PHYSICS · Multi-part · A Level · Physics · Particles and radiation · Particles and radiation
Problem
In a laboratory experiment, singly ionized helium (He⁺) is produced in a discharge tube. A spectrometer records a spectral line at a wavelength of 30.4±0.2nm. For a hydrogen-like ion with nuclear charge Z, the energy of the level with principal quantum number n is given by
En=−n2Z2(13.6eV).
Assume the uncertainty in wavelength is the only significant experimental uncertainty.
(a) Using the central value of the measured wavelength, calculate the energy of the emitted photon in electron-volts.
(b) Determine which electronic transition in He⁺ is most consistent with the measured line. Consider transitions that end at n=2 from higher levels up to n=6. Take into account the stated uncertainty in wavelength and justify your choice.
(c) When the discharge tube itself is observed directly, does the 30.4 nm line originate from emission or absorption? Explain your reasoning in terms of electron energy-state changes.