The figure shows a schematic diagram of a simple mass spectrometer, consisting o
ID: 2259890 • Letter: T
Question
The figure shows a schematic diagram of a simple mass spectrometer, consisting of a velocity selector and a particle detector and being used to separate singly ionized atoms (q = +e = 1.602e-19 C) of gold (Au) and molybdenum (Mo). The electric field inside the velocity selector has magnitude E = 1.755
The figure shows a schematic diagram of a simple mass spectrometer, consisting of a velocity selector and a particle detector and being used to separate singly ionized atoms (q = +e = 1.602e-19 C) of gold (Au) and molybdenum (Mo). The electric field inside the velocity selector has magnitude E = 1.755·104 V/m and points toward the top of the page, and the magnetic field has magnitude B1 = 1.31 T and points out of the page. Calculate the velocity, v0, of the ions that make it through the velocity selector (those that travel in a straight line). The gold ions (represented by the black circles) exit the particle detector at a distance d2 = 36.50 cm from the entrance slit, while the molybdenum ions (represented by the gray circles) exit the particle detector at a distance d1 = 18.076 cm from the entrance slit. The mass of a gold ion is mgold = 3.27·10-25 kg. Calculate the mass of a molybdenum ion.Explanation / Answer
a) The ions that move in a straight line must be perpendicular to the magnetic force at a speed such that the magnetic force and electric force cancel out. This is called the Lorentz force.
F(electric) = qE
F(magnetic)= qvB
qE= qvB
E=vB
v=E/B
b) The magnetic force supplies centripetal force, which is what causes the ions to move in a circle so
Bqv= mv^2/r
if you rearrange this to solve for mass...
m=Bqvr/v^2= Bqr/v
Since the magnetic field, charge, and velocity are the same for both ions, we can see that mass is directly proportional to radius. We are give the diameter so convert that to meters divide by 2.
mass of gold ion/radius of gold ion= mass of Mo ion/ radius of Mo ion
Solve for the Mass of Mo ion, and that should give you the answer
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