The emission spectrum of hydrogen is found to satisfy the expression for the energy change `Delta E` (in joules) such that
`Delta E = 2.18 xx 10^(-18)((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))J`
where `n_(1) = 1,2,3,....` and `n_(2) = 2,3,4,...` The spectral lines correspond to Paschen series if

Options

A. `n_(1)`=1 and `n_(2)` = 2, 3, 4
B. `n_(1)`=3 and `n_(2)` = 4, 5, 6
C. `n_(1)`=1 and `n_(2)` = 3, 4, 5
D. `n_(1)`=2 and `n_(2)` = 3, 4, 5

Answer

To determine the conditions under which the spectral lines correspond to the Paschen series in the emission spectrum of hydrogen, we can follow these steps:

### Step 1: Understand the Paschen Series
The Paschen series in the hydrogen emission spectrum corresponds to transitions where the final energy level (n1) is 3. This means that the electron transitions to the third energy level from higher energy levels.

### Step 2: Identify the Energy Levels
In the formula given:
\[ \Delta E = 2.18 \times 10^{-18} \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \text{ J} \]
- \( n_1 \) is the lower energy level (final state).
- \( n_2 \) is the higher energy level (initial state).

For the Paschen series, we set \( n_1 = 3 \).

### Step 3: Define the Initial State
Since the Paschen series involves transitions from higher energy levels to \( n_1 = 3 \), \( n_2 \) can be any integer greater than 3. Therefore, \( n_2 \) can be 4, 5, 6, etc.

### Step 4: Conclusion
Thus, the spectral lines correspond to the Paschen series if:
- \( n_1 = 3 \)
- \( n_2 = 4, 5, 6, \ldots \)

### Final Answer
The spectral lines correspond to the Paschen series if \( n_1 = 3 \) and \( n_2 \) is any integer greater than 3.

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