Final answer:
To calculate the wavelength of the spectral line for a lithium ion transitioning from n=3 to n=2, use the Rydberg formula adapted for single-electron ions, taking into account the atomic number of lithium, which is 3.
Step-by-step explanation:
The wavelength of the spectral line associated with the transition from n=3 to n=2 for a lithium ion can be calculated using the Rydberg formula for hydrogen-like atoms, which is also applicable to other single-electron ions like lithium2+. The Rydberg formula is RH = 1.097 × 107 m−1 (Rydberg constant) and the wavelength (λ) can be found using:
1 / λ = Z2 × RH × (1/n12 − 1/n22),
where Z is the atomic number of the ion (Z=3 for lithium) and n1 and n2 are the principal quantum numbers of the initial and final energy levels respectively. The energy levels n=2 and n=3 correspond to the transition of the lithium ion that parallels the hydrogen Balmer series. Using this formula, you can calculate the wavelength of the emitted photon when an electron in a lithium ion transitions from n=3 to n=2.