.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/volcanology/plot_02_rutherford_soddy_decay_law.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_volcanology_plot_02_rutherford_soddy_decay_law.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_volcanology_plot_02_rutherford_soddy_decay_law.py:


Rutherford and Soddy's decay law (1902)
=======================================

Rutherford and Soddy found that the activity of thorium emanation (radon-220)
falls by half every minute or so, whatever its temperature or chemistry, and
concluded that radioactivity is the spontaneous transformation of one element
into another at a fixed fractional rate. Decay is exponential, so a straight
line on a logarithmic plot and its slope gives the half-life.

.. GENERATED FROM PYTHON SOURCE LINES 11-34



.. image-sg:: /api/gallery/volcanology/images/sphx_glr_plot_02_rutherford_soddy_decay_law_001.png
   :alt: Half lost every 55.6 s, Straight line, half-life 55.6 s
   :srcset: /api/gallery/volcanology/images/sphx_glr_plot_02_rutherford_soddy_decay_law_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.volcanology import decay_constant, parent_fraction

    half_life = 55.6  # s, radon-220
    time = np.linspace(0, 400, 81)
    remaining = parent_fraction(decay_constant(half_life), time)
    slope = np.polyfit(time, np.log(remaining), 1)[0]
    assert np.isclose(np.log(2) / -slope, half_life)
    assert np.isclose(parent_fraction(decay_constant(half_life), 2 * half_life), 0.25)

    fig, (left, right) = plt.subplots(1, 2, figsize=(10, 4))
    left.plot(time, remaining)
    for n in range(1, 5):
        left.plot(n * half_life, 0.5**n, "ko", ms=4)
    left.set(xlabel="time [s]", ylabel="fraction of radon-220 left", title="Half lost every 55.6 s")
    right.semilogy(time, remaining)
    right.set(xlabel="time [s]", ylabel="fraction left (log scale)", title=f"Straight line, half-life {np.log(2) / -slope:.1f} s")
    fig.tight_layout()

    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.246 seconds)


.. _sphx_glr_download_api_gallery_volcanology_plot_02_rutherford_soddy_decay_law.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/volcanology/plot_02_rutherford_soddy_decay_law.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_rutherford_soddy_decay_law.ipynb <plot_02_rutherford_soddy_decay_law.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_02_rutherford_soddy_decay_law.py <plot_02_rutherford_soddy_decay_law.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_rutherford_soddy_decay_law.zip <plot_02_rutherford_soddy_decay_law.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_