Numericals of Quantum Numbers-

Quantum number

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Quantum numbers

Question1: What is value of Principal & Azimuthal Quantum Number of e’s of 3d subshell.

Ans.     n=3, l=2

Question2. What is the subshell of electron with quantum numbers-

n=4,     l=3,      m=0,    s=-1/2

Ans.     4f

Question3.Which set the quantum number is not possible?

n          l           m         s

(a)        3          2          -2         +1/2

(b)        4          0          0          -1/2

(c)        3          2          -3         +1/2

(d)       5          3          0          -1/2

Ans.     (c) is not possible because if l=2 then values of m= -2,-1,0,+1, +2

Question4 . Which set the quantum number is not possible?

1. a) n=1,     l=1,     m=1,    s=+1/2
2. b) n=1,     l=0       m=1,    s=+1/2
3. c) n=1,     l=0,      m=0,    s=-1/2
4. d) n=2,     l=0       m=0     s=+1/2

Ans.     (a)& (b) are not possible because, n=1, then l=0 to (n-1)

so if n=1, then l=0

if l=0, then m= -l to +l including zero, if  l=0, m ≠ 1

Question 5. What is the maximum No. of Electrons present in the subshell for n=3,l=1.

Ans.     if n=3, l=1, then subshell is 3p.

p- subshell accommodate        6 electrons

Question. 6. How many orbitals are possible for n=3 ?

Ans.     If n=3, l=0,1,2 means s,p,d

s- subshell= One s-orbital

p-subshell = Three p-orbital

d-subshell = Five d-orbital

Thus for  n = 3 , the possible no. of orbitals = 1+3+5 = 9

The possible no. of orbitals = 9

Question7. Write the possible values of l, m & s  for the Principal Q. No. n=1

Ans.     If n=1 then values of  l=0 to (n-1)

l=0

for l=0, m=0

for m=0, values of s=+1/2 & -1/2

n=1, l=0, m=0, s=+1/2 & -1/2

Question 8 . Write the values of  l & m for n=2

Ans.     If n=2, l=0 to (n-1)

Hence , l = 0,1

Values of m= -l to +l including zero.

for l=0, m=0

l=1, m=-1,0,+1

Question 9. Write the value of  m  for l=3

Ans.     Values of m= – l to +l including zero

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

Question 10 . Write the values of  l & m for n= 3

Ans.     n=3, l=0,1,2

If l=0, m=0

l=1, m=-1,0,+1

l=2, m=-2,-1,0,+1,+2

Question 11. Write all the possible values of  l, m & s for n=3

Ans.             n =3 , l=0,1,2

  If l= 0 (s-subshell) , Value of m= 0  , value of s = ±1/2

  If l=1 (p-subshell)  , Value of m =  -1  ,0,+1 , value of s = ±1/2 for each value of m

  If l = 2(d-subshell) , Value of m =  -2 ,-1,0,+1,+2  , value of s= ±1/2 for each value of m

Question 12. Calculate maximum Number of e’s in n=4

Total electrons = 2+6+10+14=32

Question 13. What information does 3d⁵ give about Q. No.?

Ans.     for 3d⁵

n=3, l=2 and five electrons are present in d-subshell

Question 14.What information does 2s² give about Q. No.?

Ans.     for 2s²

n=2, l=0 and two electrons are present in s-subshell

Question15 .Write the values of n & l for the following subshell

a) 3s (b) 5p (c) 4d,  (d) 4f

Ans.     (a) for 3s: n=3, l=0

(b) for 5p : n=5, l=1

(c) for 4d : n=4, l=2

(d) for 4f : n=4, l=3

Question16.Write the values of four Q. Numbers for all the 2s² electrons

Ans.     For 2s electrons:

for First  e       n=2,     l=0,      m=0,    s=+1/2

for second e    n=2,     l=0,      m=0,    s=-1/2

Question 17.Write the values of four Q. Nos. for all the 3p⁶ electrons

Ans.

Electrons      1,4   2,5    3,6

for First e        :           n=3,     l=1,      m=-1, s=+1/2

for Second e    :           n=3,     l=1,      m=0,    s=+1/2

for Third e       :           n=3,     l=1,      m=+1, s=+1/2

for Fourth        :           n=3,     l=1,      m=-1,   s=-1/2

for fifth e        :           n=3,     l=1,      m=0,    s=-1/2

for sixth e        :           n=3,     l=1,      m=+1, s=-1/2

Question 18. Write the Q. Nos. for the electron of highest energy in calcium & sodium.

Ans.     ₂₀Ca : 1s², 2s², 2p⁶, 3s², 3p⁶, 4s²

Highest energy electron in Ca is 4s²

n= 4,     l= 0,      m= 0,    s= -1/2

₁₁Na : 1s², 2s², 2p⁶, 3s¹

Highest Energy electron in Na is 3s¹

n= 3,     l= 0,      m= 0,    s = +1/2

Question 19.Write all the four Q. Nos. of 5^th electron of 3d¹⁰

Ans.

n=3,     l=2,      m=+2,  s=+1/2

Question 20 . Write all the four Q. Nos. of 10^th & 20^th electron of Ca .

Ans.     20^Ca– 1s², 2s², 2p⁶, 3s², 3p⁶, 4s²

10^th electron is last electron of  2p⁶

n= 2,     l= 1,     m= +1,  s= -1/2

20^th electron  is 4s² ,

n=4,     l=0,      m=0,    s=-1/2

Question 21. Write all the four Q. Nos. of all the electrons present in the d-orbitals of 24^Cr.

Ans.     1s², 2s², 2p⁶, 3s², 3p⁶, 4s¹, 3d⁵

for 3d¹ electron           :           n= 3,     l= 2,      m= -2,               s = +1/2

for 3d² electron          :           n= 3,     l= 2,      m= -1,               s = +1/2

for 3d³ electron          :           n= 3,     l = 2,     m= 0,                s = +1/2

for 3d⁴ electron          :           n= 3,     l = 2,    m = +1,              s=+1/2

for 3d⁵ electron          :           n= 3,     l = 2,    m = +2,              s=+1/2

Question 22. How are the following subshell represented?

a) n =2, l= 1,  b) n = 4, l = 3,                 c) n=3, l=2                   d) n= 5, l= 0

Ans.

a)  n=2      Second shell                          b)   n=4, Fourth shell

 l = 1       p-subshell                               l =3 means f-subshell

subshell    = 2p                                            subshell    =  4f

c) n= 3,     l= 2                                         d)    n= 5,  l= 0

l=2 means        d-subshell                             l= 0 means s-subshell

subshell    = 3d                                           subshell  = 5s