Out of the following which one is not a possible energy for a photon to be emitted by hydrogen atom according to Bohr's atomic model?

Options

A. 0.65eV
B. 1.9eV
C. 11.1eV
D. 13.6eV

Explanation

To determine which energy value is not a possible energy for a photon emitted by a hydrogen atom according to Bohr's atomic model, we can follow these steps:

### Step 1: Understand the Energy Levels of Hydrogen Atom
According to Bohr's model, the energy of an electron in the nth orbit of a hydrogen atom is 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 Levels
We will calculate the energy for the first few orbits (n = 1, 2, 3, 4):

- For \( n = 1 \):
\[ E_1 = -\frac{13.6}{1^2} = -13.6 \, \text{eV} \]

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

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

- For \( n = 4 \):
\[ E_4 = -\frac{13.6}{4^2} = -\frac{13.6}{16} \approx -0.85 \, \text{eV} \]

### Step 3: Calculate the Energy Differences
When an electron transitions between these energy levels, it emits or absorbs energy equal to the difference in energy between the two levels. We calculate the possible energy differences:

- Transition from \( E_3 \) to \( E_2 \):
\[ E_{3 \to 2} = E_3 - E_2 = (-1.51) - (-3.4) = 1.89 \, \text{eV} \]

- Transition from \( E_4 \) to \( E_3 \):
\[ E_{4 \to 3} = E_4 - E_3 = (-0.85) - (-1.51) = 0.66 \, \text{eV} \]

### Step 4: Identify Possible Photon Energies
The energies calculated from the transitions are:
- \( 1.89 \, \text{eV} \) (from \( E_3 \) to \( E_2 \))
- \( 0.66 \, \text{eV} \) (from \( E_4 \) to \( E_3 \))

### Step 5: Compare with Given Options
Now, we compare the calculated energies with the given options. If one of the options is not equal to any of the calculated energies or cannot be derived from any transition between the energy levels, it is the answer we are looking for.

### Conclusion
After checking the calculated energies and the options provided, we find that **11.1 eV** cannot be obtained from any transition in the hydrogen atom according to Bohr's model. Thus, it is the energy that cannot be emitted by a hydrogen atom.

### Final Answer
The energy that is not a possible energy for a photon emitted by a hydrogen atom is **11.1 eV**.

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