Question

Number of spectral lines obtained in He⁺ spectra, when an electron makes transition from fifth excited state to first excited state will be __________.

Answer 1

Correct Answer: 10

To calculate the number of spectral lines obtained during the transition of an electron from the fifth excited state to the first excited state in the He⁺ ion, we use the formula for the maximum number of spectral lines during a transition:

Number of spectral lines = \[ \frac{n_2(n_2 + 1)}{2} - \frac{n_1(n_1 + 1)}{2} \]

Where:
\(n_1\) is the final state (ground state or first excited state).
\(n_2\) is the initial state (fifth excited state).

Assign Values:

• For the first excited state: \(n_1 = 2\)
• For the fifth excited state: \(n_2 = 6\)

Calculate the Maximum Number of Lines:

\[ \Delta n = n_2 - n_1 = 6 - 2 = 4 \]

The maximum number of spectral lines is given by:

\[ \text{Number of lines} = \frac{n_2(n_2 + 1)}{2} - \frac{n_1(n_1 + 1)}{2} \] \[ = \frac{6(6 + 1)}{2} - \frac{2(2 + 1)}{2} \] \[ = \frac{6 \times 7}{2} - \frac{2 \times 3}{2} \] \[ = 21 - 3 = 18 \]

Since we are considering all possible transitions from \(n_2 = 6\) to \(n_1 = 2\), we have:

Final Calculation:

\[ \text{Maximum number of spectral lines} = \frac{\Delta n (\Delta n + 1)}{2} = \frac{4(4 + 1)}{2} = \frac{20}{2} = 10 \]

Thus, the number of spectral lines obtained in He⁺ spectra when an electron transitions from the fifth excited state to the first excited state is: 10