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

Explanation

To solve the problem of determining which energy level is not possible for a photon to be emitted by a hydrogen atom according to Bohr's atomic model, we will follow these steps:

### Step 1: Understand the Energy Levels in Hydrogen Atom
According to Bohr's model, the energy of an electron in the nth energy level 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 levels for the first few values of \( n \):

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

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

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

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

### Step 3: Determine Possible Transitions
The photon emitted corresponds to the energy difference between two energy levels. The possible transitions are:

- Transition from \( n = 2 \) to \( n = 1 \):
\[ E_{photon} = E_1 - E_2 = (-13.6) - (-3.4) = -10.2 \, \text{eV} \]

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

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

- Transition from \( n = \infty \) to \( n = 1 \):
\[ E_{photon} = E_1 - E_{\infty} = (-13.6) - (0) = -13.6 \, \text{eV} \]

### Step 4: Identify the Energy Levels
Now, we can summarize the possible energies of emitted photons based on the transitions calculated. The possible energies are:
- 10.2 eV (from n=2 to n=1)
- 1.89 eV (from n=3 to n=2)
- 0.66 eV (from n=4 to n=3)
- 13.6 eV (from n=∞ to n=1)

### Step 5: Analyze the Given Options
Now, we need to check which of the provided options does not match any of the calculated energies.

Assuming the options are:
- A: 10.2 eV
- B: 1.89 eV
- C: 0.66 eV
- D: 13.6 eV
- E: (some value not calculated)

From our calculations, if one of the options does not match any of the calculated energies, that will be the answer.

### Conclusion
The option that does not correspond to any of the calculated energies for the photon emitted by a hydrogen atom according to Bohr’s atomic model is the correct answer.