Quantum mechanical model of atom and quantum number

DAY 5 
2.5.20

GOOD MORNING, 

Today we will study about quantum mechanical model of atom and Quantum numbers through blog .
today you have a google meet scheduled at 11am the meeting id would be shared on the class group.

Learning outcomes :
student will be able to 

• understand quantum mechanical model of atom
• Define orbital and Quantum Numbers.
• Determine values of quantum number for  various electrons

  Classical mechanics : 
It  ignores the concept of dual behaviour of matter especially for sub-atomic particles and the Heisenberg’s uncertainty principle.

Quantum mechanics

It is a theoretical science that deals with the study of the motions of the microscopic objects that have both observable wave like and particle like properties.
Quantum mechanics is based on a fundamental equation which is called Schrodinger equation.

Here E is actually the quantised value of energy which an electron in an atom has and psi represent the wave function.

Physical significance of wavefunction: 

Probability density :  ψ gives us the amplitude of wave. The value of ψ has no physical significance.  Ψ² gives us the region in which the probability of finding an electron is maximum. It is called probability density.

Orbital: The region of space around the nucleus where the probability of finding an electron is maximum is called an orbital.

Features of quantum mechanical model:

1. The energy of an electron is quantized i.e. an electron can only have certain specific values of energy.

2. The quantized energy of an electron is the allowed solution of the Schrödinger wave equation and it is the result of wave like properties of electron.

3. probability of finding an electron at a position can be determined and it is |ψ|2 at that point where ψ represents the wave-function of that electron.

4. An atomic orbital is the wave-function (ψ) of an electron in an atom. All the information about the electron in an atom is stored in its orbital wave function ψ and quantum mechanics makes it possible to extract this information out of ψ.

5. The probability of finding an electron at a point within an atom is proportional to the square of the orbital wave function i.e., | ψ |2 at that point. | ψ |2 is known as probability density and is always positive.

Quantum numbers:

There are a set of four quantum numbers which specify the energy, size, shape and orientation of an orbital.

(i) Principal quantum number (n):

• It identifies shell, determines sizes and energy of orbitals.

n	1	2	3	4
Shell	K	L	M	N
Total number of orbitals in a shell = n2	1	4	9	16
Maximum number of electrons in a shell = 2n2	2	8	18	32

(ii) Azimuthal quantum number (l): 

• It is also known as orbital angular momentum or subsidiary quantum number.
• It identifies sub-shell, determines the shape of orbitals, energy of orbitals and orbital angular momentum of an electron, which is given as,

          

•  The number of orbitals in a subshell = 2l + 1.
• For a given value of n, l can have n values ranging from 0 to n – 1, that is, for a given value of n, the possible value of l are : l = 0, 1, 2, .......... (n–1)

n	l	Subshell Notation	n	l	Subshell Notation
1	0	1s	4	0	4s
2	0	2s	4	1	4p
2	1	2p	4	2	4d
3	0	3s	4	3	4f
3	1	3p
3	2	3d

(iii) Magnetic quantum number (m_l): 

• It is also known as magnetic orbital quantum number.
• It gives information about the spatial orientation of the orbital.
• Number of orbitals in each subshell = 2l+1. i.e., for each value of l, ml = – l, – (l –1), – (l–2)... 0,1...(l – 2), (l–1), l

(iv) Electron spin quantum number (m_s):

• It refers to orientation of the spin of the electron.
• It can have two values +1/2 and −1/2. +1/2 identifies the clockwisespin and −1/2 identifies the anti- clockwise spin

THATS ALL FOR THE DAY.

MARK YOUR ATTENDANCE IN FORM AS WELL AS COMMENT SECTION OF BLOG.