Consider a hydrogen atom with its electron in the nth orbital. An electromagnetic radiation of wavelength 90 nm is used to ionize the atom. If the kinetic energy of the ejected electron is 10.4 eV, then the value of n is (hc = 1242 eV nm)

Energy of 90 nm wavelength, E = hc/λ = 1242/90 = 13.8 eV
The energy required to ionize the electron from nth orbital is given by:
E = 13.6/n² eV
The kinetic energy of the ejected electron is 10.4 eV. Therefore, the total energy is the sum of the ionization energy and the kinetic energy:
13.8 eV = 13.6/n² + 10.4 eV
13.8 - 10.4 = 13.6/n²
3.4 = 13.6/n²
n² = 13.6/3.4 = 4
n = 2