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 identifying the transitions responsible for the emission of the three photons with energies of 12.1 eV, 10.2 eV, and 1.9 eV from excited hydrogen atoms, we can 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 (n = 1, 2, 3,...).

### Step 2: Calculate Energy Differences for Each Photon
We need to find the transitions that correspond to the given photon energies.

#### For 12.1 eV:
1. Calculate the energy at \( n=1 \) and \( n=3 \):
\[ E_1 = -\frac{13.6}{1^2} = -13.6 \, \text{eV} \]
\[ E_3 = -\frac{13.6}{3^2} = -\frac{13.6}{9} \approx -1.51 \, \text{eV} \]
2. The energy difference (transition from \( n=3 \) to \( n=1 \)):
\[ \Delta E = E_1 - E_3 = -13.6 - (-1.51) = -13.6 + 1.51 = -12.1 \, \text{eV} \]
This corresponds to the photon energy of 12.1 eV.

#### For 10.2 eV:
1. Calculate the energy at \( n=1 \) and \( n=2 \):
\[ E_2 = -\frac{13.6}{2^2} = -\frac{13.6}{4} = -3.4 \, \text{eV} \]
2. The energy difference (transition from \( n=2 \) to \( n=1 \)):
\[ \Delta E = E_1 - E_2 = -13.6 - (-3.4) = -13.6 + 3.4 = -10.2 \, \text{eV} \]
This corresponds to the photon energy of 10.2 eV.

#### For 1.9 eV:
1. Calculate the energy at \( n=2 \) and \( n=3 \):
\[ \Delta E = E_2 - E_3 = -3.4 - (-1.51) = -3.4 + 1.51 = -1.89 \, \text{eV} \]
This is approximately equal to 1.9 eV, corresponding to the transition from \( n=3 \) to \( n=2 \).

### Step 3: Summarize the Transitions
- The photon with energy **12.1 eV** corresponds to the transition from **n=3 to n=1**.
- The photon with energy **10.2 eV** corresponds to the transition from **n=2 to n=1**.
- The photon with energy **1.9 eV** corresponds to the transition from **n=3 to n=2**.

### Conclusion
These photons must come from transitions in hydrogen atoms where:
- One photon (12.1 eV) comes from a transition of one atom from n=3 to n=1.
- Another photon (10.2 eV) comes from a transition of another atom from n=2 to n=1.
- The last photon (1.9 eV) comes from a transition of a third atom from n=3 to n=2.

Thus, the answer is that these photons must come from **two or three different hydrogen atoms**.