Atomic emission spectra , Bohr’s atomic theory & Wave mechanical theory of the atom

On heating atoms of a pure elements – in gaseous or vapor state – to a high temperature or exposing them to a low pressure in an electrical discharge tube , they emit a radiation called emission spectrum ( line spectrum ) .

Atomic emission spectra

On examining this radiant light by a device called spectroscope , it was found that it is composed of a limited number of restricted colored lines separated by dark areas , So , it is called line spectrum , It is worth mentioning that the physicists – at that time – were not able to explain this phenomenon .

Line spectrum is a type of spectrum composed of a small number of restricted coloured lines separated by dark areas , The radiant light is named as line spectrum , because it is composed of a limited number of restricted coloured lines which are separated by dark areas .

Application : The line spectrum of hydrogen atom appears ( on examining ) as four coloured lines separated by dark areas , It was found experimentally that the spectral lines are essential characteristics for each element , because there are no two elements have the same spectral lines .

Bohr's atomic theory

Bohr’s atomic theory

Bohr’s atomic model ( 1913 )

The study of atomic spectra is considered the key which solved the puzzle of the atomic structure , That was the work of the Danish scientist Niels Bohr upon which he was rewarded the Nobel Prize in 1922 .

Bohr’s Postulates

Points that agree with Rutherford’s postulates 

  1. A positively charged nucleus exists in the center of the atom .
  2. The number of negative electrons ( revolving around the nucleus ) equals the number of positive protons inside the nucleus .
  3. During the revolving of the electron around the nucleus , a centrifugal force arises which is equal to the attraction force of the nucleus on the electron .

New postulates

Electrons orbit the nucleus in a rapid movement without emission or absorption of any amount of energy and the atom in this case named stable atom .

Electrons orbit the nucleus in definite allowed energy levels , They can not be found at intermediate distances , at which electron moves from an energy level to another one via a complete jumping .

Each electron in the atom has a definite amount of energy depending on the distance between its energy level and the nucleus , the energy of any level increases as its radius increases , Each energy level expressed by a whole number called the principal quantum number ( n ) .

When the electron acquires a quantity of energy – known as quantum – by heating or by electric discharge , the electron jumps temporarily to a higher energy level , This is in case that the absorbed quantum of energy is equal to the difference in energies between the two levels , and the atom is known as excited atom .

Since the electron in the excited atom is unstable , it returns back to its original level with emission of the same quantum of energy ( emission spectrum ) in the form of radiant light that appears in the form of characteristic spectral line of a certain wavelength and frequency .

Quantum is the amount of energy absorbed or emitted , when an electron is transferred ( jumps ) from an energy level to another , Excited atom is an atom acquired an amount of energy by heating or by electric discharge . 

The multitude of atoms absorb different amounts of energy , then radiate their energies producing spectral lines , These spectral lines correspond to the energy levels from which their electrons are transmitted back to the ground state .

The spectral line of the hydrogen atom does not represent the electron transferring from :

  • The different energy levels to the first energy level , because the wavelength of the emitted ray from the excited electron is located in the invisible region of the ultraviolet rays .
  • The seventh energy level to the second energy level , because the wavelength of the emitted ray from the excited electron is located in the invisible region of the infrared rays .

The quantum of energy required to transfer an electron between the different energy levels is not equal , One quantum is the energy difference between the two energy levels .

It is impossible for an electron to move from its energy level to another , if the energy absorbed or emitted is less than one quantum , ( there is a half quantum for instance ) .

The quantum of energy required to transfer an electron between the different energy levels is not equal , because the distance and the difference in energy between them are not equal .

The quantum of energy required to transfer an electron from an energy level to another decreases as we go further from the nucleus , Because the energy gap decreases , as we go further from the nucleus .

Advantages & disadvantages of Bohr’s atomic model 

Despite of the great effort of Bohr to construct his atomic model , the quantitative calculations of his theory did not agree with all the experimental results .

Advantages ( success ) of Bohr’s atomic model :

  1. It explained the hydrogen atom spectrum .
  2. It introduced the idea of quantized energy to determine the electron energy in different energy levels in the atom .
Inadequacies of Bohr’s atomic model 

The most important defects of Bohr’s theory :

  1. It failed to explain the spectrum of any other element , except hydrogen atom , as it is considered the simplest electronic system which contains one electron only , even that of the helium atom contain only 2 electrons .
  2. It considered the electron as a negative charged particle only and ignored its wave properties .
  3. It postulated that it is possible to determine precisely both of the location and speed of an electron at the same time , but in fact this is experimentally impossible .
  4. It described the electron as a particle moving in a circular planar orbit , this means that hydrogen atom is planar , In fact , hydrogen atom has a spherical shape ( three dimensional coordinates ) .
Principle of modern atomic theory ( modification of Bohr’s model ) :

The most important modifications are the following : 

  1. The dual nature of electron .
  2. The Heisenberg uncertainty principle .
  3. The wave-mechanical theory of the atom .
Dual nature of electron 

The electron is a material particle which has wave properties : All the previously mentioned theories considered the electron just as a minute negatively charged particle , However , all experimental data showed that the electron has a dual nature , as it is a material particle which also has wave properties .

Heisenberg uncertainty principle

Bohr’s theory postulated that it is possible to determine both of the location and velocity of the electron precisely at the same time , but by applying the principles of quantum mechanics , Heisenberg concluded that the determination of both the velocity and position of an electron at the same time is practically impossible , So , to speak in terms of probability seems to be more precise , This is because the electron wave motion does not have a certain location .

Heisenberg uncertainty principle : The determination of both the velocity and position of an electron at the same time is practically impossible and this is subjected to the laws of probability .

Wave-mechanical theory of the atom

The Austrian scientist Schrodinger ( 1926 ) applied the idea of Plank , Einstein , De Broglie and Heisenberg and could to :

  • Establish the wave-mechanical theory of the atom .
  • Derive a wave equation that could describe the electron wave motion in the atom .

On solving Schrodinger’s equation , it is possible to :

  1. Determine the allowed energy levels .
  2. Define the regions of space around the nucleus , where it is most probable to find the electron in each energy level .

The wave-mechanical theory changed our concept about the movement of the electron , where instead of speaking about the stable circular orbits as being completely forbidden for the electrons , the concept of the electron cloud is used to express the region of space around the nucleus .

The electron cloud is the region of space around the nucleus , in which the electron probable exists in all directions & distances ( dimensions ) , There are regions inside the electron cloud in which probability of finding the electron increases , each of them is termed by the orbital , Orbital is the region within the electron cloud of high probability of finding the electron .

Atoms components , Rutherford and Bohr’s Atomic Models

Evolution concept of the atomic structure , Atomic theory & Properties of cathode rays

The quantum numbers and principles of distributing electrons

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