The theory published in 1913 by Niels Bohr to explain the line spectrum of hydrogen. He assumed that a single electron of mass m travelled in a circular orbit of radius r, at a velocity v, around a positively charged nucleus. The angular momentum of the electron would then be mvr. Bohr proposed that electrons could only occupy orbits in which this angular momentum had certain fixed values, h/2π‎, 2h/2π‎, 3h/2π‎,…nh/2π‎, where h is the Planck constant. This means that the angular momentum is quantized, i.e. can only have certain values, each of which is a multiple of n. Each permitted value of n is associated with an orbit of different radius and Bohr assumed that when the atom emitted or absorbed radiation of frequency ν‎, the electron jumped from one orbit to another; the energy emitted or absorbed by each jump is equal to hν‎. This theory gave good results in predicting the lines observed in the spectrum of hydrogen and simple ions such as He⁺, Li²⁺, etc. The idea of quantized values of angular momentum was later explained by the wave nature of the electron. Each orbit has to have a whole number of wavelengths around it; i.e. nλ‎ = 2π‎r, where λ‎ is the wavelength and n a whole number. The wavelength of a particle is given by h/mv, so nh/mv = 2π‎r, which leads to mvr = nh/2π‎. The Bohr theory was extended in various ways by Arnold Sommerfeld (1868–1951) and others in the subsequent decade; one important extension was from circular orbits to elliptical orbits. Modern atomic theory does not allow subatomic particles to be treated in the same way as large objects, and Bohr’s reasoning is somewhat discredited. However, the idea of quantized angular momentum has been retained.