.. _sphx_glr_api_gallery_particle_radioactivity:

Radioactivity
---------------

The exponential decay law and Bateman's closed-form solution for
multi-species radioactive decay chains, from
:mod:`physicskit.particle.decays`.


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    <div class="sphx-glr-thumbcontainer" tooltip="Becquerel&#x27;s 1896 chance discovery -- a uranium salt spontaneously exposing a photographic plate with no external excitation -- opened radioactivity as a field; Rutherford and Soddy (1902-1903) showed the underlying law is a simple exponential,">

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  .. image:: /api/gallery/particle/radioactivity/images/thumb/sphx_glr_plot_01_decay_law_thumb.png
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  :doc:`/api/gallery/particle/radioactivity/plot_01_decay_law`

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      <div class="sphx-glr-thumbnail-title">The radioactive decay law: Becquerel, Rutherford, and Soddy</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Real radioactive samples rarely decay in one step: uranium and thorium each head long chains of successive daughters. Bateman (1910) solved the resulting linear system in closed form, giving the population of the k-th species in a chain N_1\to N_2\to\cdots\to N_n as an explicit sum of exponentials in the decay constants \lambda_1,\ldots,\lambda_n. This example builds a three-species chain with bateman_decay_chain, watches the parent deplete while an intermediate daughter first rises and then falls (it has to be produced before it can decay away), and checks total population conservation at every instant.">

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  .. image:: /api/gallery/particle/radioactivity/images/thumb/sphx_glr_plot_02_decay_chains_thumb.png
    :alt:

  :doc:`/api/gallery/particle/radioactivity/plot_02_decay_chains`

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      <div class="sphx-glr-thumbnail-title">Bateman's equations for radioactive decay chains</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/particle/radioactivity/plot_01_decay_law
   /api/gallery/particle/radioactivity/plot_02_decay_chains