A mass spectrometer splits a beam of ¹⁰B and ¹¹B singly charged ions having the same velocity by passing the beam through a uniform magnetic field. If the radius of the path for the ¹⁰B ions is 12.0 cm, what will be the radius for the ¹¹B ions? A) 9.90 cm B) 10.9 cm C) 12.0 cm D) 13.2 cm E) 14.5 cm

Question

Quizplus · Accepted Answer

The radius of the path in a magnetic field for a charged particle is directly proportional to its mass when the velocity and charge are constant. Since ¹¹B has a slightly higher mass than ¹⁰B, its path radius will be proportionally larger. Given that the mass difference is about 1/110 (or approximately 1%), the increase in radius will be similar, making 13.2 cm (a 10% increase from 12.0 cm) the correct answer.

A Mass Spectrometer Splits a Beam of 10B and 11B

A Mass Spectrometer Splits a Beam of ¹⁰B and ¹¹B