A mass spectrometer is used to analyze carbon isotopes in a laboratory experiment. In the separation chamber, a uniform magnetic field is directed perpendicular to the plane of the paper.
Doubly-charged carbon-12 ions (12C2+^{12}\text{C}^{2+}12C2+) of mass 12 u 12\,u\,12u and speed v1 v_1\,v1 enter the chamber and move in a circular arc of radius r1=16.0 cmr_1 = 16.0\text{ cm}r1=16.0 cm.
Singly-charged carbon-14 ions (14C+^{14}\text{C}^{+}14C+) of mass 14 u 14\,u\,14u and speed v2=1.5v1v_2 = 1.5v_1v2=1.5v1 enter the same magnetic field.
What is the radius R R\,R of the circular path of the carbon-14 ions?
14.0 cm14.0\text{ cm}14.0 cm
28.0 cm28.0\text{ cm}28.0 cm
37.3 cm37.3\text{ cm}37.3 cm
56.0 cm56.0\text{ cm}56.0 cm