Which statement is `//` are correct about hydrogen spectrum?

Options

A. Energy of 2nd orbit is different for `._(1)H^(1), ._(1)H^(2)` and `._(1)H^(3)`
B. Visible spectrum can be obtained in Lyman series and Balmer series
C. Infrared spectrum can be obtained in Paschen, brackett and Pfund series.
D. Total number of emission lines obtained in Balmer series is `n-2` , where n is principal quantum number an `n gt 2`

Answer

To determine which statements are correct about the hydrogen spectrum, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding the Energy Levels of Hydrogen Isotopes:**
- The energy levels of hydrogen isotopes (1H1, 1H2, 1H3) are determined by the formula:
\[ E_n = -\frac{Z^2 \cdot R_H}{n^2} \]
where \(Z\) is the atomic number, \(R_H\) is the Rydberg constant, and \(n\) is the principal quantum number.
- For hydrogen isotopes, \(Z = 1\) for all isotopes (1H1, 1H2, 1H3), and the principal quantum number \(n\) is the same for corresponding energy levels. Thus, the energy of the second orbit (n=2) will be the same for all isotopes.
- **Conclusion:** The first statement is incorrect.

2. **Identifying the Visible Spectrum:**
- The visible spectrum of hydrogen is produced by transitions in the Balmer series, which corresponds to electron transitions from higher energy levels (n ≥ 3) to n = 2.
- The Lyman series produces ultraviolet light, not visible light.
- **Conclusion:** The second statement is incorrect.

3. **Identifying the Infrared Spectrum:**
- The Paschen series, Bracket series, and Pfund series correspond to transitions that produce infrared radiation.
- These series involve transitions to the n = 3, n = 4, and n = 5 energy levels, respectively, which fall in the infrared region.
- **Conclusion:** The third statement is correct.

4. **Determining the Number of Emission Lines in the Balmer Series:**
- The number of emission lines in the Balmer series can be calculated using the formula:
\[ \text{Number of lines} = n - 2 \]
where \(n\) is the principal quantum number of the initial state.
- This means that for n = 3, there is 1 line; for n = 4, there are 2 lines, and so on.
- **Conclusion:** The fourth statement is incorrect.

### Final Conclusion:
- The only correct statement about the hydrogen spectrum is the third statement regarding the infrared spectrum being produced by the Paschen, Bracket, and Pfund series.