Physics · Atomic and quantum physics · Grade 11

Detecting particles

How can invisible radiation be seen, counted and guarded against?

The situation

In a school physics room the teacher puts a piece of felt soaked in alcohol inside a glass vessel with a black base and places dry ice underneath. After a few minutes thin white lines appear inside the vessel and at once begin to vanish — these are the tracks of cosmic rays and natural radioactivity. Next to it a Geiger counter crackles, while a gamma spectrometer in a hospital can tell exactly which isotope is radiating. How can we “see” invisible particles, count them, measure their energy and protect ourselves from them?

Topic

Particle detection and dosimetry. Tracks in a cloud chamber, a Geiger counter and a dosimeter

Key ideas

Cloud chamber
Geiger counter
Dose: Gy and Sv

Formulas

r = \frac{p}{| q | B}, p [GeV / c] = 0.3 B [T] r [m]

The radius of a track in a magnetic field gives the momentum of the particle.

- \frac{d E}{d x} \propto \frac{z^{2} n_{e}}{v^{2}} \ln \frac{2 m_{e} v^{2}}{I}

Bethe formula: a slow, highly charged particle ionises a lot — at the end of the track there is a Bragg peak.

n = \frac{m}{1 - m τ}, σ_{N} = \sqrt{N}

Correction for the dead time $τ$ of a Geiger counter, and Poisson statistics.

I = I_{0} e^{- μ x}, μ = \frac{\ln 2}{x_{1 / 2}}

Attenuation of γ-radiation in a layer of matter; $x_{1 / 2}$ is the half-value layer.

H = w_{R} D, \dot{H} = Γ \frac{A}{r^{2}} e^{- μ x}

Equivalent dose (Sv) = radiation weighting factor × absorbed dose (Gy); dose rate of a point γ-source.

Theory

Track-forming detectors

All these detectors make use of the ionisation of matter by a charged particle. In a Wilson cloud chamber (1912) supersaturated vapour condenses into droplets on the ions: the path of the particle appears as a line of mist. In the diffusion chamber on the stage, alcohol vapour becomes supersaturated above dry ice (−78 °C). In a bubble chamber (1952) bubbles form in a superheated liquid, and in a nuclear emulsion silver grains darken. The thickness of the track shows the charge and speed of the particle, its curvature in a magnetic field shows the momentum, and its length shows the energy. Measuring track photographs is a classic lab work: in “Photo” mode you measure the radius and find the energy from $p = q B r$ .

Counting and spectrometric detectors

Geiger–Müller counter: a particle ionises the gas, an avalanche starts in the strong field, and an identical pulse is produced — it counts particles but does not know their energy; after each pulse there is a dead time of ≈ 100 µs. A scintillator (a NaI(Tl) crystal) gives a flash of light proportional to the particle's energy, which a photomultiplier tube amplifies. In semiconductor detectors (Ge, Si) ≈ 3 eV is needed for one electron–hole pair (in a gas ≈ 30 eV), so the energy resolution is tens of times better. In astronomy light is recorded on CCD arrays; infrared, ultraviolet, X-ray and gamma detectors are sent into space because the atmosphere absorbs these rays, and radio waves are received with antennas. Neutrino detectors watch for Cherenkov light in huge pools of water (Super-Kamiokande, 50 thousand t of water), and gravitational waves are detected with laser interferometers (see the “Interferometers and LIGO” experiment).

Charged particles in matter

Heavy particles (α, p) lose energy by ionising electrons: according to the Bethe formula the loss is proportional to $z^{2} / v^{2}$ , so it grows as the particle slows down and a Bragg peak forms at the end of the track. A 5.5 MeV α-particle travels ≈ 4 cm in air and ≈ 40 µm in living tissue — its range is definite. Proton therapy makes use of this: a 150 MeV proton gives up most of its energy at a depth of ≈ 16 cm in water. Electrons are light and are deflected noticeably at each collision — their track is winding (multiple scattering; in the “e⁻ + foil” mode measure the scattering angles in a thin aluminium foil). A fast electron emits bremsstrahlung (radiative) radiation near heavy nuclei: in lead above ≈ 7 MeV this is the main loss. If a particle travels faster than the speed of light in the medium ( $c / n$ ), Vavilov–Cherenkov radiation appears (in water for an electron $T > 0.26$ MeV) — the blue glow in reactor pools.

