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Atomic Structure: Definition, Short Question & Answer

 Question 1: Which quantum number is also called sub-shell quantum number?

Answer. The Azimuthal quantum number describes the shape of sub-shell, therefore it is  also called sub-shell quantum number. 

It is denoted by the symbol ' â„“ ', Its values are 0, 1, 2, 3.............. n-1. It means its values depends upon the n value. For n = 3, â„“  values are 0, 1,2.  For â„“  = 0,  sub-shell is s, for   â„“  = 1 subshell is p sub-shell and for  â„“  = 2, sub-shell is p.

 Question 2: What is difference between orbit and orbital?

   Answer


Question. What is the relationship between: a, energy and wavelength  b. frequency and wave length
Answer.
Energy and wavelength
The energy of radiation is inversely proportional to its wave length. 
Mathematically, 
E ∝ 1/λ 
E = hc/λ 
Where,
E = Energy of radiation
λ= Wave length of any light radiation
c = speed of light = 3×10 8 m/s
h = Plank's constant = 6.625 1034 Js
Frequency and wavelength
frequency of radiation is inversely related to  its wavelength 
Mathematically, 

ν ∝ 1/λ 
ν = c/λ 
Where,
ν = frequency of radiation
λ= Wave length of any light radiation
c = speed of light = 3×10 8 m/s

Question: Hydrogen atom and He+ are mono electron system, but the size of He+ is much smaller than H, why?
Answer
Both hydrogen and He+ have only one electron in their valence shell. However, He+ has two protons in its nuclues while hydrogen has only one proton in its nucleus. Hence, nucleus of He+ attracts its one electron  towards itself with much greater force than that of hydrogen. So, electron in He+ becomes relatively closer to the nucleus and size of He+ is much smaller.
OR 
According to Bohr radius,

From equations i and ii, it is clear that size of He+ is smaller than H.

Question: Why is 4s orbital lower in energy than 3d orbital?
Answer.
According to n + â„“ rule,  relative energy of orbitals can be decided from calculating their  n + â„“ values.
The orbital with  lower n + â„“  value will have lower energy than orbital with higher n + â„“ value. Therefore, 4s orbital is lower in energy because its n + â„“  is 4 (i.e, n = 4, â„“ = 0) while 3d orbital is higher in energy as its n + â„“  is 5 (i.e.,  n = 3, â„“ = 2).

Question: What is n + â„“ rule?
Answer. This rule states that, energy of orbitals can be decided from calculating their  n + â„“ values. The orbital with  lower n + â„“  value will have lower energy than orbital with higher n + â„“ value. For example
4s orbital is lower in energy because its n + â„“  is 4 (i.e, n = 4, â„“ = 0) while 3d orbital is higher in energy as its n + â„“  is 5 (i.e.,  n = 3, â„“ = 2).
However, if two orbitals have same  n + â„“  value, then orbital with lower n value will be lower in energy.
For example,  3d orbital lower in energy than 4p orbital because n value of 3d is lower although both have same n + â„“ value. i.e., 

For 3d orbital, n =3 and â„“ = 2 , n + â„“ = 3 + 2 = 5 ( lower in energy)
For 4p orbital, n =4 and â„“ = 1 , n + â„“ = 4 + 1 = 5  ( higher in energy)
 

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