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

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