Number of spectral lines obtained in atomic spectra, when an electron makes a transition from the fifth excited state to the first excited state will be _________.
Detailed Step-by-Step Solution
This problem tests your understanding of the formula for the number of spectral lines and your ability to correctly identify the principal quantum number (\(n\)) from the "excited state" terminology.
Step 1: Identify the Quantum Numbers (\(n_1\) and \(n_2\))
Crucial Concept: The \(x^{\text{th}}\) excited state corresponds to the principal quantum number \( n = x + 1 \). The ground state is always \(n = 1\).
- The electron jumps from the fifth excited state.
Therefore, \( n_2 = 5 + 1 = \mathbf{6} \). - The electron jumps to the first excited state.
Therefore, \( n_1 = 1 + 1 = \mathbf{2} \).
Step 2: Apply the Spectral Lines Formula
The total number of spectral lines (\(N\)) emitted when an electron transitions between two generic energy levels \(n_2\) and \(n_1\) is given by the formula:
Step 3: Substitute Values and Calculate
Substitute \( n_2 = 6 \) and \( n_1 = 2 \) into the formula:
\( N = \frac{(4)(4 + 1)}{2} \)
\( N = \frac{4 \times 5}{2} \)
\( N = \frac{20}{2} = 10 \)
Conclusion: The total number of spectral lines obtained during this transition is exactly 10.
Mastering Emission Spectra Tricks
Many students lose marks in JEE Main (+4/-1 format) simply by mistaking "excited state" for the orbit number. Remember, ground state is \(n=1\), so the first excited state is always \(n=2\). If you want to dive deeper into the various spectral series and their transitions, read our detailed conceptual guide on the Structure of Atom Class 11 Chemistry.
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