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

Options

A. a simple atom
B. two atoms
C. three atoms
D. either two atoms or three atoms

Answer

To solve the problem of determining the transitions responsible for the emission of the three photons with energies 12.1 eV, 10.2 eV, and 1.9 eV from a hydrogen atom, we will follow these steps:

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

### Step 2: Calculate the Energy Levels
1. For \( n = 1 \):
\[ E_1 = -\frac{13.6 \text{ eV}}{1^2} = -13.6 \text{ eV} \]
2. For \( n = 2 \):
\[ E_2 = -\frac{13.6 \text{ eV}}{2^2} = -3.4 \text{ eV} \]
3. For \( n = 3 \):
\[ E_3 = -\frac{13.6 \text{ eV}}{3^2} = -1.51 \text{ eV} \]
4. For \( n = 4 \):
\[ E_4 = -\frac{13.6 \text{ eV}}{4^2} = -0.85 \text{ eV} \]
5. For \( n = 5 \):
\[ E_5 = -\frac{13.6 \text{ eV}}{5^2} = -0.544 \text{ eV} \]

### Step 3: Calculate the Energy Differences
To find the transitions corresponding to the emitted photons, we need to calculate the energy differences between the levels:

1. **For the photon with energy 12.1 eV**:
\[ E_3 - E_1 = (-1.51) - (-13.6) = 12.09 \text{ eV} \quad \text{(approximately 12.1 eV)} \]
This transition corresponds to \( n = 3 \) to \( n = 1 \).

2. **For the photon with energy 10.2 eV**:
\[ E_2 - E_1 = (-3.4) - (-13.6) = 10.2 \text{ eV} \]
This transition corresponds to \( n = 2 \) to \( n = 1 \).

3. **For the photon with energy 1.9 eV**:
\[ E_2 - E_3 = (-3.4) - (-1.51) = -1.89 \text{ eV} \quad \text{(approximately 1.9 eV)} \]
This transition corresponds to \( n = 3 \) to \( n = 2 \).

### Step 4: Conclusion
The three photons with energies 12.1 eV, 10.2 eV, and 1.9 eV correspond to the following transitions:
- 12.1 eV: Transition from \( n = 3 \) to \( n = 1 \)
- 10.2 eV: Transition from \( n = 2 \) to \( n = 1 \)
- 1.9 eV: Transition from \( n = 3 \) to \( n = 2 \)

Since these transitions can occur in different hydrogen atoms, the answer is that these photons must come from either two or three different atoms.