The wavelength of radiation required to remove the electron of hydrogen atom (Ionisation energy 21.7×10–12 erg) from n = 2 orbit to n = $\infty$ is

To calculate the energy required to remove electron from atom, n = ∞ is to be taken.

Energy of an electron in nth orbit of hydrogen is given by

E = 21.7 * 10⁻¹² X 1/n² ergs

∴ ∆E = 21.7 X 10⁻¹² (1/2² – 1/∞²)

= - 21.7 X 10⁻¹² (1/4 – 0) = 21.7 X 10⁻¹² * 1/4

= - 5.42 X 10⁻¹² ergs

∴ ∆E = hc/λ (∵ v = c/λ)

Or λ = hc/∆E

Substituting the values, λ = 6.627 X10⁻²⁷ *3 X1010/5.42 X 10⁻¹²

= 3.67 X 10⁻⁵ cm