In the emission line spectra of hydrogen atom, how many lines can be accounted for all possible electronic transitions from `5^(th)` energy level within the atom?

Options

A. 4
B. 5
C. 10
D. 20

Answer

To determine how many lines can be accounted for all possible electronic transitions from the 5th energy level of a hydrogen atom in its emission line spectra, we can follow these steps:

### Step 1: Understand the Energy Levels
The hydrogen atom has discrete energy levels denoted by principal quantum numbers (n). For the 5th energy level, we have n = 5. The energy levels below n = 5 are n = 4, n = 3, n = 2, and n = 1.

### Step 2: Identify Possible Transitions
From the 5th energy level (n = 5), an electron can transition to any of the lower energy levels (n = 4, n = 3, n = 2, n = 1). We will count all possible transitions from n = 5 to these lower levels.

- Transition from n = 5 to n = 4
- Transition from n = 5 to n = 3
- Transition from n = 5 to n = 2
- Transition from n = 5 to n = 1

### Step 3: Count Transitions from Each Level
Next, we consider transitions that can occur from each of the lower levels:

1. **From n = 4**:
- Transition to n = 3
- Transition to n = 2
- Transition to n = 1

2. **From n = 3**:
- Transition to n = 2
- Transition to n = 1

3. **From n = 2**:
- Transition to n = 1

### Step 4: List All Unique Transitions
Now, we will list all unique transitions:
- From n = 5 to n = 4
- From n = 5 to n = 3
- From n = 5 to n = 2
- From n = 5 to n = 1
- From n = 4 to n = 3
- From n = 4 to n = 2
- From n = 4 to n = 1
- From n = 3 to n = 2
- From n = 3 to n = 1
- From n = 2 to n = 1

### Step 5: Count the Total Unique Transitions
Counting the unique transitions listed above, we have:
1. 5 → 4
2. 5 → 3
3. 5 → 2
4. 5 → 1
5. 4 → 3
6. 4 → 2
7. 4 → 1
8. 3 → 2
9. 3 → 1
10. 2 → 1

Thus, the total number of unique transitions is **10**.

### Conclusion
Therefore, the total number of lines that can be accounted for all possible electronic transitions from the 5th energy level in the emission line spectra of a hydrogen atom is **10**.

---