If a photon with `12`eV energy is incidented on hydrogen atom then what will be true statement from the following `:-`

Options

A. Electron will transfer in first excited state and its energy will be increased by `1.8` eV
B. In atom electron will remain in ground state but its total energy
will be `-` `1.6` eV
C. Atom will not absorb the photon.
D. None of these

Explanation

To solve the question regarding the interaction of a photon with 12 eV energy incident on a hydrogen atom, we will follow these steps:

### Step 1: Understand the Energy Levels of Hydrogen Atom
The energy levels of a hydrogen atom are given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( n \) is the principal quantum number (n = 1, 2, 3, ...).

### Step 2: Calculate the Energy for Different Levels
1. For \( n = 1 \):
\[ E_1 = -\frac{13.6 \, \text{eV}}{1^2} = -13.6 \, \text{eV} \]

2. For \( n = 2 \):
\[ E_2 = -\frac{13.6 \, \text{eV}}{2^2} = -\frac{13.6}{4} = -3.4 \, \text{eV} \]

3. For \( n = 3 \):
\[ E_3 = -\frac{13.6 \, \text{eV}}{3^2} = -\frac{13.6}{9} \approx -1.51 \, \text{eV} \]

### Step 3: Determine the Energy Differences Between Levels
1. The energy difference between \( n = 1 \) and \( n = 2 \):
\[ \Delta E_{1 \to 2} = E_2 - E_1 = (-3.4) - (-13.6) = 10.2 \, \text{eV} \]

2. The energy difference between \( n = 2 \) and \( n = 3 \):
\[ \Delta E_{2 \to 3} = E_3 - E_2 = (-1.51) - (-3.4) \approx 1.89 \, \text{eV} \]

### Step 4: Compare Photon Energy with Energy Differences
The photon energy is given as 12 eV. We need to check if this energy can be absorbed by the hydrogen atom:
- The energy required to move from \( n = 1 \) to \( n = 2 \) is 10.2 eV.
- The energy required to move from \( n = 2 \) to \( n = 3 \) is approximately 1.89 eV.

Since 12 eV is greater than the energy difference between any two levels in hydrogen, the photon energy exceeds the energy required for transitions between the ground state and the first excited state.

### Step 5: Conclusion
Since the photon energy (12 eV) is greater than the energy difference between the ground state and the first excited state (10.2 eV), the hydrogen atom will not absorb the photon. Instead, the photon energy is too high for the atom to absorb, and thus the atom will remain in its ground state.

### Final Answer
The true statement is that the hydrogen atom will not absorb the photon with 12 eV energy.

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