Imagine a hypothetical world where angular momentum is quantized as even integral multiples of h/2 . Based on Bohr's model, what would be the longest possible wavelength emitted by hydrogen atoms in the visible range in such a world?

Step-by-step solution

In Bohr's model, the angular momentum is given by L = nh 2 . Given that angular momentum is quantized as even integral multiples of h 2 , the allowed principal quantum numbers are n = 2, 4, 6, 8, The energy of an electron in the n -th orbit of a hydrogen atom is E_n = - 13.6 n^2 eV . For a transition to emit a photon in the visible range (approximately 400 nm to 700 nm , corresponding to energies between 1.8 eV and 3.1 eV ), the electron must transition to the n = 2 state. The allowed transitions to n = 2 in this h