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Cathode rays and the electron gun
A few kilovolts across a low-pressure gas produces cathode rays, which travel in straight lines and deflect in fields as negative particles do. An electron gun supplies the same particles more cleanly, by thermionic emission from a heated filament in a vacuum. The speed of the emerging beam follows from eV = ½mv².
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Cathode rays and the electron, part 1 of 2. Part 2 is The specific charge of the electron.
Builds on Current, charge and potential difference.
IN THIS TOPIC
- Describe how cathode rays are produced in a discharge tube.
- Explain thermionic emission, and how an electron gun turns it into a beam.
- Use eV = ½mv² for an electron accelerated from rest.
COMMON MISCONCEPTION
An electron gun works just as well with air left in the tube.
An electron gun needs a vacuum: with air in the tube the beam electrons collide with gas molecules and are scattered or absorbed within millimetres. The residual-gas glow is how cathode rays were noticed, but a working gun pumps the air out.
Glows in a tube
Seal a gas at very low pressure into a glass tube, put several thousand volts across two electrodes, and the tube glows. Nineteenth-century physicists found that the glow traces something streaming from the negative electrode, the cathode, and named the something cathode rays before anyone knew what they were. The mechanism runs in stages. The pd first ionises some of the remaining gas. Positive ions then strike the cathode and knock particles out of it, and those particles accelerate away towards the anode, exciting the gas they pass through so that it glows.
Cathode rays travel in straight lines and are deflected by electric and magnetic fields in the direction expected for negatively charged particles. The same rays are produced using different cathode materials and gases, indicating a common constituent of matter. Their sharp shadows are the evidence for the straight-line travel, and the direction of the deflection is the evidence for the negative charge.
The electron gun
The discharge tube is a messy source. Every experiment that follows uses a clean one, thermionic emission. Heat a metal filament and its free electrons gain enough kinetic energy to escape the surface, much as molecules evaporate from a liquid. Place a positive anode nearby in a vacuum and the escaped electrons accelerate towards it. Drill a hole in the anode and a narrow, fast beam sails through. That arrangement is an electron gun.
The vacuum is not incidental. The discharge tube needs its trace of gas, because the glow is the gas being excited; the gun needs none of it, and any gas left in the tube would scatter the beam, as electrons collide with molecules and lose energy instead of arriving together at one speed.
The beam's speed comes straight from the work-energy idea. An electron of charge e falling through a pd V has work eV done on it, and starting from next to nothing, all of it becomes kinetic energy:
WORKED EXAMPLE
The speed out of the gun
An electron gun accelerates electrons from rest through 2500 V. Calculate the speed of the emerging beam (e = 1.60 × 10−19 C, me = 9.11 × 10−31 kg).
eV = ½mv2, so v = = √(2 × 1.60 × 10−19 × 2500 / (9.11 × 10−31)).
v = 3.0 × 107 m s−1. A tenth of the speed of light, from a bench-top supply.
Remember this fraction: it returns in the relativity lessons, which test whether this formula still holds at high speed.
GUIDED PRACTICE
The energy first, then the speed
An electron gun runs at 620 V. Find the kinetic energy an electron gains crossing it, in joules, and its speed leaving the anode hole (e = 1.60 × 10−19 C, me = 9.11 × 10−31 kg).
Show the working
The energy needs no rearranging at all: Ek = eV = 1.60 × 10−19 × 620 = 9.9 × 10−17 J.
Then v = √(2Ek/m) = √(2 × 9.9 × 10−17 / (9.11 × 10−31)) = 1.5 × 107 m s−1. Five per cent of light speed, from a pd under three times the mains voltage.
Neither the tube nor the gun identifies the particles. Because every cathode material and every gas produces identical rays, the identification has to come from a quantity measured on the beam itself, and the quantity available is its charge-to-mass ratio.
Thomson and the specific charge has moved to the next part of this lesson.
ASSESSMENT FOCUS
- Give the discharge-tube mechanism in order. Low-pressure gas, kilovolt pd, ionisation, positive ions striking the cathode, particles released and accelerated towards the anode, gas glowing along the path.
- Thermionic emission is one sentence. Electrons in a heated metal gain enough kinetic energy to escape its surface. The word "heated" carries the mark, so do not write "electrons are released from the filament" and stop there.
- eV = ½mv2 assumes the electron starts from rest in a vacuum. State that assumption, and quote the emerging speed to two significant figures.
- The vacuum can carry a mark of its own. Gas in the gun would scatter the beam, electrons losing energy in collisions with molecules; the discharge tube needs its trace of gas to glow, and the gun needs none of it.
CHECK YOURSELF
An electron gun accelerates electrons from rest through 850 V. Calculate the kinetic energy each electron gains and the speed of the emerging beam, and explain why the gun is operated in a vacuum.
Show a hint
The energy is eV directly; the speed follows from setting it equal to ½mv².
Show the answer
Ek = eV = 1.60 × 10−19 × 850 = 1.4 × 10−16 J.
v = = √(2 × 1.36 × 10−16 / (9.11 × 10−31)) = 1.7 × 107 m s−1.
In a gas the electrons would collide with molecules, scattering the beam and spreading its energy, so a narrow single-speed beam only exists once the air is pumped out.
A discharge tube glows because ions freed by the pd strike the cathode and knock out particles that stream towards the anode.
Thermionic emission boils electrons off a hot filament, and eV = ½mv² sets the speed the anode pd delivers.
WORKBOOK
Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.
Or read them with their mark schemes on the cathode rays and the electron gun questions page.
USED LATER IN
CHECK YOUR PROGRESS
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- Describe how cathode rays are produced in a discharge tube.
- Explain thermionic emission, and how an electron gun turns it into a beam.
- Use eV = ½mv² for an electron accelerated from rest.
Open the full revision checklist to track your progress across the whole unit.