Atomic Structure Part -1

Properties of Canal Rays: 

• These rays produce fluorescence on the ZnS plate.
• They have low penetrating power but can ionize the gas.
• These rays produce reddish fluorescence while cathode rays produce greenish fluorescence.
• These rays deflected downward in the magnetic field.
• These rays contain protons only when hydrogen gas is used in the discharge tube and for other gasses, it contains positive ions.
• The e/m value of canal rays is 1836 times less than the e/m value of cathode rays.

Max Planck 1900 discover the particle behavior of light and according to him, energy travels in a discontinuous manner and in the form of energy packets called photons in the case of light. His formula is E=hc/λ where h is planked constant its value is 6.626x10^-34Js.

Concept of orbital:

            The volume of space around an atom in which the probability of finding electrons is 95% is called orbital. It can be basically the spread of charge around the nucleus or electronic cloud. It is different from the concept of orbit proposed by Bhor.

It is proposed by Schrodinger. We cannot find the exact location of an electron in the atom. The maximum probability of finding the electron is at a distance of 0.053nm. The electron is either closer or to the outside of the radius of 0.0529nm.

The space in which there is only a 5% probability of electron presence or a 95% probability of electron absence is called the nodal plane.

• In 1s orbital, there is no nodal plane.
• In 2s orbital, there is 1 nodal plane.
• In 3s orbital, there is 2 nodal plane.

Quantum Numbers:

There are four quantum numbers in an atom for the complete address of an electron.

Principal Quantum Number:

           The different energy levels in the Bhor model are represented by "n". These are principal Quantum numbers. Its value is non-zero and always starts from positive integers and up to infinity. These energy levels are denoted by K, L, M, N, etc. 

When n=1, it is k shell. When n=2, it is the L shell, when n=3, it is the M shell, and so on.

It tells the location of an electron in an atom. The distance of the electron from the nucleus or the radius of an atom can be determined by " n". 

    R=0.0529nm x n°2. 

It also determines the period number of an element.

It also determines the energy of the electron in the shell.            E=1313.31kj /n°2 

It is also the quantitative measure of the electronic shell.

The number of electrons in a shell is determined by the formula 2n°2.

Azimuthal Quantum Number:

It is represented by "l" is value always starts from 0.

 it is also called subsidiary or angular moment quantum number.  In defects of the Bhor model, when the spectrum is seen with high resolving power, the spectral lines are further split into serval tiny lines. So only one quantum number is insufficient to explain the electron position in an atom. Its value depends upon the value of n. It tells about the number of subshells in a shell. for k shell, the value of l is zero. For L shall the value of l is 1.  For M shell the value of l is 3 and so on. It also tells the shape of the subshell and the subshells are represented by s, p, d, f. These stand for sharp, principal, diffused, and fundamental respectively. These are the spectral terms used to describe the spectral series observed in the spectrum. The number of electrons in a subshell is determined by a formula 

2( 2 l+1). The value of l is always less than the value of n. It can never equal or be greater than the value of n. 

magnetic quantum number: 

             It is also called a special orientation number. It tells the number of orbitals in a subshell. The maximum number of electrons in an orbital is 2. It is represented by the alphabet "m". As the spectral lines separate further in the magnetic field as observed in the Zeeman effect. So the magnetic quantum number is used to describe this splitting. Its value may be zero, positive, or negative.  It tells the degeneracy of the subshell or the possible orientation of the orbital in three-dimensional space. The formula for the value of m is m= 2l+1. 

for the s sub-shell the value of l=0, so the m value is 1. So s subshell has only one space orientation in three-dimensional space.

for the p sub-shell the value of l=1, so the m value is 3. So p subshell has three space orientations in three-dimensional space.  

for the d sub-shell the value of l=2, so the m value is 5. So f subshell has five space orientations in three-dimensional space.

for the f sub-shell the value of l=3, so the m value is 7. So f subshell has seven space orientations in three-dimensional space.

The number of orbitals in a shell is determined by "n^2".orbitals

Spin Quantum Number:

                All alkali metals have one electron in their outermost shell. When their spectra were observed by high resolving power, each line consist of further two spectral lines. This is called doublet line strcture. These spectral lines are different from the fine spectrum of hydrogen as discussed in azimuthal quantum number. An electron while revolving in a shell also revolves on its own axis. This is called self-rotation. This spinning creates a magnetic field and in this way a magnetic moment. Electron revolves are either clockwise or anticlockwise. It is represented by "s". Its value is +1/2 or -1/2. 

 This quantum number is not derived by Schrodinger equation.

The value of the spin quantum number can never be the whole number for a single electron.

Bhors results also help us to know the relationship of the distance and the energy of the shell.

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