Problem 6: Find the longest wavelength of light capable of ionizing a hydrogen atom. How much energy is needed to ionize a hydrogen atom?

Solution

Ionization of hydrogen atom means the electron of the atom absorbs so much energy that it goes to infinity from its shell, n = 1. Now, if the electron falls from an infinite shell to the n = 1, it will emit the same amount of energy as it had absorbed in the ionization. The emitted energy will be in the form of photon of wavelength equal to the wavelength of the light which had ionized the hydrogen atom. Therefore, we find the wavelength of the photon emitted when an electron falls from an infinite level to the innermost level, n = 1. This wavelength will be equal to the wavelength of light of ionization.

Apply formula,

Where P in this case is the innermost shell with value 1 and n is the energy level at ∞. R is the Rydberg’s constant = 1.0974 × 107 m-1. Put the values,

This is the wavelength of the incident light (photon) capable of ionizing the hydrogen atom.

(b) Now to find the ionization energy, we have to find the energy possessed by this photon. As E = h/cλ,