The electrons in hydrogen atoms are raised from ground state to third excited state. The number of emission lines will be

Options

A. 10
B. 6
C. 4
D. 3

Answer

To determine the number of emission lines when electrons in hydrogen atoms are raised from the ground state to the third excited state, we can follow these steps:

### Step 1: Identify the Ground State and Excited States
- The ground state of a hydrogen atom corresponds to the principal quantum number \( n = 1 \).
- The third excited state corresponds to \( n = 4 \) (since the first excited state is \( n = 2 \), the second excited state is \( n = 3 \), and the third excited state is \( n = 4 \)).

### Step 2: Use the Formula for the Number of Emission Lines
- The number of emission lines can be calculated using the formula:
\[ \text{Number of emission lines} = \frac{n(n-1)}{2} \]
where \( n \) is the number of excited states.

### Step 3: Calculate the Number of Excited States
- In this case, the electrons can transition from the third excited state (n=4) down to all lower energy levels (n=1, 2, and 3).
- The total number of states from which the electrons can emit is 4 (ground state + 3 excited states).

### Step 4: Substitute into the Formula
- Substitute \( n = 4 \) into the formula:
\[ \text{Number of emission lines} = \frac{4(4-1)}{2} = \frac{4 \times 3}{2} = \frac{12}{2} = 6 \]

### Conclusion
- Therefore, the number of emission lines when electrons transition from the ground state to the third excited state is **6**.

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