According to the Bohr theory of the hydrogen atom, electrons starting in the `4^(th)` energy level and eventually ending in the ground state could produce a total of how many lines in the hydrogen spectra?

Answer

To determine how many spectral lines can be produced when an electron transitions from the 4th energy level to the ground state (1st energy level) in a hydrogen atom, we can follow these steps:

### Step 1: Identify the Energy Levels
The energy levels in a hydrogen atom are denoted by quantum numbers (n). For this problem, we are starting from the 4th energy level (n=4) and transitioning down to the ground state (n=1).

### Step 2: Determine Possible Transitions
When an electron falls from a higher energy level to a lower one, it can do so in multiple steps. The possible transitions from n=4 to n=1 are:
- n=4 to n=3
- n=4 to n=2
- n=4 to n=1
- n=3 to n=2
- n=3 to n=1
- n=2 to n=1

### Step 3: Count the Transitions
We can count the number of unique transitions:
1. From n=4 to n=3
2. From n=4 to n=2
3. From n=4 to n=1
4. From n=3 to n=2
5. From n=3 to n=1
6. From n=2 to n=1

This gives us a total of 6 transitions.

### Step 4: Calculate the Number of Spectral Lines
Each transition corresponds to a spectral line. Therefore, the total number of spectral lines produced when an electron transitions from the 4th energy level to the ground state is 6.

### Final Answer
The total number of lines in the hydrogen spectrum produced by an electron transitioning from the 4th energy level to the ground state is **6**.

---