Mass Spectrometer (Show My Homework: Physics 1142)

4) The device diagrammed below is a mass spectrometer. It has three main components: a chamber where a uniform magnetic field of magnitude $0.0014 T$ directed into the page is maintained, a velocity selector as in question 3 and an accelerator which uses an electric field to accelerate ions of atomic oxygen essentially from rest.  There are two movable collectors attached to the chamber and the magnetic field is used to steer ions into the collectors. The beam of ions consists of several isotopes of oxygen: $^{16}O$ (mass=15.995 amu), $^{17}O$(mass=16.999 amu ) and $^{18}O$ (mass=17.999 amu). $1 amu=1.66*10^{-27} kg$. All of the ions are missing one electron (singly ionized) and they enter the velocity selector with a range of velocities that overlaps the selector’s “un-deflected” velocity. If the electric and magnetic fields in the velocity selector have magnitudes 235.0 N/C and 0.045 T respectively,

a) Determine the speed at which the $^{16}O$ ions enter the chamber. Repeat for the $^{17}O$ ions. Does the mass of the ion affect the speed at which it enters the chamber?

b) Determine the position of the two collectors, relative to the selector opening into the chamber, to that $^{16}O$ and $^{17}O$ are collected. Repeat for $^{17}O$ and $^{18}O$.

c) Will the device as shown work for negatively charged ions with the same masses? If not, what would have to be different? Explain your reasoning.

a) In the velocity selector the condition of un-deflected velocity is electric force=magnetic force

$e E = e v B$

since all Oxygen atoms are single charged ($+e$).

$v = E/B = 235/0.045 =5222.22 m/s$

This un-deflected velocity is the same for all ions of Oxygen since it does not depend on the mass of the ions.

b)

Ions in the chamber will travel half a circle in the chamber. Condition in the chamber is

Centripetal force = Magnetic force

$m*v^2/R = e*v*B2$

$R = (m/e)*(v/B2)$

The collectors are positioned at a distance $L =2R$ from the selector.

$L(O16) = 2*(15.995*1.66*10^{-27}/1.6*10^{-19})*(5222.22/0.0014) =1.2380 m$

$L(O17) =2*(16.999*1.66*10^{-27}/1.6*10^{-19})*(5222.22/0.0014) =1.3157 m$

$L(O18) =L(O17)*17.999/16.999 =1.3931 m$

c)

The device as shown will not work for negatively charged ions.This is because negatively charged ions will be deflected the other way (to the right of the chamber) since Magnetic force will be

$F = -e*v*B$

To make the chamber work for negatively charged ions one will need to reverse the magnetic field direction in the chamber (upwards). In this case the deflection of negatively ions will be again to the left.