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| 1. |
Write a note on radioactivity. |
| Answer» <html><body><p></p>Solution :<a href="https://interviewquestions.tuteehub.com/tag/law-184" style="font-weight:bold;" target="_blank" title="Click to know more about LAW">LAW</a> of radioactive decay : <br/> At any instant t , the number of decays per unit time, called rate of decay `((dN)/(dt))` is proportional to the number of nuclei (N) at the same instant. <br/> `(dN)/(dt) infty N` <br/> By introducing a proportionality constant, the relation can be written as<br/> `(dN)/(dt) = lambda N` <br/> Here proportionality constant `lambda` is called decay constant which is different for differentradioactive sample and the negative sign in the equation implies that the N is decreasing withtime. By rewriting the equation (1) we get <br/> `dN = lambda Ndt`...(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)<br/> Here dN represents the number of nuclei decaying in the interval dt. Let <a href="https://interviewquestions.tuteehub.com/tag/us-718298" style="font-weight:bold;" target="_blank" title="Click to know more about US">US</a> assume that at time `t = 0` s, the number of nuclei <a href="https://interviewquestions.tuteehub.com/tag/present-1163722" style="font-weight:bold;" target="_blank" title="Click to know more about PRESENT">PRESENT</a> in the radioactive sample is `N_(0)`. By integratingthe equation (2), we can calculate the number of underdecayed nuclei N at any time t. <br/> From equation (2) we get, <br/> `(dN)/(N) = - lambda dt` ....(3) <br/> `int_(N_(0))^(N) (dN)/(N) = - int_(0)^(t) lambdadt` <br/> `[In N]_(N_(0))^(N) = - lambda t` <br/> `In [(N)/(N_(0))] = - lambdat` <br/> Taking exponentials on both <a href="https://interviewquestions.tuteehub.com/tag/sies-3028721" style="font-weight:bold;" target="_blank" title="Click to know more about SIES">SIES</a>, we get <br/> `N = N_(0)e^(-lambda t)` ...(4) <br/>` [Note : e^(Inx) = e^(y) Rightarrow x = e^(y)]` <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/FM_PHY_XII_V02_C08_E01_052_S01.png" width="80%"/> <br/> Equation (4) is called the law of radioactive decay. Here N denotes the number of underdecayednuclei present at any time t and `N_(0)` denotes the number of nuclei at initial time t = 0. Note that the number of atoms is decreasing exponentially over the tie. This implies that the time taken for all the radioactive nuclei to decay will be infinite. Equation(4) is plotted. We can also define another useful quantity called activity (R) or decay rate whichnumber of nuclei decayed per second and it is denoted as `R = |(dN)/(dt)|` <br/> Note : that activity R is a positive quantity. From equation (4), we get <br/> `R = |(dN)/(dt)| = lambda N_(0)e^(-lambdat)` ....(5) <br/> `R = R_(0)e^(-lambdat)` ...(6) <br/> where `R_(0) = lambda N_(0)` <br/> The equation (6) is also equivalent to radioactive law of decay. Here `R_(0)` is the activity of thesample at `t = (0) ` and R is the activity of the sample at any time t. From equation(6), activityalso shows exponential decay behavior. The activity R also can be expressed in terms of number of undecayed atoms present at any time t, From equation(6), since `N = N_(0)e^(-lambdat)` wewrite ` <br/> R = lambda N`...(7)<br/> Equation (4) implies that the activity at any time t is equal to the product of decay constant and number of undecayed nuclei at the same time t. Since N decreases over time, R also decreases.</body></html> | |