Question

prove that energy of shell increase by increasing number of shells​

Answer 1

Answer:

Total energy in negative is directly proportional to Z^2/n^2. Since PE is negative,it is actually directly proportional to n^2 (modulus is inversely proportional) Hence on increasing n,energy also increases.

Another method to look at it is the electrostatic force of attraction. Bohr's model concludes that the nucleus is a positive mass of charge attracting the electrons.As n increases the distance from the nucleus also increases,so the attraction becomes less,as the attraction is less according to F=-dU/dx, potential energy is more, and total energy is 1/2 of potential energy,so energy increases.