in this video we're working an example of a bainbridge mass spectrometer and i made a
larger video about the design and operation of a mass spectrometer like this and i'll post a link
to that real quick but let's review the basic design real quick the point of this device is
that you can figure out the masses of all the atoms and molecules and fragments of molecules
in a sample by first ionizing that sample so we take a sample and we vaporize it then we hit it
with high energy electrons to ionize the particles in that sample that means we're knocking electrons
off those particles for the most part those particles end up singly ionized meaning they're
missing one electron there will be some double ionization events and you'll see that in your data
but it's rare compared to the single ionizations so we have a bunch of positively charged particles
now that came from our sample we push them out of the sample container with a positively charged
plate called the ion repeller that gets us into an accelerating potential where we accelerate
those positive ions from a high potential to a low potential to speed them up we fine tune the
velocity of this beam of particles by passing through a speed selector and that's constructed
by crossing electric and magnetic fields so that only one special speed is allowed to pass through
that filter now we have a narrow beam with a very narrow range of velocities entering what's called
the analyzer region of the mass spectrometer and the point of this region is to bend the path of
those charged particles until they land on a detector now the radius of curvature of those
particles depends on their mass and so knowing all the parameters in this mass spectrometer you're
able to calculate the mass of the particles hitting the detector so in practice this mass
spectrometer is going to sweep through a bunch of different settings you can catch particles
of different masses by tweaking the strength of the magnetic field in the analyzer region
you can change the accelerating potential if you need to explore a different regime of velocities
you can fine-tune those velocities by changing electric and magnetic fields in the speed selector
so by sweeping through different settings in this mass spectrometer you can catch the masses of all
the different species that are in your sample in this particular example we're just looking at a
nitrogen 14 atom that's been singly ionized that means it's missing one electron so it has a charge
of plus qe plus 1 elementary charge or 1.6 times 10 to the negative 19 coulombs and we're exploring
some of the settings in the mass spectrometer to get a better understanding of how it works
so in part a i'm asking what's the accelerating potential required so that the ion has a final
speed of 3.5 times 10 to the fifth meters per second before it gets to the speed selector
and so i have a nitrogen 14 ion that ends up entering the region of the accelerating potential
and it's going to move from high to low potential and the speed at the end of that process is
determined by an energy conservation calculation and the change in potential energy of a charged
particle is given by q delta v where delta v is the potential difference and the magnitude of that
potential energy change well that turns into the kinetic energy of that particle now the magnitude
of the change in voltage is just capital v because the potential of the other plate is zero so i end
up with a qv capital v for the voltage it's equal to one half mv squared and the way this particular
problem is set up i'm trying to calculate the accelerating potential corresponding to a known
speed so we solve for v and i get mv squared over 2q so if we just plug in the mass the
desired speed the charge on these ions i should be able to get the required accelerating potential
there's a little bit of prep work that has to be done because we were given the mass of this ion
in atomic mass units 14.003 atomic mass units i have to multiply by a conversion factor here
there are 1.66 times 10 to the negative 27 kilograms in an atomic mass unit
and when i run the numbers on this i get a mass of 2.324 times 10 to the negative 26
kilograms so we're ready to plug in our numbers and i put that mass in there 2.324
times 10 to the negative 26. the speed of our particle beam is 3.5 times 10 to the fifth meters
per second and then the charge on these singly ionized nitrogen 14 atoms is 1.6 so times 10 to
the negative 19 coulombs when i run the numbers on this and round to three significant digits
i get 8 900 volts so an accelerating potential of 8 900 volts
would cause nitrogen 14 atoms in particular to be moving with this speed of 3.5 times 10 to the
fifth meters per second if our speed selector is set to that value we get a very narrow range of
velocities in this particle beam entering the analyzer region in part b we want to determine
what magnetic field strength would actually cause these particles to hit the detector and when we
get to this special magnetic field strength we're going to register a current in the machine because
we have all these positive particles hitting a detector that's part of a larger detection
circuit so first we're told the detector is 35 centimeters from the point of entry and this means
the radius of curvature of this particle beam is half that that's 17 and a half centimeters
or i could say the radius of curvature is 0.175 meters and these nitrogen ions are moving in
cyclotron motion so that's the motion of a charged particle curved into a circular path in a magnetic
field there's the velocity vector for one of these particles always perpendicular to the trajectory
and when i apply the right hand rule for the lorentz force law i can take my fingers in the
direction of v sweep out to the direction of b and my thumb points in the direction of the
magnetic force well that's perpendicular to v and pointing to the center of curvature and there's
our center pointing force that causes circular motion when we do a force analysis on this
it goes back all the way to newton's second law f net equals m a and the force experienced by
this ion is the lorentz force and that's q v b times the sine of theta where theta is the angle
between the velocity vector and the magnetic field well that's just 90 degrees because the velocity
is in the plane of the page and the field points out of the page and the sine of 90 degrees is 1.
our acceleration is related to the speed and the radius of curvature by v squared over r
and now we should be able to solve for the magnetic field corresponding to this
radius of curvature so we cancel one factor of r and isolate b on the left-hand side and b is
going to be mv over qr we plug in our numbers and when we round to three significant digits
we get 0.291 teslas so if we imagine what this looks like in practice you can set up a narrow
beam of positively charged particles fine-tune the speed distribution very closely around
3.5 times 10 to the fifth meters per second and then sweep through a bunch of different strengths
of magnetic fields just by turning a knob when you hit .219 teslas you're going to detect a current
in this mass spectrometer and you can quickly compute the mass of that particular species
this contributes a line to the mass spectrum of your sample and you can say you detected nitrogen
14 in your sample you continue to sweep through different settings on the mass spectrometer
and you can find a bunch of lines corresponding to the masses of all the different atoms
molecules and fragments of molecules in your sample if you enjoyed this video or
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