In one version of Thomson's measurement of m/e, non-relativistic electrons were accelerated through a measured potential difference of V knot. This means that KE=eVknot. Then they are passed into a known magnetic field B and the radius r=mv/eB of their circular orbit is measured. Eliminate the speed v from these two equations and derive an expression for m/e in terms of the measured quantities V knot, B and r.

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Deanna HettingerLv2

20 Oct 2019

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Mass Spectrometer

J. J. Thomson is best known for his discoveries about the nature of cathode rays. Another important contribution of his was the invention, together with one of his students, of the mass spectrometer. The ratio of mass m to (positive) charge q of an ion may be accurately determined in a mass spectrometer. In essence, the spectrometer consists of two regions: one that accelerates the ion through a potential difference V and a second that measures its radius of curvature in a perpendicular magnetic field. (Figure 1)

The ion begins at potential V and is accelerated toward zero potential. When the particle exits the region with the electric field it will have obtained a speed u.

Part A

With what speed u does the ion exit the acceleration region?

Find the speed in terms of m, q, V, and any constants.

Part B

After being accelerated, the particle enters a uniform magnetic field of strength B0 and travels in a circle of radius R (determined by observing where it hits on a screen--as shown in the figure). The results of this experiment allow one to find m/q in terms of the experimentally measured quantities such as the particle radius, the magnetic field, and the applied voltage.
What is m/q?

Express m/q in terms of B, V, R, and any necessary constants.

azurefish181

In a cyclotron, a magnetic field confines charged particles to circular paths while an oscillating electric field accelerates them. It is useful to understand the details of this process.

Consider a cyclotron in which a beam of particles of positive charge q and mass m is moving along a circular path restricted by the magnetic field B? (which is perpendicular to the velocity of the particles).

A) Before entering the cyclotron, the particles are accelerated by a potential difference V. Find the speed v with which the particles enter the cyclotron. (Express your answer in terms of V, m, and q.)

B) Find the radius r of the circular path followed by the particles. The magnitude of the magnetic field is B. (Express your answer in terms of v, m, B, and q.)

C) Find the period of revolution T for the particles. (Express your answer in terms of m, B, and q.)

D) Find the angular frequency ? of the particles. (Express your answer in terms of m, B, and q.)

azuremuskrat765

1. Consider the Helmholtz coils, which have 130 turns per coil.Suppose that their
diameter is 2Rcoi1 = 0.304 m. Calculate the resulting magneticfield per ampere of
current, expressing your answer in units of milliTesla perAmpere.
2. Suppose that you apply a current of 1.5 Amperes through theHelmholtz coils.
Calculate the magnetic field, in milliTesla.
3. Suppose that the electrons are accelerated by a potential V =250 Volt, and they then
move in the magnetic field that you calculated in the previousstep. If the electrons
have the accepted value of elm = 1.76 x lOll [C/kg], what will bethe radius of the
circular orbit that they make?
4. In the' experiment, you will measure r, the radius of theelectron orbit, and you will
compute B, for various values of the current I flowing through theHelmholtz coils. _
You will then make a plot, with l/r2 on the vertical axis and B2 onthe horizontal axis.
The data points will fall mainly on a straight line of slope Q. Tofind elm from this
plot, you will need an expression for elm, in terms of the slope Qof this graph. Your
pre-lab question is to use Eq. (7.5) to find this expression.Please express it in the
forn1 elm = .... , where the expression on the right-hand-sideshould include the slope
a of the plot.

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