A certain transition to H spectrum from an excited state to ground state in one or more steps gives rise to total `10` lines .How many of these belong to UV spectrum ?

Options

A. `2`
B. `3`
C. `4`
D. `5`

Explanation

To solve the problem of how many lines from the transition of an excited state to the ground state in the hydrogen spectrum belong to the UV spectrum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We are given that a transition from an excited state to the ground state in hydrogen gives rise to a total of 10 spectral lines. We need to determine how many of these lines belong to the UV spectrum.

2. **Formula for Total Lines**:
The formula to calculate the total number of spectral lines (N) when an electron transitions from a higher energy level (n2) to a lower energy level (n1) is given by:
\[ N = (n2 - n1 + 1) \times (n2 - n1) / 2 \]

3. **Setting Up the Equation**:
In this case, since the transition ends at the ground state, we have:
- \( n1 = 1 \) (ground state)
- \( N = 10 \) (total lines)

Plugging in the values into the formula:
\[ 10 = (n2 - 1 + 1) \times (n2 - 1) / 2 \]
Simplifying this gives:
\[ 10 = n2 \times (n2 - 1) / 2 \]

4. **Solving for n2**:
Multiplying both sides by 2 to eliminate the fraction:
\[ 20 = n2 \times (n2 - 1) \]
Rearranging gives us a quadratic equation:
\[ n2^2 - n2 - 20 = 0 \]

5. **Factoring the Quadratic**:
To solve for \( n2 \), we can factor the quadratic:
\[ (n2 - 5)(n2 + 4) = 0 \]
This gives us two possible solutions:
- \( n2 = 5 \)
- \( n2 = -4 \) (not physically meaningful)

Therefore, \( n2 = 5 \).

6. **Determining Lines in the UV Spectrum**:
The lines that belong to the UV spectrum correspond to the Lyman series, which is the series of transitions that end at \( n1 = 1 \). The number of lines in the Lyman series is given by:
\[ \text{Number of lines in Lyman series} = n2 - 1 \]
Substituting \( n2 = 5 \):
\[ \text{Number of lines in Lyman series} = 5 - 1 = 4 \]

### Final Answer:
Thus, the number of lines that belong to the UV spectrum is **4**.