What would the calculation of energy En (in electron volts) of a hydrogen atom's electron with n=5 ?

Answer 1

Supposing that you don't want to solve Schroedingers equation the formula for the energy is:

E_n = Z^2 e^4 m_e / (8 h^2 epsilon_0^2 n^2)

with Z = charge number (1 for Hydrogen), e the charge of an electron, m_e = the mass of an electron, h = Planck constant, epsilon_0 the permittivity of the vacuum.

Filling in all constants and converting everything to electron-volts you end with the handy formula

E_n = 13.6 eV / n^2 = 0.544 eV

Answer 2

According to Neils bohr the mass structure of the Electron is constant . If he was correct then the Energy content of the electron is the constant mass of the electron multiplied by the speed of light square.E=Me x C^2.
This is where Einstein and quantum mechanics disagreed. According to Einstein the Greater the mass of the electron the greater energy the electron would have.That means that Bohr's Hydrogen atom was really subject to mass increase and decrease.And this is where Heisenberg found an uncertainty.So the Uncertainty principle of the electron energy indicated that we can only guess on what the Energy of the electron is at a certain position in the Atom. Hence the Answer to the question is that the electrons energy inside an atom is not exactly determinable.

Answer 3

En = E1 / n^2
for Hydrogen E1 = -13.6 eV
so E5 = -13.6/25 = -0.544 eV