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Quantum chemistry

Fundamentals of Quantum Chemistry
Michael Mueller
Rose-Hullman Institute of Technology

Terre Haute, Indiana(BOOK SUGGESTED)

Quantum chemistry is a branch of chemistry whose primary focus is the application of quantum mechanics in physical models and experiments of chemical systems. It is also called molecular quantum mechanics.


1) The number of radial nodes of 3s and 2p orbitals are respectively :

(IIT JEE 2005)
a) 2, 0 
b) 0, 2 
c) 1, 2 
d) 2, 11
Logic:
For a given orbital with principal quantum number, n and azimuthal quantum number, l
Number of radial nodes = (n - - 1)
Solution:
For 3s orbital: n = 3 and l = 0
Therefore, number of radial nodes = 3 - 0 - 1 = 2
For 2p orbital: n = 2 and l = 1
Therefore, number of radial nodes = 2 - 1 - 1 = 0



2) The radial probability distribution curve obtained for an orbital wave function (Ψ) has 3 peaks and 2 radial nodes. The valence electron of which one of the following metals does this wave function (Ψ) correspond to ?
 (Eamcet 2010-M)

a) Cu 
b) Li 
c) K 
d) Na 
Solution:
The orbital corresponding to valence electron and number of radial nodes for the given elements are shown below:
Element
Orbital corresponding to valence electron
Number of radial nodes
Cu
4s
4 - 0 - 1 = 3
Li
2s
2 - 0 - 1 = 1
K
4s
4 - 0 - 1 = 3
Na
3s
3 - 0 - 1 = 2
Only 3s orbital in Na contain 2 radial nodes.

3) The number of radial nodes present in the radial probability distribution curves for the orbital wave function with quantum number n=4, l=0 and m=0 is : 

(Eamcet - 2011-E) 
a) 4 
b) 3 
c) 2 
d) 1 

Solution:
 The number of radial nodes = (n - - 1) = 4 - 0 - 1 = 3
 Note: Do not confuse. No need of "m" value to get the number.

                                          DO IT YOURSELVES 
1) How many nodal planes are present in 2p, 3p and 4p orbitals?
2) Calculate the number of i) angular nodes ii) radial nodes and  iii) total number of nodes for 4f orbital.
3) Which node in the atomic orbital passes through the nucleus? 
4) Which atomic orbital has zero nodes?
author

DESH DEEPAK A P S CHAUHAN

M.Sc. CHEMISTRY!

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