Lab
Mass of an Electron
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This lab uses a vacuum tube once used in tuning radios. The electrons emitted by the cathode are accelerated by the potential difference between the cathode and the anode. They move radially outward and reach their maximum speed by the time they emerge from under the protective metal cap covering the center of the tube. For the remainder of their trip to the edge of the anode, their speed remains relatively constant.
On the left is an electron tube with its glass envelope removed. On the right the metal center cap has been cut away from its wire supports and removed, revealing the important parts of the tube structure.
K
is the electron-emitting cathode.
D
and
D’
are the deflecting electrodes that form the shadow and
A
is the anode.
The anode is coated with a fluorescent material which emits light when electrons strike it. Since it is conical in shape, we can see the path the electrons follow as they move outward from the cathode; when we look straight down from above, the conical anode slices the electron beam diagonally, showing the position of the electrons at different distances from the cathode. Two deflecting electrodes are connected to the cathode and, with no magnetic field present, they repel electrons moving toward them from the cathode and form a wedge-shaped shadow behind them.
When the tube is placed in a uniform magnetic field, the electrons are deflected in an almost circular path as shown by the curvature of the edge of the shadow. We will put a uniform magnetic field on the tube by inserting the tube into the center of a solenoid.
Equations
An electron, initially at rest, accelerates in an electric field and acquires kinetic energy equal to the product of its charge and the potential difference through which it moves.
If the electron with velocity v then moves through a uniform magnetic field perpendicular to its direction of motion, the field exerts a centripetal force perpendicular to the electron’s motion and the direction of the field. This force depends on the magnetic field strength B, the charge of the electron, and its speed
F = qvB
. The electron will follow a circular path of radius R given by
Equating the two expressions for the magnetic force,
gives
or
Substitute this expression for v
^{2}
in the equation for centripetal force and solve for m.
Procedure
As a class we will initially measure the diameter of the actual anode and cap within the glass tube. These class averages will be used as your diameters for calculating scaling factors in the table below.
To complete the experiment you will begin by using a Vernier magnetic field probe to measure the strength of the solenoid's field when its voltage is set between 6-8 volts. Remember that edge effects become noticable at the ends of a solenoid so make sure that your probe is facing down the center of its field.
Next, we will set the tube's accelerating potential to 250 volts, place the solenoid over the tube, and use the document camera to project the tube and electron beam onto the whiteboard. Each group will start by tracing an outline of the anode and cap on the whiteboard so you can scale your projection with the actual tube's dimensions. In addition, each group must outline the beam's path so that the radius can be measured. Printouts of each trial will be distributed for measuring.
Once all measurements have been taken, you will need to first calcuate a scaling factor so that you can convert your beam's radius to its appropriate size based on the dimensions of the tube. Using the fact that the charge on an electron is 1.6 x 10
^{-19}
coulombs, and your values for the solenoid's magnetic field strength, the tube's accelerating potential, and the beam scaled radius, you will calculate the mass of an electron and a percent error on how close your value is to the accepted value of 9.11 x 10
^{-31}
kilograms.
Initial Settings
solenoid voltage (V)
B-field of solenoid (T)
cathode voltage (V)
Scaling Factors (based on Method #1 in the
attached sample data and directions
)
diameter of "actual" anode (cm)
diameter of "actual" cap (cm)
"printout" diameter of anode (cm)
"printout" diameter of cap (cm)
scaling ratio of anode = actual diameter/projected diameter
scaling ratio of cap = actual diameter/projected diameter
average scaling ratio (to 3 significant digits)
Electron Beam Measurements (from printout)
"printout" chord length,
blue line
(cm)
"printout" length of the perpendicular bisector between the chord and the arc,
red line
(cm)
Calculations
Remember that all values must be expressed in MKS units: meters, teslas, coulombs, volts.
Based on trigonometry, what was the calculated radius of the electron's beam on your printout? (cm)
What is the scaled radius of the electron's beam? (m)
Based on the LHR and beam's curvature, what was the direction of the magnetic field inside the solenoid?
What was the momentum of the accelerated electrons? (kg m/sec)
What was the KE of the accelerated electrons? (J)
What was the velocity of the accelerated electrons? (m/sec)
What was your experimental mass of an electron? (kg)
What was the percent error for your experiment?
Calculate the magnetic force on the electrons using the accepted mass of an electron. (N)
The procedure for this lab was adapted from the PSSC lab on the mass of an electron using a tuning eye. The solenoid and power supply were equipment procured with the Project Physics series. The tuning tube is original PSSC equipment.
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