In one type of mass spectrometer, ions having the same velocity move through a uniform magnetic field. The spectrometer is being used to distinguish ¹²C⁺ and ¹⁴C⁺ ions. The ¹²C⁺ ions move in a circle of diameter 25 cm. 

(a) What is the diameter of the orbit of ¹⁴C⁺ ions? 

(b) What is the ratio of the frequencies of revolution for the two types of ions?

In each of these problems, the ions entering the mass spectrometer have the same charges. Except in Problem 30, the ions enter the magnetic field with equal kinetic energies (not equal speeds). Use these atomic mass values: ¹²C, 12.00 u; ¹⁴C, 14.00 u; ¹⁶O, 15.99 u. The conversion between atomic mass units and kilograms is 1 u = 1.66 × 10⁻²⁷ kg.