Physics › Quantum phenomena › Collisions of electrons with atoms

Collisions of electrons with atoms

An atom will not absorb an arbitrary amount of energy. Hit it with an electron and either nothing happens, or it absorbs exactly one energy-level gap, or it loses an electron altogether. That all-or-nothing rule is what makes a fluorescent tube work, and it is where the electronvolt comes from.

Year 12AQA 3.2.2.2CIE 22.1.4, 22.4.1, 22.4.3OCR A 4.5.1(d), 5.5.2(a), 5.5.2(d)EDEXCEL 94

IN THIS TOPIC

  • Distinguish excitation from ionisation in collisions between electrons and atoms.
  • Explain how excitation and ionisation operate inside a fluorescent tube.
  • Use the electronvolt, converting between eV and joules in both directions.

COMMON MISCONCEPTION

Any collision can nudge an atom just a little.

All or nothing

The electrons in an atom occupy fixed energy levels, so an atom can only accept energy in exact level-sized amounts. A free electron colliding with one therefore has two productive options. In excitation the collision hands over exactly the gap to a higher level, promoting an atomic electron, and the incident electron flies on with the change in its pocket. In ionisation the collision supplies at least enough to free an atomic electron from the atom altogether.

Collisions with atoms: all or nothing (animated figure)excitation is all or nothingtoo small bounces off; big enough lifts a whole runggroundexcitedthe full gap or nothing
FIG. 1An atom's electron sits on the ground rung. A slow electron arrives carrying less than the gap: it bounces away with exactly what it brought, because the atom cannot accept part of a rung. A faster one carries more than enough: the bound electron jumps the full gap at the instant of impact, the projectile leaves with the change, and moments later the atom relaxes, dropping the electron back and posting the gap's worth of energy out as a single photon.

Offer the atom less than its smallest available gap and no internal excitation can occur: the collision comes out elastic, the electron bouncing off with its kinetic energy all but unchanged, since the atom, thousands of times heavier, takes only a negligible recoil. There is no such thing as slightly warming one atom's electrons.

The fluorescent tube

The standard application chains both processes together. A high pd across the tube accelerates free electrons; ionisation by collision keeps the mercury vapour supplied with those free electrons. Collisions also excite mercury atoms, which promptly de-excite and emit photons, mostly ultraviolet.

Inside a fluorescent tube: collisions excite mercury atoms, which emit UV, which the coating turns visiblefast electronmercury atomUV photonvisible lightcollision → excitation → UV emission → coating glowseach arrow is an exact energy-level gap changing hands
FIG. 2The fluorescent chain: a fast electron excites a mercury atom, the atom emits an ultraviolet photon, and the phosphor coating absorbs it and glows visibly.

Ultraviolet is no use for lighting a kitchen, so the tube's inner phosphor coating absorbs the UV photons, its own electrons climbing and then descending in smaller steps, re-emitting the energy as visible light. Every arrow in the chain is an exact energy gap changing hands.

The electronvolt

Atomic energies are absurdly small in joules, so this scale uses a unit of its own. One electronvolt is the energy gained by an electron accelerated through a pd of one volt, and 1 eV = 1.60 × 10−19 J. That definition doubles as a mental shortcut. An electron crossing 500 V gains 500 eV, with nothing to calculate.

Fluent conversion both ways is expected. Multiply by 1.60 × 10−19 to reach joules; divide to come back. The traffic is constant in this unit, because level diagrams speak eV while h and every SI formula speak joules.

WORKED EXAMPLE

Can this electron excite this atom?

An electron is accelerated from rest through 5.0 V and strikes a mercury atom whose first excited state sits 4.9 eV above the ground state. What can happen?

The electron gains exactly 5.0 eV, the accelerating pd read straight off in the natural unit, and 5.0 × 1.60 × 10−19 = 8.0 × 10−19 J.

5.0 eV clears the 4.9 eV gap, so the collision can excite the atom and the electron flies on with 0.1 eV. Accelerate the same electron through 4.5 V and it cannot excite the atom at all, because the atom takes the exact gap or takes nothing.

The excited atom then returns the 4.9 eV as a photon of frequency f = 4.9 × 1.60 × 10−19/(6.63 × 10−34) = 1.2 × 1015 Hz. That is ultraviolet, at about 250 nm, so the tube still needs its phosphor coating before it makes light you can see.

ASSESSMENT FOCUS

  • Give the definitions to the letter. Excitation moves an electron to a higher energy level, and ionisation removes it from the atom. Vague talk of “gaining energy” scores neither.
  • The fluorescent-tube story has fixed beats. Acceleration by the pd, excitation of mercury by collision, ultraviolet emission as the atom de-excites, absorption by the coating, visible re-emission. Missing the ultraviolet step is the classic dropped mark.
  • An electron accelerated through V volts gains V electronvolts, so use the shortcut and convert only when the question asks for joules. Multiply by 1.60 × 10−19 going to joules and divide coming back. An atomic process quoted at 1019 eV means the conversion ran the wrong way.
  • When a collision offers less than the smallest gap, name the outcome. The collision is elastic and the atom absorbs nothing.

CHECK YOURSELF

In a fluorescent tube, describe the energy story that turns the kinetic energy of a free electron into visible light. Name each process.

Show a hint

There are four hand-offs, and the ultraviolet step is the one candidates forget.

Show the answer

The tube's pd accelerates a free electron, giving it kinetic energy. A collision excites a mercury atom, transferring one exact level gap.

The atom de-excites almost at once, emitting the gap as an ultraviolet photon (hf equal to the gap).

The phosphor coating absorbs that ultraviolet, and its own electrons de-excite in smaller steps, emitting visible photons. Kinetic energy went in and light came out, and every hand-off along the way was an exact level gap.

Atoms accept exact gaps, or nothing.

The tube is that rule, run as a chain.

WORKBOOK

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  • Distinguish excitation from ionisation in collisions between electrons and atoms.
  • Explain how excitation and ionisation operate inside a fluorescent tube.
  • Use the electronvolt, converting between eV and joules in both directions.

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