An alpha particle (4He2+^{4}\text{He}^{2+}4He2+) is moving at a speed vvv perpendicular to a uniform magnetic field of flux density BBB. It follows a circular path of radius RRR.
A helium-3 ion (3He+^{3}\text{He}^{+}3He+) is projected into the same magnetic field at a speed of 4v4v4v perpendicular to the field.
Assuming the mass of a nucleon is mmm and the elementary charge is eee, what is the radius of the path of the helium-3 ion?
32R\frac{3}{2}R23R
3R3R3R
6R6R6R
12R12R12R