With a knowlege/intuition that the angular momentum of an electron in a hydrogen atom is quantized he asserted that the electron would be a standing wave in its orbit. Let λ be the de Broglie wavelength for the electron, where

mc² = hc/λ
or λ = h/(mc)

For a cicular orbit of radius r the number of waves that can fit into the circumference 2πr is then

n = 2πr/λ = 2πr(mc/h)
or, equivalently
mcr = n(h/2π)