Lab in a Box Measuring the e/m ratio

Transcription

1 Safety Precautions All the signal voltages are small and harmless. The mains voltages in the mains powered equipment is dangerous but is screened in normal use. The fine beam tube requires dangerous contact voltages up to 300 V. Dangerous contact voltages are therefore present at the connection panel of the holder and at the Helmholtz coils when the fine beam tube is in operation. only use the supplied safety connecting leads switch off all power supplies before altering the setup do not switch on power supplies before the circuit is fully assembled do not touch the setup, particularly the Helmholtz coils, during operation The fine beam tube is an evacuated glass vessel and presents a danger of implosion. do not subject the fine beam tube to mechanical stresses do not remove the tube from its holder take care with the plug at the glass base

2 Principles The mass m of the electron is hard to come by experimentally. It is easier to determine the charge to mass ratio e/m, from which the mass m can be calculated if the elementary charge e is known. An electron moving at velocity v perpendicularly to a homogeneous magnetic field B, is subject to the Lorentz force F = evb which is perpendicular to the velocity and to the magnetic field. As a centripetal force it forces the electron into an orbit of radius r (see Fig. 1), thus In the experiment, the electrons are accelerated in a fine beam tube by a potential V. The resulting kinetic energy is ev = ½ mv 2 Thus, by substituting for the velocity v, the charge to mass ratio of the electron is e/ m = 2V / (Br) 2

3 Experiment: Part 1 The fine beam tube contains hydrogen molecules at low pressure, which are caused to emit light through collisions with electrons. This makes the orbit of the electrons indirectly visible, and their orbit radius r can be directly measured with a ruler. The magnetic field B is generated by a pair of Helmholtz coils and is proportional to the current I in the coils: B = ki. Question Why are Helmholtz coils used? Ask a demonstrator if you are not sure. So the ratio e/ m = 2V / (kir) 2 The proportionality factor k has been determined previously and recorded for your apparatus. The apparatus should already be connected. If not, ask a demonstrator to connect the leads. Turn all the dials to zero and switch on the power. Set the beam potential to V = 250 V (do not go higher than this). Adjust the 50 V supply to give a narrow, well-defined electron beam with clear edge definition. Adjust the DC power supply of the Helmholtz coils and look for the current I at which the electron beam is deflected into a closed orbit. Use the sliders and mirrors to measure the radius of the orbit. This exploits the parallax effect. Move the left slide so that its inner edge, mirror image, and the escape aperture of the electron beam all lay on the same line of sight. Now move the right slide so that its inner edge, mirror image, and the right hand side of the circular electron beam orbit all lay on the same line of sight. Compare the circuit diagram on the apparatus with what is connected, and determine how you can vary and measure the beam potential, V,and the Helmholtz coil current, I. Thus you can measure the diameter of the orbit to find the radius. From these measurements, use the formula for V to calculate e/m. Remember that there will be an uncertainty on V, I, k and r. Which has the highest uncertainty? Estimate the uncertainty in the measurement.

4 Results V=. I =. r =.. k =.. Accepted value for e/m= 1.76X Ckg -1 Attention Before you pass this point a demonstrator must discuss your results with you.

5 Experiment: Part 2 The dependence of the accelerating potential V and the current I can be found by rearranging the equation for e/m and substituting for B: V= ( e/ m ) 0.5 k 2 r 2 x I 2 Next, you will use a graphical method that should improve your measurement of e/m and its uncertainty. Position the left slide to align with the escape aperture, as before. Now set the right slide so that the inside edges are separated by 80 mm. Sight the inside edge of the right slide, align it with its mirror image, and adjust the coil current I until the electron beam runs tangentially along the slide edge covering the mirror image. Reduce the acceleration potential V in steps of 10 V down to 150 V, and adjust the coil current I so that the orbit of the electron beam has a diameter of 80 mm. Record the values of V, I,. From a suitable plot, determine the value of e/m. (Remember that the theory predicts that V is proportional to I 2.) Question Compare your results for e/m. Do they agree with each other. The graphical method should give a better result. Does it? Pd/ V Current/ A I 2 / A

6 Risk Assessment Task: Laboratory demonstrations of determining the specific charge on an electron Department Physics Assessment ID Assessor Phil Furneaux Date of assessment Authorised by Review date Step 1 List significant hazards Step 2 who might be harmed Step 3 determine appropriate controls Step 4 make it happen Electric shock From the plug to the power supply Person setting up experiment Do not turn on plug switch until plus is safely plugged into socket procedure Damage to equipment The apparatus will only be used under supervision of a demonstrator supervision Glass discharge tube is at low pressure so may implode Experimenter The tube should not be moved while the experiment is being performed. The apparatus should only be moved in its protective box. Schools might prefer tpo have a protective Perspex screen in front of the tube. procedure Electric Shock from high voltage Experimenter All the connections to the apparatus are made by the teacher following the instructions so no pupil should touch the wires procedure