# Problem: In one type of mass spectrometer, ions having the same velocity move through a uniform magnetic field. The spectrometer is being used to distinguish 12 C+ and 14 C+ ions that have the same charge. The 12 C+ 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?

###### FREE Expert Solution

a.

Consider acceleration of a uniform circular motion:

α = v2/r = F/m

α = |q|vB/m

The speed and the magnetic field are the same for both ions.

The radius must be directly proportional to the mass. ###### Problem Details

In one type of mass spectrometer, ions having the same velocity move through a uniform magnetic field. The spectrometer is being used to distinguish 12 C+ and 14 Cions that have the same charge. The 12 C+ 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?