutherford’s nuclear model assumed the electrons outside the nucleus, either to be stationary, or moving in a circle. Thus if electrons were stationary, they would have been attracted towards nucleus and would have fallen into the nucleus.

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On the other hand, have the electrons been moving in a circle, then according to electron magnetic theory the accelerated charge of electron would have continuously lost its energy and would have gone down into the nucleus. Thus the deficiencies of Rutherford’s nuclear model could be described as follows-

i. Theory could not explain the distribution of electrons in the orbit.

ii. The theory did not explain the stability of the atom as a whole.

3. Bohr’s Atomic Model (1913):

The drawbacks of Rutherford’s atomic model were overcome by Prof. Neil Bohr by applying Planck’s quantum theory as given below:

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I. The electron can revolve in certain orbits governed by the equation based on quantum theory without losing energy. These orbits are called stationary orbits. On addition of energy to the atom, the electron jumps to an orbit of higher energy.

On the other hand, when an electron jumps from higher energy to lower energy level, then excess energy is given out as one photon or a packet of light. The energy is hC / λ where h is Planck’s constant, C is the velocity of light and λ is the wavelength of light emitted.

II. As in the Rutherford’s model, the centripetal force due to the electrostatic attraction between the electron and the nucleus is equal to the centrifugal force of the electrons moving in circular orbits.

III. The angular momentum of the electron is equal to an integral multiple nh / 2π where n is an integer called quantum number.

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IV. The radius of the orbit is proportional to n² and the velocity of electron revolving in nucleus is inversely proportional to n (where n is the quantum number). These assumptions led to results which have been found correct on being tested. This has given birth to the Modern Quantum Theory of Atoms.

V. This model however, has the following deficiencies:

1. It applies to one electron atom, i.e., hydrogen atom and is not easily extended to describe more complicated atoms.

2. It speaks nothing about any rules or restrictions regarding electron transitions from one level to another.

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3. It introduces only one quantum number n whereas experimental evidence concerning fine structure of spectral lines suggests additional quantum numbers.

4. Quantitative explanation of chemical bonding cannot be explained by it.

a. Quantum Numbers:

The studies have revealed that four quantum numbers are necessary to fully explain the energy and location of electrons, in an atom.

These quantum numbers are enumerated and described below:

1. Principal quantum number (n).

2. Orbital or azimuthal quantum number (I).

3. Magnetic quantum number (m_i).

4. Spin quantum number (m_s).

1. Principal Quantum Number (n):

It gives the information about the main energy level to which an electron belongs. This number takes only the integral values, i.e., 1, 2, 3, 4, … and so on. Thus for first energy level n = 1, for second energy level n = 2 and so on.

2. Orbital or Azimuthal Quantum Number (l):

It gives the information about the shape of the sublevel of main energy level to which an electron belongs. This number also takes only the integral values. But its value depends upon n. For a particular value of n the different values of n range from 0 to n — 1. Thus for n = 4 the different values of I and 0, 1, 2 and 3.

3. Magnetic Quantum Number (m_l):

This quantum number gives the information about the orientation (or arrangement) of sublevel in space to which an electron belongs. Its values are determined by the value I and may range from – 1 → 0 → +1, i.e., a total of 2l + 1 values. Thus for I = 1 the different values of m_l are -1, 0 and + 1.

4. Spin Quantum Number (m_s):

This number gives the information about the spin of electrons about their own axis in the orbital, i.e., whether the spin is counter-clockwise or clockwise. There are only two possible values of m_s, i.e., + 1/2 and -1/2.

Calculations of Bohr’s Atomic Model:

(i) Radii of Orbits:

The above two equations (i) and (ii) concerning Bohr’s atomic model can be utilized in calculating the velocity and orbital frequency possessed by different electrons and also the radii of different orbits.

The stationary orbit having minimum energy of the electron is known as the ground orbit or state. The hydrogen atom in Bohr’s theory has the first stationary orbit as the ground orbit or state.

The values obtained from kinetic energy of gases and other methods agree remarkably well with this result. In the normal state, the electrons in case of hydrogen atom occupies the lowest of the permissible stationary orbits. From the equation (1) it is concluded that radii of the permitted orbits vary as the square of principal quantum number n.

Now for hydrogen atom-

r₁ = 0.53 x 10^-10m, r₂ = 2² x 0.53 x 10^-10 m = 2.12 x 10^-10 m

Further, the spacing between adjacent orbits (See Fig. 3) increases progressively. Since the spectral formula of hydrogen atom derived theoretically, agreed remarkably well with the observed spectral values, therefore, the explanation of hydrogen spectrum is responsible for success of Bohr’s theory.

(ii) Velocity of Revolving Electrons:

The velocity of a revolving electron as found from the above equation is-

(iii) Orbital Frequency:

The orbital rotational frequency of an electron is given by the relation-

(iv) Energy of Electron:

The orbital energy of the electron (E_n) = K.E. due to motion of the electron + P.E. (because the electron lies in the electric field of the positive nucleus).