.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/photochem/actinometry/plot_01_hatchard_parker_ferrioxalate.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_photochem_actinometry_plot_01_hatchard_parker_ferrioxalate.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_photochem_actinometry_plot_01_hatchard_parker_ferrioxalate.py:


Hatchard and Parker's ferrioxalate actinometer: counting photons chemically
=============================================================================

Every quantum yield needs the number of photons absorbed. Hatchard and
Parker (1956) introduced potassium ferrioxalate as a sensitive chemical
photon counter: light reduces Fe(III) to Fe(II) with a known quantum
yield (about 1.21 at 365 nm), and the Fe(II) is measured by the red
phenanthroline complex at 510 nm
(:func:`~chemistrykit.photochem.ferrioxalate_fe2_moles`). Dividing by the
quantum yield and the irradiation time gives the lamp's photon flux
(:func:`~chemistrykit.photochem.ferrioxalate_photon_flux`). Here
synthetic readings from a series of irradiation times are converted back
into the flux of a lamp of known output.

.. GENERATED FROM PYTHON SOURCE LINES 18-49



.. image-sg:: /api/gallery/photochem/actinometry/images/sphx_glr_plot_01_hatchard_parker_ferrioxalate_001.png
   :alt: Ferrioxalate actinometry at 365 nm
   :srcset: /api/gallery/photochem/actinometry/images/sphx_glr_plot_01_hatchard_parker_ferrioxalate_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Flux from each exposure (einstein/s): [2.804e-09 2.310e-09 2.516e-09 2.486e-09 2.492e-09]
    Flux from slope: 2.483e-09 einstein/s (true 2.500e-09)






|

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.photochem import ferrioxalate_fe2_moles, ferrioxalate_photon_flux

    q_true = 2.5e-9  # einstein/s reaching the cell (unknown to the "experimenter")
    Phi_Fe = 1.21
    V_developed = 0.010  # L after adding phenanthroline and buffer
    t = np.array([15.0, 30.0, 60.0, 90.0, 120.0])  # s

    rng = np.random.default_rng(3)
    n_fe2_true = Phi_Fe * q_true * t  # total absorption (concentrated actinometer)
    A510 = n_fe2_true * 1.11e4 / V_developed + rng.normal(0.0, 0.003, t.size)

    n_fe2 = ferrioxalate_fe2_moles(A510, V_developed)
    q_each = ferrioxalate_photon_flux(n_fe2, t, quantum_yield=Phi_Fe)
    slope = np.polyfit(t, n_fe2, 1)[0]
    q_fit = ferrioxalate_photon_flux(slope, 1.0, quantum_yield=Phi_Fe)
    print("Flux from each exposure (einstein/s):", np.array2string(q_each, precision=3))
    print(f"Flux from slope: {q_fit:.3e} einstein/s (true {q_true:.3e})")

    fig, ax = plt.subplots()
    ax.plot(t, n_fe2 * 1e9, "o", label=r"Fe$^{2+}$ from $A_{510}$")
    ax.plot(t, slope * t * 1e9, "k--", label=rf"fit: $q_p$ = {q_fit:.2e} einstein/s")
    ax.set_xlabel("Irradiation time (s)")
    ax.set_ylabel(r"Fe$^{2+}$ formed (nmol)")
    ax.set_title("Ferrioxalate actinometry at 365 nm")
    ax.legend()
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.039 seconds)


.. _sphx_glr_download_api_gallery_photochem_actinometry_plot_01_hatchard_parker_ferrioxalate.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_hatchard_parker_ferrioxalate.ipynb <plot_01_hatchard_parker_ferrioxalate.ipynb>`

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

      :download:`Download Python source code: plot_01_hatchard_parker_ferrioxalate.py <plot_01_hatchard_parker_ferrioxalate.py>`

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

      :download:`Download zipped: plot_01_hatchard_parker_ferrioxalate.zip <plot_01_hatchard_parker_ferrioxalate.zip>`


.. only:: html

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

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