Question

To use a mass spectrometer we first need to ionize the incoming particles, so we do the following. First there is a particle of known charge q = 2 |e|, entering the left side of the velocity selector, which has a voltage of 884V between the plates, a plate separation of d = 1cm, and a magnetic field of Bin = 2T. This particle then enters the region of a second magnetic field of B0,in = 0.5T, and moves in a semicircle where we measure the radius r = 9.4cm. We want to learn about this particle, so we will consider the following questions.

(a) First calculate what is the velocity of this particle as it enters the second magnetic field region, i.e. what is the velocity that was selected?

(b) Now we want to find an equation for the mass of the particle. You will need to find a symbolic answer for the mass of this particle in terms of the variables given in the question.

(c) What is the numerical value of this mass in kilograms?

(d) What is the mass of this in atomic mass units? Additionally what element could this particle be? To do this you should simply google something like ”what element has the atomic mass of ...”.

(e) What is the sign of charge of the particle?

Answer 1

a)velocity of particle v=E/B

E=electric field=Voltage/distance=884/0.01=88400N/C (distance d=1cm=.01m)

B=magnetic field=Bin=2T (first magnetic field)

velocity of particle v=E/B=88400/2=44200m/s=velocity selected

b) When it enters second magnetic field =0.5T,  

Radius of path

  

m=mass of the particle

q=charge

Therefore mass

c)r=9.4cm=.094m

q=charge=2e=2x1.6xC

m=2x1.6xx0.5x.094/44200=3.4027xkg

d)1amu=1.660539xkg

m=3.4027x/1.660539x=204.915amu

Hence the element may be thalium