A photon strikes a hydrogen atom in its ground state to eject the electron with kinetic energy 16.4 eV. If 25% of the photon energy is taken up by the electron, the energy of the incident photon is (24 x X) eV then ‘X’ is:

Explanation

To solve the problem, we can break it down into the following steps:

### Step 1: Understand the energy levels of the hydrogen atom
The ground state energy of a hydrogen atom is given as -13.6 eV. This means that the total energy of the electron in the ground state is -13.6 eV.

### Step 2: Calculate the total energy of the electron after being ejected
When the photon strikes the hydrogen atom, it provides enough energy to eject the electron and give it kinetic energy. The kinetic energy (KE) of the ejected electron is given as 16.4 eV. Therefore, the total energy (E') of the electron after being ejected can be calculated as:
\[ E' = \text{Ground state energy} + \text{Kinetic energy} \]
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