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Quantum mechanical model of the atom

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By Expert Faculty of Sri Chaitanya
Question

The wave function ψn,l,ml is a mathematical function whose value depends upon spherical polar coordinates (r,θ,ϕ) of the electron and characterized by the quantum numbers n, l and ml. Here r is distance from nucleus, θ  is colatitude and ϕ is azimuth. In the mathematical functions given in the Table, Z is atomic number and a0 is Bohr radius.

Column 1Column 2Column3
(I) Is orbital (i)  ψn,l,mi αZa032ezra0

(P) 

 

(II) 2S  orbital(ii) one radial node 

(Q) Probability density  at nucleusα1a03

 

(III) 2Pz orbital(iii) ψn,l,mjαZa052reZr2a0COSθ(R) Probability density is maximum at nucleus
(IV) 3dz2 orbital(iv) xy-plane is a nodal plane(S) Energy needed to excite electron from n=2 state to n= 4 state is 2732 times the energy needed to excite electron from n=2 state to n=6 state

For hydrogen atom, the only CORRECT combination is 

Difficult
Solution

1s ® 0  radial  nodes , no angular  component (Þ no cos q)

2s ®1 radial node, , no angular  component (Þ no cos q)

2pz 0 radial node, angular component is present (Þ no cos q)

3dz2 0 radial node, angular component is present (Þ no cos q)

a) 2s ®1radial node / coloumn(2) (i)  no radial node  Þ  wrong

b) 1s ®no node plane  Þ wrong

c) 1s ® no  radial node  Þ coloumn (3) ‘p’ ® 1 radial node Þ  wrong

d) correct


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