Gce Model Questions Vol1 2025 Physics Question 25

An electron in a hydrogen atom makes a transition from the \(n=5\) level to the \(n=2\) level, emitting a photon. The rest wavelength of this photon is calculated from the Rydberg formula. Because the source is moving away from the observer, the observed wavelength is \(440\ \text{nm}\) instead of the rest wavelength.\n\n(a) Determine the rest wavelength of the photon (in nanometres) using the Rydberg constant \(R=1.097\times10^{7}\ \text{m}^{-1}\).\n(b) Using the non‑relativistic Doppler shift formula \(\lambda_{\text{obs}}=\lambda_{0}(1+v/c)\), find the speed \(v\) of the source as a fraction of the speed of light \(c\).\n(c) Calculate the kinetic energy of the moving hydrogen atom (mass \(1.673\times10^{-27}\ \text{kg}\)) in joules, expressing the result in scientific notation to two significant figures.