What will be the energy corresponding to the first excited state of a hydrogen atom if the potential energy of the atom is taken to be 10 eV when the electron is widely separated from the proton? Can we still write En = Ei/n2, or rn = a0 n2 ?

While deriving formula for energy for the Bohr’s Model of an atom, we take the potential energy to be zero when the electron and proton are far apart (infinite distance). But, here the potential energy is not zero; it is 10 eV.

So the formula of energy will be modified as,



where n= Principal Quantum Number.


For the first excited state, n=2. Therefore,



The formula of radius of orbit remains unchanged as it does not involve any concept of potential energy and can be derived just by taking into consideration the Quantization Rule and Coloumb's Law.


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