# Which of the following sets of quantum numbers is correct for an electron in $\dpi{100} 4f$ orbital?                 Option 1) $n=4,l=3,m=+4,s=+\frac{1}{2}$ Option 2) $n=4,l=4,m=-4,s=-\frac{1}{2}$ Option 3) $n=4,l=3,m=+1,s=+\frac{1}{2}$ Option 4) $n=3,l=2,m=-2,s=+\frac{1}{2}$

As we learnt in

Principal Quantum Number (n) -

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

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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)

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Magnetic Quantum Number (m) -

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

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

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Spin Quantum Number (s) -

It has two values +1/2 and -1/2

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For $4f\: orbital \: electrons,\: n=4$

$l=3\left ( because\: 0\: 1\: 2\: 3\: \right )$

$m= +3,+2,+1,0,-1,-2,-3$

$s= \pm 1/2$

Option 1)

$n=4,l=3,m=+4,s=+\frac{1}{2}$

Incorrect option

Option 2)

$n=4,l=4,m=-4,s=-\frac{1}{2}$

Incorrect option

Option 3)

$n=4,l=3,m=+1,s=+\frac{1}{2}$

Correct option

Option 4)

$n=3,l=2,m=-2,s=+\frac{1}{2}$

Incorrect option

N

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