The arrangement of orbitals on the basis of energy is based upon their (n+l ) value. Lower the value of (n+l ), lower is the energy. For orbitals having same values of (n+l), the orbital with a lower value of n will have lower energy.
I. Based upon the above information, arrange the following orbitals in the increasing order of energy
(a) 1s, 2s, 3s, 2p
(b) 4s, 3s, 3p, 4d
(c) 5p, 4d, 5d, 4f, 6s
(d) 5f, 6d, 7s, 7p
II. Based upon the above information, solve the questions given below :
(a) Which of the following orbitals has the lowest energy?
4d, 4f, 5s, 5p
(b) Which of the following orbitals has the highest energy?
5p, 5d, 5f, 6s, 6p
(a) the increasing order of energy of the given orbital is : 1s >2s >2p> 3s
(n+l) value of 1s orbital – 1 + 0 = 1
(n+l) value of 2s orbital – 2 + 0 = 2
(n+l) value of 2p orbital – 2+ 1 = 3
(n+l) value 3s orbital – 3 + 0 = 3, among 2p and 3s, 2p has lower value of n therefore it has lower energy than 3s.
(b) the increasing order of energy of the given orbital is : 3s<3p<4s<4d
(n+l) value of 3s: 3 + 0 = 3
(n+l) valueof 3p: 3+1 = 4
(n+l) value of 4s: 4 + 0 = 4
(n+l) value of 4d: 4 + 2 = 6
Among 3p and 4s both has same n+l value but 3p has lower n value hence, 3p<4s.
(c)the increasing order of energy of the given orbital is : 4d<5p<6s<4f<5d
(n+l) value of 4d : 4 + 2 = 6
(n+l) value of 4f : 4 + 3 = 7
(n+l) value 5p : 5 + 1 = 6
(n+l) value of 5d : 5 + 2 = 7
(n+l) value of 6s = 6 + 0 = 6
Among 4d, 5p and 6s the n value is greater in 5p and 6s which is the case for 4f and 5d also therefore despite of having equal (n + l )value .
(d)the increasing order of energy of the given orbital is: 7s<5f<6d<7p
(n+l) value of 5f : 5 + 3 = 8
(n+l) value of 6d : 6 + 2 = 8
(n+l) value of 7s : 7 + 0 = 7
(n+l) value of 7p : 7 + 1 = 8 , among 5f, 7s and 7p the energy order is in accordance with n values.
II. (a) among the orbitals, 5s has the lowest energy.
the (n+l) value for 5s is the lowest = 5 + 0 = 5. Other orbitals have (n+l )value more than 5 –
5p= 5 + 1 = 6 , 4f = 4 + 3 = 7 , 4d = 4 + 2 = 6.
(b) among the orbitals , 5f has the highest energy because the (n +l ) value - 5 + 3 = 8 is highest.
5d = 5 + 2 = 7 , 5p = 5 + 1= 6 , 6s =6 + 0 = 6 , 6p =6 + 1 = 7 .