Hydrogen atom is exited from ground state to another state with principal quantum number equal to `4` Then the number of spectral line in the emission spectra will be

Options

A. 2
B. 3
C. 5
D. 6

Explanation

To find the number of spectral lines in the emission spectrum of a hydrogen atom that has been excited to a principal quantum number \( n = 4 \), we can follow these steps:

### Step 1: Understand the formula for spectral lines
The number of spectral lines \( N \) in the emission spectrum when an electron transitions from a higher energy level to lower energy levels can be calculated using the formula:
\[ N = \frac{n(n - 1)}{2} \]
where \( n \) is the principal quantum number of the excited state.

### Step 2: Substitute the value of \( n \)
In this case, the electron is excited to the principal quantum number \( n = 4 \). We will substitute this value into the formula:
\[ N = \frac{4(4 - 1)}{2} \]

### Step 3: Simplify the expression
Now, we simplify the expression:
\[ N = \frac{4 \times 3}{2} \]
\[ N = \frac{12}{2} \]
\[ N = 6 \]

### Step 4: Conclusion
Thus, the number of spectral lines in the emission spectrum when the hydrogen atom is excited to the principal quantum number \( n = 4 \) is \( 6 \).

### Final Answer
The number of spectral lines in the emission spectra will be **6**.

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