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href="../368/nuclear-physics.html">Nuclear physics</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">AHL Nuclear radius</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 10 minutes"><i class="fa fa-clock-o"></i> 10'</span> </ol> <article id="main-article"> <p><img alt="" src="../../quantum/neutrino.jpg" style="float: left; width: 150px; height: 203px;">The structure of matter can be investigated using scattering experiments, both of whole nuclei and of electrons.</p> <p>Knowledge of the radius of one nuclear isotope can be used to calculate the radius of any other.</p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div>There are two techniques to measure the radius of a nucleus.</div> <div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Rutherford scattering</p> </div> </div> <div class="panel-body"> <div> <p>The Rutherford scattering experiment can be used to determine the radius of a nucleus.</p> <p style="text-align: center;"><img alt="" src="../../quantum/588px-rutherford_scattering.svg.png" style="width: 400px; height: 251px;"></p> <p>As the angle is increased from the initial beam direction, the number of alpha particles decreases. This is due to the repulsive elecric forces between the alpha particles and the nucleus, which increases in magnitude with shorter distances. The scattering distribution can be predicted by an equation devised by Rutherford (not required for the course).</p> <p style="text-align: center;"><img alt="" src="../../quantum/rutherford-s_scattering_equation_illustrated.svg" style="width: 250px; height: 185px;"></p> <p>In high energy scattering experiments, the alpha particles move close enough to the nucleus to be within the range of the strong nuclear force. This means that the scattering distribution is affected. The point at which the Rutherford scattering equation no longer applies can be used to find the effective nuclear radius. </p> <p style="text-align: center;"><img alt="Eisberg, R. M. and Porter, C. E., Rev. Mod. Phys. 33, 190 (1961)" src="../../quantum/ruthdepart.png" style="width: 300px; height: 325px;"></p> <h6 style="text-align: center;">Eisberg, R. M. and Porter, C. E., Rev. Mod. Phys. 33, 190 (1961)</h6> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Electron diffraction</p> </div> </div> <div class="panel-body"> <div> <p>An alternative method for finding the nuclear radius uses the diffraction of electrons and the angle of the first minimum intensity in the scattering pattern:</p> <ul> <li>Electrons may interact with matter as a wave when the nucleus is comparable in size to the de Broglie wavelength (<a href="../1134/wave-particle-duality.html" title="Wave particle duality">Wave particle duality</a>)</li> <li>The diffraction pattern around a spherical object leads to an approximate equation for the angle of the first minimum intensity in the scattering pattern: <span class="math-tex">\(\sin\theta\approx{\lambda\over D}\)</span>, where <span class="math-tex">\(D\)</span> is the nuclear diameter. The small angle approximation is usually not appropriate.</li> </ul> <p>Electron microscopes are more effective than optical microscopes for imaging small objects due to the small wavelengths that can be achieved.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <p>The strong nuclear force is short range; unlike gravitation, the magnitude of force does not vary as an inverse square law. Nuclear density is approximately the same for all nuclei. The consequence is that the radius of any nucleus is related only to the number of nucleons:</p> <p style="text-align: center;"><span class="math-tex">\(R=R_0A^{1\over 3}\)</span></p> <ul> <li><span class="math-tex">\(R\)</span> is the radius of a nucleus (m)</li> <li><span class="math-tex">\(R_0\)</span> is a constant (m)</li> <li><span class="math-tex">\(A\)</span> is the number of nucleons</li> </ul> <p>The only macroscopic objects with the same density as nuclei are neutron stars.</p> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-has-colored-body panel-has-border panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Nuclear energy levels</p> </div> </div> <div class="panel-body"> <div> <p>Just like electrons, the nucleus has energy levels for different excited states. Experimental evidence for these nuclear energy levels is the specific energies of gamma photons during radioactive decay.