Question

What is the highest energy photon that can be absorbed by a ground-state hydrogen atom without causing ionization?

Answer 1

Highest energy photon absorbed: $2.18\cdot 10^{-18}J$

Explanation:

An atom is said to be (positively) ionised when it absorbs a photon, and as a consequence, an electron becomes energetic enough to escape the atom, leaving an excess of positive charge behind.

In order for the electron to escape, the energy of the absorbed photon must be exactly equal to the (negative) energy of the level in which the electron lies.

For an hydrogen atom, the energy levels are given by

$E_n = -13.6 \frac{1}{n^2}$

where this energy is measured in electronvolts, and n is the number of the energy level.

Since the energy is negative, this means that the electron which requires most energy is the one lying in the ground state (n=1). Therefore, for an electron in the ground state, the most energy that can be absorbed from the incoming photon is

$E_1 = -13.6 eV$

Converting into Joules, this is equal to

$E_1 = 13.6 \cdot 1.6\cdot 10^{-19}=2.18\cdot 10^{-18}J$

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