A hydrogen atom is excited up to 9th level. The total number of possible spectral lines emitted by the hydrogen atom is

Options

A. 36
B. 35
C. 37
D. 38

Answer

To find the total number of possible spectral lines emitted by a hydrogen atom excited to the 9th energy level, we can use the formula for calculating the number of spectral lines emitted when an electron transitions between energy levels. The formula is given by:

\[ \text{Number of spectral lines} = \binom{n}{2} = \frac{n(n-1)}{2} \]

where \( n \) is the highest energy level the electron can transition from.

### Step-by-step Solution:

1. **Identify the highest energy level (n)**:
The problem states that the hydrogen atom is excited to the 9th level, so \( n = 9 \).

2. **Apply the formula for spectral lines**:
We will use the formula \( \binom{n}{2} \) to find the number of possible transitions (spectral lines) from the 9th energy level.

\[ \text{Number of spectral lines} = \binom{9}{2} = \frac{9 \times (9 - 1)}{2} \]

3. **Calculate the values**:
Substitute \( n = 9 \) into the formula:

\[ \text{Number of spectral lines} = \frac{9 \times 8}{2} \]

4. **Perform the multiplication**:
Calculate \( 9 \times 8 \):

\[ 9 \times 8 = 72 \]

5. **Divide by 2**:
Now, divide by 2 to find the total number of spectral lines:

\[ \frac{72}{2} = 36 \]

6. **Conclusion**:
Therefore, the total number of possible spectral lines emitted by the hydrogen atom when excited to the 9th level is **36**.

### Final Answer:
The total number of possible spectral lines emitted by the hydrogen atom is **36**.