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Neutrino</p> </div> </div> <div class="panel-body"> <div> <p>The neutrino is a fundemental particle in the lepton family. Electron neutrinos (<span class="math-tex">\(\nu_e\)</span>), muon neutrinos (<span class="math-tex">\(\nu_\mu\)</span>) and tau neutrinos (<span class="math-tex">\(\nu_\tau\)</span>) are affected by the weak nuclear force. Their mass and charge are zero (thus, their interactions with matter are limited) and their spin is <span class="math-tex">\(1\over 2\)</span>. Neutrinos also have antiparticles, antineutrinos.</p> <p>Neutrinos were discovered when beta particle energies were measured following <span class="math-tex">\(\beta^-\)</span> decay. The particles had a range of energies, which should not have been the case for just one particle from a nucleus.</p> <p style="text-align: center;"><img alt="" src="../../quantum/beta.jpg" style="width: 300px; height: 210px;"></p> <p>Instead, the neutrino was consuming some of the energy, but was undetected in isolation.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <p> </p> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p><em>Use flashcards to practise your recall.</em></p> <div class="tib-flashcard"><a class="show-flashcards btn btn-success btn-xs-block btn-block " data-levels="3" data-mode="" data-topics="1023" data-subject-id="6" data-n-flashcards="5" style="text-align:center">Show flashcards</a></div><hr> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="1152"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>AHL Nuclear radius</strong> have you understood?</p><div class="slider-container text-center"><div id="self-assessment-slider" class="sib-slider self-assessment " data-value="1" data-percentage=""></div></div> <label class="label-lg">My notes</label> <textarea name="page-notes" class="form-control" rows="3" placeholder="Write your notes here..."></textarea> </div> <div class="panel-footer text-xs-center"> <span id="last-edited" class="mb-xs-3"> </span> <div class="actions mt-xs-3"> <button id="save-my-progress" type="button" class="btn btn-sm btn-primary text-center btn-xs-block"> <i class="fa fa-fw fa-floppy-o"></i> Save </button> </div> </div></div> <div id="modal-feedback" class="modal fade" tabindex="-1" role="dialog"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <h4 class="modal-title">Feedback</h4> <button type="button" class="close hidden-xs hidden-sm" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> </div> <div class="modal-body"> <div class="errors"></div> <p><strong>Which of the following best describes your feedback?</strong></p> <form method="post" style="overflow: hidden"> <div class="form-group"> <div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Recommendation"> Recommend</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Problem"> Report a problem</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Improvement"> Suggest an improvement</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Other"> Other</label></div> </div> <hr> <div class="row"> <div class="col-md-6"> <div class="form-group"> <label for="feedback-name">Name</label> <input type="text" class="form-control" name="feedback-name" placeholder="Name" value=" "> </div> </div> <div class="col-md-6"> <div class="form-group"> <label for="feedback-email">Email address</label> <input type="email" class="form-control" name="feedback-email" placeholder="Email" value="@airmail.cc"> </div> </div> </div> <div class="form-group"> <label for="feedback-comments">Comments</label> <textarea class="form-control" name="feedback-comments" style="resize: vertical;"></textarea> </div> <input type="hidden" name="feedback-ticket" value="082b9c9c4ae3624d"> <input type="hidden" name="feedback-url" value="https://studyib.net/physics/page/1152/ahl-nuclear-radius"> <input type="hidden" name="feedback-subject" value="6"> <input type="hidden" name="feedback-subject-name" value="Physics"> <div class="pull-left"> </div> </form> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary btn-xs-block feedback-submit mb-xs-3 pull-right"> <i class="fa fa-send"></i> Send </button> <button type="button" class="btn btn-default btn-xs-block m-xs-0 pull-left" data-dismiss="modal"> Close </button> </div> </div> </div></div> <div id="fc-viewer" class="modal fade modal-flashcard" tabindex="-1" role="dialog"><div class="modal-dialog" role="document"><div class="modal-content"><div class="modal-header" style="background-color: #fafafa;"><div class="row" style="width: 100%;"><div class="col-md-12 tags-heading"><div style="display: flex; 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