Question

Assuming expression for energy of electron, derive an expression for wavelength of spectral lines in hydrogen atom.

Answer 1

From Bohr’s energy equation for an electron in a hydrogen atom

`En = − 13.6/n^2` eV

where nnn is the principal quantum number.

For a transition from a higher energy level n2​ to a lower energy level n1, the energy difference is

`ΔE = E_"n2"​​ − E_"n1​​"`

Using Planck’s relation ΔE = hv and v = `c/λ` we get

`1/λ = R_H(1/(n^2 1 ) − 1/(n^2 2))`

where R_H (Rydberg constant) = 1.097 xx 10⁷ m ⁻¹.