Three photons coming from excited atoms hydrogen sample are picked up .There energies are `12.1eV, 10.2eV and 1.9eV` these photons must come from

Options

A. a single atom
B. two atom
C. three atom
D. either two atom or three atom

Explanation

To solve the problem of determining how many atoms emitted the three photons with energies of 12.1 eV, 10.2 eV, and 1.9 eV, we can analyze the energy levels of the hydrogen atom and the transitions that correspond to these photon energies.

### Step-by-Step Solution:

1. **Understanding Photon Energy and Electron Transitions**:
The energy of a photon emitted during an electron transition in a hydrogen atom can be calculated using the formula:
\[ E = -13.6 \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \text{ eV} \]
where \( n_i \) is the initial energy level and \( n_f \) is the final energy level.

2. **Calculating the Transitions for Each Photon**:
- For the photon with energy **12.1 eV**:
\[ E = -13.6 \left( \frac{1}{1^2} - \frac{1}{3^2} \right) = -13.6 \left( 1 - \frac{1}{9} \right) = -13.6 \left( \frac{8}{9} \right) \approx 12.1 \text{ eV} \]
This transition corresponds to \( n = 3 \) to \( n = 1 \).

- For the photon with energy **10.2 eV**:
\[ E = -13.6 \left( \frac{1}{1^2} - \frac{1}{2^2} \right) = -13.6 \left( 1 - \frac{1}{4} \right) = -13.6 \left( \frac{3}{4} \right) \approx 10.2 \text{ eV} \]
This transition corresponds to \( n = 2 \) to \( n = 1 \).

- For the photon with energy **1.9 eV**:
\[ E = -13.6 \left( \frac{1}{2^2} - \frac{1}{3^2} \right) = -13.6 \left( \frac{1}{4} - \frac{1}{9} \right) = -13.6 \left( \frac{5}{36} \right) \approx 1.9 \text{ eV} \]
This transition corresponds to \( n = 3 \) to \( n = 2 \).

3. **Identifying the Number of Atoms**:
- The transitions indicate that:
- One atom transitions from \( n = 3 \) to \( n = 1 \) (12.1 eV).
- Another atom transitions from \( n = 2 \) to \( n = 1 \) (10.2 eV).
- A third atom transitions from \( n = 3 \) to \( n = 2 \) (1.9 eV).
- Since hydrogen has only one electron, each transition must come from a different atom if they are independent.

4. **Conclusion**:
The three photons must come from either two or three atoms, depending on whether the transition from \( n = 3 \) to \( n = 2 \) occurs in the same atom as the transition from \( n = 2 \) to \( n = 1 \) or in a different atom. Therefore, the answer is that the photons must come from either two atoms or three atoms.

### Final Answer:
The photons must come from either two atoms or three atoms.