If an electron transits from n = 7 to n = 1 in a hydrogen atom then the maximum number of spectral lines that can form will be?

Options

A. 15
B. 10
C. 5
D. 6

Explanation

To find the maximum number of spectral lines that can form when an electron transitions from n = 7 to n = 1 in a hydrogen atom, we can use the formula for calculating the maximum number of spectral lines produced during electronic transitions:

**Step 1: Identify the values of n1 and n2.**
- Here, n2 (the higher energy level) is 7, and n1 (the lower energy level) is 1.

**Step 2: Use the formula for maximum spectral lines.**
- The formula to calculate the maximum number of spectral lines is given by:

\[ \text{Maximum Spectral Lines} = \frac{(n_2 - n_1)(n_2 - n_1 + 1)}{2} \]

**Step 3: Substitute the values into the formula.**
- Plugging in the values of n2 and n1:

\[ \text{Maximum Spectral Lines} = \frac{(7 - 1)(7 - 1 + 1)}{2} \]

**Step 4: Simplify the expression.**
- Calculate \(n_2 - n_1\):

\[ 7 - 1 = 6 \]

- Calculate \(n_2 - n_1 + 1\):

\[ 7 - 1 + 1 = 7 \]

- Now substitute these results back into the formula:

\[ \text{Maximum Spectral Lines} = \frac{(6)(7)}{2} \]

**Step 5: Perform the multiplication and division.**
- Multiply:

\[ 6 \times 7 = 42 \]

- Divide by 2:

\[ \frac{42}{2} = 21 \]

**Final Answer:**
- Therefore, the maximum number of spectral lines that can form when an electron transitions from n = 7 to n = 1 in a hydrogen atom is **21**.

---