List these electron subshells in order of increasing energy. 6p , 7s , 6s , 4f note for advanced students: you may assume these subshells are all in an atom with many electrons, not a hydrogen atom.
The difference in energy of two subshells is decided by comparing their n+l value.
n = Principle Quantum Number (main Shell)
l = Azimuthal Quantum Number
The greater the n+l value the greater is the energy of subshell. Also, if two subshells have same n+l value, the the subshell with lower n value will be having lesser energy.
6p = 6 + 1 = 7
7s = 7 + 0 = 7
6s = 6 + 0 = 6
4f = 4 + 3 = 7
Hence, 6s has the lowest energy, among 6p, 7s and 4f (all having same n+l values) 4f has lowest energy compared to 6p and 7s as it has lowest n value. And 6p has less energy than 7s.
The increasing order of energy for the electron sub-shells are 5s 4d 5p 6s.
Using Nuclear Shell model and Aufbau principle, the orbitals are arranged in terms of increasing energy as follows. Even though 4d is in 4th shell compared to 5s in 5th shell, the energy level of 4d is more than in 5s because of the more number of electrons.
This is because of the aufbau rule of filling the lower n+l value orbital before filling the higher n+l orbitals. As the states are given as 4d and 5s, the n and l value for 4d is 4 and 2, respectively.
Similarly, the n and l value for 5s is 5 and 0. So the lower n+l state will be 5s and then 4d. Similarly, the states are followed by 5p and 6s. So the increasing order of energy for electron subshells are 5s 4d 5p 6s.