γ-radiation in matter

A photon is absorbed in three ways: the photoelectric effect (at low energy, strong in heavy materials), Compton scattering (the photon gives part of its energy to an electron) and, at $E > 1.022$ MeV, the formation of an electron–positron pair. So the intensity falls exponentially: $I = I_{0} e^{- μ x}$ . For Cs-137 (662 keV) in lead $μ \approx 1.25$ cm⁻¹, and the half-value layer is ≈ 0.55 cm (narrow beam). $μ$ depends on energy: in lead it is ≈ 2.6 at 0.4 MeV and ≈ 0.67 cm⁻¹ at 1.25 MeV (Co-60). So energy can be found by the absorption method: measure $μ$ for an unknown source and read off $E$ from the table (graph) of $μ (E)$ — try it on the “γ ?” source in “Geiger” mode. In lead $μ$ is smallest between 3 and 4 MeV, so the method gives a single value up to about 3 MeV. In the spectrum: the photopeak (complete absorption), the Compton edge $E_{C} = E - E / (1 + 2 E / m_{e} c^{2})$ (477 keV for 662 keV), and the backscatter peak of photons reflected from the surroundings (≈ 184 keV). The photoelectric and Compton effects are covered in detail in separate experiments.

Counting statistics

Radioactive decay is random, so even under identical conditions the count is different each time. When $N$ pulses are counted, the statistical error is $σ = \sqrt{N}$ and the relative error is $1 / \sqrt{N}$ : 10 000 pulses are needed for 1 % accuracy. Many measurements give a Poisson distribution (compare it in the histogram). During its dead time $τ$ the counter does not notice a new particle: the measured rate $m$ is lower than the true rate $n$ , $n = m / (1 - m τ)$ . The background (≈ 0.4 counts/s — cosmic rays and radioactivity of the surroundings) is subtracted from every result. From a point source the intensity falls according to the $1 / r^{2}$ law; β-particles are in addition absorbed in air.

Dosimetry and protection

The absorbed dose $D$ is the energy given to 1 kg of matter; its unit is the gray (1 Gy = 1 J/kg). The equivalent dose is $H = w_{R} D$ , with the unit sievert (Sv): $w_{R} = 1$ for γ, β and muons, 2 for protons, 20 for α-particles and 2.5–20 for neutrons. The effective dose, which takes the sensitivity of organs into account, is also in sieverts. A person receives on average ≈ 2.4 mSv per year from natural background. Limits: an extra 1 mSv/year for the public and 20 mSv/year for workers (averaged over 5 years). A single dose above ≈ 0.5–1 Gy causes acute radiation sickness; at small doses the cancer risk is about 5 % per Sv. **Protection: time, distance ( $1 / r^{2}$ ), shielding.** α — paper; β — a few mm of plastic or aluminium (in lead bremsstrahlung is strong); γ — lead, concrete. Neutrons are first slowed down by light nuclei (water, paraffin): ≈ 18 collisions are needed in hydrogen and ≈ 1 900 in lead.

Did you know?

The Wilson cloud chamber was invented by the Scottish physicist Charles Wilson, who received the Nobel Prize in Physics in 1927. The positron (1932) and the muon (1936) were discovered precisely in photographs from cloud chambers.
A person receives on average about 2.4 mSv of natural radiation per year; roughly half of it comes from radioactive radon gas in the air.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

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De Broglie waves — Grade 11
Rutherford's experiment — Grade 11
The atomic nucleus and binding — Grade 11
Thermonuclear fusion — Grade 11
Elementary particles — Grade 11
Spin, the Zeeman effect and MRI — Year 1
Many-electron atoms — Year 1
Bands in solids — Year 1
Schrödinger and quantum tunnelling — Year 3