PHAS0007 Experimental Physics Training

Experiment Q2-A : Determination of the  charge to mass ratio of an electron

Experiment Objectives:

To become familiar with three experiments from Q1 to Q6 that make measurements of the Planck constant, the charge to mass ratio of the electron and the Rydberg constant, which plays an essential role in the theory of spectral lines. In carrying out the experiment, you will develop skills in taking and analysing data, recording experimental procedures, estimating uncertainty and drawing conclusions.

Note, that there are two similar experimental kits (A and B) for each of the three experiments.

1.   Atomic spectra (Q1-A and Q1-B)

2.   Determination of the charge to mass ratio of an electron (Q2-A and Q2-B)

3.   Measurement of Planck’s constant (Q3-A and Q3-B)

Relevant Lecture Courses:

Atoms, Stars and the Universe PHAS0004

Waves, Optics and Acoustics PHAS0005

Introduction

During your PHAS0007 laboratory course, you will carry out three experiments. Each demonstrates a separate and fundamental concept in our current understanding of physics. Depending on which experiment you conduct, values for the Planck constant  (h), the charge to mass ratio of the electron (e/m) or the Rydberg constant (R ) will be determined and compared with accepted values.

As this is your first undergraduate physics laboratory, we will focus on developing your experimental scientific method. A full record of your experimental procedure, results and data analysis should be kept within your laboratory notebook. You will be given guidance on how to conduct and record your experimental work by the Demonstrators who will use a guide (which you will have a copy of) to help you to do this. You should   record your data in an appropriate table in your notebook. The data should also be plotted on a computer-generated graph using Python (or similar). Remember to include error bars and label the axes correctly. Finally, you should conduct a least squares fit of  the appropriate mathematical model to your data, stating the x2 value of your fit and discussing its significance. You will learn how to do this in your statistics course.

Your record-keeping will be assessed through a Digital Retrieval Test which explores the information you have stored in your lab book. You will also submit a formal report of one experiment.

Q2. Determination of the charge to mass ratio of the electron

Q2.1 Introduction

In the early 1900’s J.J.Thomson investigated how moving electrons behave in both electric and magnetic fields. From these studies he developed a balanced-field experiment where a beam of electrons is subjected to magnetic and electric fields in such a way that the forces on the electrons from each field cancel and they suffer no overall deflection. This enabled him to determine the charge to mass ratio, em, of the electron.

An electron having a charge e  moving in a uniform. electric field of intensity E is subjected to a force FE  in the direction of the field where

FE  = Ee .                                                                 (2.1)

Similarly an electron moving in a uniform magnetic field of flux density B with a velocity v at right angles to B, experiences a force FB which is perpendicular to both B and  v  of  magnitude

FB   = Bev .                                                                 (2.2)

The effect of applying electric and magnetic fields to a moving electron (as part of a

beam of electrons) is shown in figure 2.1.

Figure 2.1 The forces on moving electrons due to applied electric and magnetic fields

Provided the magnetic and electric field directions are at right angles the two forces can be anti-parallel. If the field strengths are adjusted the two forces can cancel and the electron will travel undeflected. For null deflection we require:

Ee = Bev                                                            (2.3)

In the experiment the electrons are accelerated to speed v as a result of a potential difference in an electron gun. The law of conservation of energy requires that the kinetic energy of the electron as it leaves the electron gun (determined by the voltage on the anode) must equal the change in its electrical potential energy. For an anode voltage of Va this gives the following,

2/mv2 = eVa                                                                                              (2.4)

Where m is the mass of the electron.

From equation 2.4:

m/e = 2Va/v2                                                                (2.5)

Substituting equation 2.3 into 2.5 gives:

m/e = 2Va/v2 = 2B2Va/E2                                                             (2.6)

Consequently with knowledge of the applied electric and magnetic field strengths and the accelerating voltage on the electron gun it is possible to determine the charge to mass ratio, m/e, of the electron.

Q2.2 Overview of Apparatus

The main components of the apparatus are illustrated in figure 2.1 and 2.2 and the connections to the power supplies are shown in figure 2.3.

The electron gun and deflecting plates are contained within an evacuated glass envelope. This whole unit is known as a Thompson tube.

Electric connections between the Thomson tube and the various power supplies are  achieved by connecting the supplies to the appropriately labelled inputs on the tube housing. The tube cathode is heated by a filament carrying a current driven by a 6V a.c. voltage. Electrons are emitted by the heated cathode and are accelerated through the potential difference Va towards the anode, passing through an aperture (slot) in it.

A further aperture allows a planar beam of electrons to continue into the region between the deflector plates and the magnetic field coils. Here the electron beam experiences deflections, in the directions identified in figure 2.1, due to the electric field derived from the potential difference Vp across the plates and the magnetic field generated by the current IH through the pair of coils which are in series.

An arrangement of parallel coils like this, called Helmholtz coils, has the advantage that, provided they are set a distance apart equal to their radius (in this case 6.9cm), the field can be considered to be uniform. between them. The deflector plates are also designed so that an acceptable level of field uniformity is achieved in the region of the beam path.

Note that the electron beam in the region between the coils and plates illuminates the surface of a curved luminescent screen, making its trajectory visible. The curvature of this screen enables electrons across the width of the planar beam to ‘impact’ it at different points along the whole beam’s length. As a result, the influence of the two fields can be seen across the length of the planar electron-beam path.

Figure 2.1 Schematic diagram of the e/m Thompson tube

The uniform magnetic field between the coils in this case is given by:-

B = kIH                                                                                                             (2.7)

Where k = 4.17 × 10-3 TA-1 . The current, IH,   (in mA) is given on the right hand display of the Thurlby power supply (ignore the flashing decimal points).

The plate supply voltage is supplied by the ‘in-house’ power supply and is monitored via a 1/100 potential divider via a DVM. The magnitude of the electric field E between the plates depends on the separation of the plates, d, and the potential  Vp  applied to the plates as:

E = d/Vp (2.8)

The separation of the plates, d, in the Thompson tube is 8.0mm.

Figure 2.2 Experimental apparatus used to conduct a determination of the charge to mass ratio of the elctron

Figure 2.3 Connection of the Thompson tube to power supplies and meters