Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0001 362552 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0725 1211976 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0725 1211976 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1416 4127544 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1429 4155192 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1436 4172904 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1438 4203424 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1448 4226144 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1448 4226144 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.1978 4903768 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.2013 5095920 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.2019 5116848 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.2122 5313864 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.2122 5314120 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182

Radioactive Decay and Half Life

Any radioactive atom of a particular element with a certain number of protons and neutrons has a fixed and constant probability of decaying in a certain time period, usually taken as one second. The decay constant,is a measure of this. We may write:

(1)

The expression on the left hand side is the proportion of the N atoms at the start of the time period that decay in that time period.is the probability that an individual atom decays in the that second and the negative sign means thatis decreasing, or that atoms are decaying. We can show exponential decay in more than one way. We can show a graph of mass of undecayed substance – illustrated below, number of mols,(the activity), or N against t. All these graphs will show exponential decay.

We can integrate (1) to find N in terms of t.

N in the equation above could be replaced by(for mass),(or activity),(number of mols) and would still exhibit radioactive decay.

Half Life

The half life of a radioactive substance is the time take for half of the material to decay. We can find an equation for the half lifein terms ofWhen half the material has decayed,