https://ejercicios-fyq.com/ Ejercicios Resueltos, Situaciones de aprendizaje y VÍDEOS de Física y Química para Secundaria y Bachillerato es SPIP - www.spip.net https://ejercicios-fyq.com/local/cache-vignettes/L144xH25/siteon0-da713.png?1758361862 https://ejercicios-fyq.com/ 25 144 https://ejercicios-fyq.com/Calculation-of-the-half-life-of-a-radioactive-element-8299 https://ejercicios-fyq.com/Calculation-of-the-half-life-of-a-radioactive-element-8299 2024-09-04T03:49:25Z text/html es F_y_Q Radioactive activity Nuclear physics Half-life period Radioactive SOLVED <p>A sample of 300 grams of a radioactive element remains 18.75 grams after 24 hours. Calculate the half-life.</p> - <a href="https://ejercicios-fyq.com/Nuclear-physics-282" rel="directory">Nuclear physics</a> / <a href="https://ejercicios-fyq.com/Radioactive-activity" rel="tag">Radioactive activity</a>, <a href="https://ejercicios-fyq.com/Nuclear-physics" rel="tag">Nuclear physics</a>, <a href="https://ejercicios-fyq.com/Half-life-period" rel="tag">Half-life period</a>, <a href="https://ejercicios-fyq.com/Radioactive" rel="tag">Radioactive</a>, <a href="https://ejercicios-fyq.com/SOLVED" rel="tag">SOLVED</a> <div class='rss_texte'><p>A sample of 300 grams of a radioactive element remains 18.75 grams after 24 hours. Calculate the half-life.</p></div> <hr /> <div <div class='rss_ps'><p>You must use the decay law, but referring to the mass of the substance: <br/> <br/> <img src='https://ejercicios-fyq.com/local/cache-TeX/a7837110049bd6922afc8fc688568fce.png' style="vertical-align:middle;" width="149" height="23" alt="\color[RGB]{2,112,20}{\bm{m = m_0\cdot e^{- \lambda\cdot t}}}" title="\color[RGB]{2,112,20}{\bm{m = m_0\cdot e^{- \lambda\cdot t}}}" /> <br/> <br/> Solving for the value of <img src='https://ejercicios-fyq.com/local/cache-TeX/c6a6eb61fd9c6c913da73b3642ca147d.png' style="vertical-align:middle;" width="18" height="40" alt="\lambda" title="\lambda" />, you get: <br/> <br/> <img src='https://ejercicios-fyq.com/local/cache-TeX/d4cf9a033527abef837296344e1fafe8.png' style="vertical-align:middle;" width="302" height="57" alt="- \lambda = \frac{ln \frac{18.75\ \cancel{g}}{300\ \cancel{g}}}{86\ 400\ s} = \color[RGB]{0,112,192}{\bm{3.2\cdot 10^{-5}\ s^{-1}}}" title="- \lambda = \frac{ln \frac{18.75\ \cancel{g}}{300\ \cancel{g}}}{86\ 400\ s} = \color[RGB]{0,112,192}{\bm{3.2\cdot 10^{-5}\ s^{-1}}}" /> <br/> <br/> You know that radioactive activity is related to the half-life and this to the half-life period: <br/> <br/> <img src='https://ejercicios-fyq.com/local/cache-TeX/1370bc65dcc71d914e193ccf3b8e984b.png' style="vertical-align:middle;" width="90" height="65" alt="\left \lambda = \frac{1}{\tau} \atop \tau = \frac{t_{1/2}}{ln\ 2} \right \}" title="\left \lambda = \frac{1}{\tau} \atop \tau = \frac{t_{1/2}}{ln\ 2} \right \}" /> <br/> <br/> Substituting and solving: <br/> <br/> <p class="spip" style="text-align: center;"><img src='https://ejercicios-fyq.com/local/cache-TeX/711305399e214577f0e8adc0477070ef.png' style="vertical-align:middle;" width="229" height="45" alt="t_{1/2} = \frac{ln\ 2}{\lambda} = \fbox{\color[RGB]{192,0,0}{\bf 21\ 661\ s}}" title="t_{1/2} = \frac{ln\ 2}{\lambda} = \fbox{\color[RGB]{192,0,0}{\bf 21\ 661\ s}}" /></p> <br/> Expressed in hours, it will be: <br/> <br/> <p class="spip" style="text-align: center;"><img src='https://ejercicios-fyq.com/local/cache-TeX/ab3616446fa7cd3f753a71f3383d802a.png' style="vertical-align:middle;" width="299" height="45" alt="t_{1/2} = 21\ 661\ \cancel{s}\cdot \frac{1\ h}{3\ 600\ s} = \fbox{\color[RGB]{192,0,0}{\bf 6\ h}}" title="t_{1/2} = 21\ 661\ \cancel{s}\cdot \frac{1\ h}{3\ 600\ s} = \fbox{\color[RGB]{192,0,0}{\bf 6\ h}}" /></p> </math></p></div>