Question

Energy levels of hydrogen atom in terms of rydberg constant

Answer 1

The formula defining the energy levels of a Hydrogen atom are given by the equation: E = -E0/n2, where E0 = 13.6 eV (1 eV = 1.602×10-19 Joules) and n = 1,2,3… and so on. The energy is expressed as a negative number because it takes that much energy to unbind (ionize) the electron from the nucleus.

Answer 2

The Rydberg equation for absorption is

1/λ=R(1/n2i−1/n2f)

Where λis the wavelength of the absorbed photon, R is the Rydberg constant, ni denotes the energy level the electron started in and nfthe energy level it ends up in.

We are calculating ionisation energy so the electron goes to infinity with respect to the atom, ie it leaves the atom. Hence we set nf=∞.

Assuming we ionise from the ground state, we set ni=1

1/λ=R

E=hc/λ⇒E=hcR

E=6.626×10−34⋅3×108⋅1.097×107

= 2 .182×10^−18J

When we deal with such small energies, it is often helpful to work in electron volts. 1eV=1.6×10^−19J so to convert to eV we divide by 1.6×10^−19

2.182×10^−18/1.6×10^−19=13.6eV