In the figure, electrons accelerated through $54\ \text{V}$ strike a nickel crystal along the normal. The strongest scattered beam leaves at $50^\circ$ to the normal. It comes from the first order diffraction by the rows of atoms on the surface, spaced $D$ apart, so that $D \sin\varphi = \lambda$. The accelerating voltage is raised to $216\ \text{V}$. At what angle to the normal does the strongest first order beam now leave?

Fig. 1: A schematic of a beam of electrons striking a nickel crystal. An electron gun at the lower left sends a beam along a dashed normal line to the crystal face, a row of equally spaced atoms with spacing D marked. A second beam, the strongest scattered beam, leaves the crystal at 50 degrees to the normal on the right of it, towards a detector drawn on a circular arc. The accelerating voltage is marked 54 V.