Gce Model Questions Vol1 2025 Physics Question 4

An electron in a hydrogen atom makes a transition from the \(n=5\) level to the \(n=2\) level, emitting a photon.\n\n(a) Calculate the wavelength of the emitted photon (in nanometres, to three significant figures).\n(b) The photon is then absorbed by another hydrogen atom, causing the ejection of its electron with a kinetic energy of \(2.0\;\text{eV}\). Determine the magnetic field at the centre of the electron's orbit in the original atom (the \(n=4\) orbit) and the magnetic moment of the electron in that orbit, expressing the magnetic moment as a multiple of the Bohr magneton \(\mu_B = 9.274\times10^{-24}\;\text{J\,T}^{-1}\). (Use \(a_0 = 5.29\times10^{-11}\;\text{m}\), \(v_1 = 2.19\times10^{6}\;\text{m\,s}^{-1}\), \(\mu_0 = 4\pi\times10^{-7}\;\text{H\,m}^{-1}\), and \(e = 1.602\times10^{-19}\;\text{C}\).)