A monochromatic beam of light having photon energy `12.5 eV` is incident on a simple `A` of atomic hydrogen gas in which all almost are in the ground state. The emission spectra obtained from this sample is incident on another sample `B` of atomic hydrogen gas in which all atoms are in the first excited state.
Based on above information, answer the following question:
The emission spectra of sample `A`

Options

A. must have `3` lines
B. must have `2` lines
C. may have `2` lines
D. it is not formed

Explanation

To solve the problem, we need to analyze the situation involving the emission spectra of atomic hydrogen when exposed to a monochromatic beam of light with a photon energy of 12.5 eV.

### Step-by-Step Solution:

1. **Understanding the Energy Levels of Hydrogen:**
- The energy levels of hydrogen are given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
- For the ground state (n=1):
\[ E_1 = -13.6 \, \text{eV} \]
- For the first excited state (n=2):
\[ E_2 = -3.4 \, \text{eV} \]
- For the second excited state (n=3):
\[ E_3 = -1.51 \, \text{eV} \]
- For the third excited state (n=4):
\[ E_4 = -0.85 \, \text{eV} \]

2. **Photon Energy Incident on Sample A:**
- The incident photon energy is given as 12.5 eV. This energy is much higher than the energy required to excite electrons from the ground state to any of the higher energy levels.

3. **Calculating the Energy Gap:**
- The energy required to excite an electron from the ground state (n=1) to the first excited state (n=2) is:
\[ E_2 - E_1 = -3.4 \, \text{eV} - (-13.6 \, \text{eV}) = 10.2 \, \text{eV} \]
- The energy required to excite an electron from the ground state to the second excited state (n=3) is:
\[ E_3 - E_1 = -1.51 \, \text{eV} - (-13.6 \, \text{eV}) = 12.09 \, \text{eV} \]
- The energy required to excite an electron from the ground state to the third excited state (n=4) is:
\[ E_4 - E_1 = -0.85 \, \text{eV} - (-13.6 \, \text{eV}) = 12.75 \, \text{eV} \]

4. **Determining Possible Transitions:**
- The photon energy of 12.5 eV can excite electrons to the second excited state (n=3) since it is less than 12.75 eV but greater than 12.09 eV.
- However, it cannot excite electrons to the first excited state (n=2) since the required energy is 10.2 eV, and it can also excite to n=3.

5. **Emission Spectra from Sample A:**
- Since the electrons can transition from the second excited state (n=3) back to the ground state (n=1), we can expect emission lines corresponding to these transitions.
- The possible transitions from n=3 to n=1 will produce one emission line.

6. **Conclusion:**
- As the only transition possible is from n=3 to n=1, the emission spectra of sample A will consist of one line.

### Final Answer:
The emission spectra of sample A will have **one line**.