Radioactive Decay (Part One) – A2 Physics Revision

Decay

  • Unstable nuclei decay by emitting radiation (without external stimulus)
  • Alpha radiation is composed of helium nuclei (balls of two protons and two neutrons, with no electrons)
  • Beta radiation is the emission of electrons or positrons
  • Gamma radiation is the loss of energy only: a high-energy photon is emitted, but no protons, neutrons or electrons are lost
  • Emitting radiation changes the nucleus to a more stable state
  • (In the case of alpha emission, its position on the periodic table also changes)

By The Way

  • An alpha particle has a positive charge of 3.2×10-19 C, because it is an ion lacking two electrons
  • A beta particle has a negative charge of 1.6×10-19 C, unless it’s a positron, in which case the charge is positive
  • Positrons are the antiparticle of electrons, with the opposite properties, apart from their mass, which is the same
  • A gamma particle (photon) has no charge, and also no mass
  • Only energy is lost in gamma emission (it tends to happen when the atom rearranges into a lower energy state following alpha or beta emission)
  • Elements can have long decay chains in which they switch between several different elements and isotopes by emitting various types of radiation

Randomness and Probability

  • Radioactive decay is completely random. There’s no way to tell how long it’ll take an individual nucleus to decay
  • If you have enough nuclei, however, you can predict quite accurately how many will decay within a given time, or how long it’ll take before a certain number of them decay, for example
  • This is because radioactive decay behaves according to probability, as long as the sample size is large enough

It’s Exponential

  • The rate of change is proportional to the quantity present, because:
  • Each nuclei in the sample has the same, fixed chance of decaying each second
  • …so when there are lots of nuclei left, more will decay in a given time
  • …and when there aren’t many left, fewer will decay in the same amount of time
  • (It’s like rolling dice – each has the same chance of landing on a six, but the more you roll at once, the more sixes you’ll get each time)
  • The fixed chance of decaying in one second is the decay constant
  • The units of the decay constant are s-1 and its symbol is λ
  • (You may remember the Greek letter lambda from such equations as c=fλ for waves, where it was used to represent wavelength)

Graphs

  • Plotting the number of remaining (not decayed yet) nuclei on the y-axis against time on the x-axis should produce an exponential decay curve
  • You can call these N (number of nuclei) and t (time), to change the y=e-x equation into something useful:
  • N = N0e-λt
  • N is the nuclei remaining at time t, and N0 is how many there were originally, when t was zero
  • This can be used to work out how many nuclei will be remaining at a certain time, or, with a bit of rearranging, how long it’ll take for a certain number of nuclei to decay, for example
  • Theoretically, the exponential decay curve never reaches the x-axis, but since nuclei are a discrete quantity, there can’t be fractions of intact nuclei remaining, so eventually the number will reach zero
  • By this time, the graph will probably be a bit wobbly anyway, since the sample size will be small and randomness will be more evident
  • It can be turned into a linear natural log graph
  • The graph of ln(N) against t should have a straight line, with a gradient of -λ, which makes it a good way to find the decay constant

Data, Formulae and Relationships Booklet

  • N = N0e-λt is in the formula booklet
  • You may want to remember that ln(N/N0) = -λt for the natural log graph
  • I also mentioned c=fλ in this post. It’s in the formula booklet as v=fλ, which is more general because it also applies to waves which don’t travel at the speed of light
  • The charge on an electron is in the formula booklet
  • The charge on an alpha particle isn’t in the formula booklet. It’s likely to be given in the question if you need it, but if it isn’t, just remember that an alpha particle is a helium nucleus with two protons, so it has two missing electrons’ worth of net charge

Be sure to read the second part of this post.

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About Matt

I like writing, filmmaking, programming and gaming, and prefer creating media to consuming it. On the topic of consumption, I'm also a big fan of eating.
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