In a multi­-electron atom, which of the following orbitals described by the three quantum numbers will have the same energy in the absence of magnetic and electric fields?

(i)\; \; n=1,l=0,m=0

(ii)\: \: n=2,l=0,m=0

(iii)\: \: n=2,l=1,m=1

(vi)\: \: n=3,l=2,m=1

(v)\: \: n=3,l=2,m=0

 

  • Option 1)

    (i) and (ii)

  • Option 2)

    (ii) and (iii)

  • Option 3)

    (iii) and (iv)

  • Option 4)

    (iv) and (v)

 

Answers (2)

As we learnt in

Principal Quantum Number (n) -

 It is a positive integer with value of n = 1,2,3.......

-

 

 

Azimuthal Quantum Number(l) -

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)

-

 

 

Magnetic Quantum Number (m) -

 For any sub-shell (defined by ‘l ’value) 2\: l+1values of m are possible and these values are given by :

m = – l , – ( l –1), – ( l – 2)... 0,1... ( l – 2), ( l –1),l

-

 

 

 

Orbitals having same \left ( n+1 \right ) value in the absence of electric and magnetic field will have same energy.

 

In the given problem the n+l value is same for \left ( IV \right ) and \left ( V \right )

ie. 3 + 2=5


Option 1)

(i) and (ii)

Incorrect Option

Option 2)

(ii) and (iii)

Incorrect Option

Option 3)

(iii) and (iv)

Incorrect Option

Option 4)

(iv) and (v)

Correct Option

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