In the figure, the de Broglie wave of the electron of a hydrogen atom closes on itself along the circular orbit of radius $0.846\ \text{nm}$. The standing wave makes the orbit allowed, and the number of whole waves round it is the quantum number of the orbit. Take $h = 6.63 \times 10^{-34}\ \text{J s}$ and an electron mass of $9.1 \times 10^{-31}\ \text{kg}$. What is the speed of the electron in this orbit?

Fig. 1: A circular orbit round a nucleus marked with a plus sign, with a centre-to-orbit line labelled r equal to 0.846 nm. A wave is drawn along the whole orbit, as a thick line oscillating just inside and just outside a thin dashed circle. The wave closes on itself after going once round the orbit, with whole waves and no break at the join.