FC 021
Physical Sciences
Charge to mass ratio of electrons
Lab Report
Abstract
The electron gun is used to produce a beam of electrons in an evacuated tube and the Helmholtz coils are used to change direction of the beam. The values of the kilovolt power supply and the dc power supply was adjusted to different values of voltage and current for the graph V againstI2
. The gradient of the graph was found to be 12742, then the value of m/e was found to be 3.61 × 1011C/kg, but it was about two times bigger then the theoretical value which is 1.76 × 1011C/kg. This difference could be due to the random and systematic error.
Introduction
The aim of the experiment is to use the electron gun and Helmholtz coils to calculate the value of the charge to mass ratio. In the electron gun, the cathode is being heated with an ac power supply. Electrons are then emitted from the cathode and accelerated by the anode with a high voltage, then the beam of electrons is form. as shown in Figure 1. The Helmholtz coils generate a uniform. magnetic field which is perpendicular to the electron beam, with that the resulting force of the electrons is form. and perpendicular to both magnetic field and electron beam. This will cause the electron beam to deflect into a circular form.
The resulting force of the electron beam can be found using the (Fleming’s left hand rule) with the following equation (1). (BBC – GCSE Bitesize, 2014)
Where F = force, B = magnetic field, Q = charge and v = velocity. The force of a moving charge can also be written as equation (2).
Q is also e so by rewriting equation (2), equation (3) can be formed as follow:
The electron gains kinetic energy equal to the amount of energy transferred from the electrical supply and with that the speed of the electron can be found using the equation (4). (IOP, 2014)
Where m = mass of electron, v = velocity, e = charge and V = Volt. The equation (4) can be rewritten as equation (5).
The magnitude of the magnetic field can be calculate using equation (6).
Where B = magnetic field, I = current and k is a constant which is equal to 4.231 × 10−3 (TA−1).
By substituting equation (6) and equation (5) into equation (3), the equation (7) can be form. and the charge to mass ratio can be found.
Materials & Method
The materials needed for this experiment is shown as follow:
Materials
• Ruler x 1
• Desk x 1
• Pen x 1
• Logbook x 1
• Helmholtz coil x 2
• Electron gun x 1
• Dc power supply x 1
• Kilovolt power supply x 1
• Luminescent screen x 1
• Evacuated tube x 1
Figure 2 and Figure 3 will show the Arrangement of equipment.
Method
Firstly, the kilovolt power supply was switched before the dc power supply was switched on for safety purpose.
The kilovolt power supply was adjusted to 3kV and the current of dc power supply was adjusted to 0.165A, the electron beam bended to the point (7, 1) and it was used as point (x1,y1). After that the position of the wires at the dc power supply were switched place and the value of the current was automatically changed to 0.182A, new point (7, -1.2) was formed and used as (x1,−y1).
The position of the wires were switched back to original again. The kilovolt power supply was then adjusted to 4.5kV and the current of dc power supply was adjusted to 0.503A, the electron beam bended to the point (6, 2) and it was used as point (x2,y2). After that the position of the wires at the dc power supply were switched place and the value of the current was automatically changed to 0.509A, new point (6, -1.9) was formed and used as (x2,−y2).
Then the position of the wires were switched back to original again. The electron beam was adjusted to a fixed point (4, 1) for 2kV, 2.5kV, 3kV, 3.5kV, 4kV and 0.384A, 0.427A, 0.475A, 0.512A, 0.550A. With these values the table was tabulated and the graph V against I2 were plotted using Excel. The value of m/e was then found.