If the probability that an alpha will deflect is $1/10000$, for $n$ layers, is the probability is only $1/10000n$? - Physics Stack Exchange most recent 30 from physics.stackexchange.com 2019-07-21T17:57:37Z https://physics.stackexchange.com/feeds/question/460217 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://physics.stackexchange.com/q/460217 1 If the probability that an alpha will deflect is $1/10000$, for $n$ layers, is the probability is only $1/10000n$? Alice https://physics.stackexchange.com/users/222487 2019-02-11T20:13:33Z 2019-02-12T03:20:11Z <p>I have attached a picture of an extract I read on Wikipedia (also in the AQA A-Level Physics specification and textbook). It says that 1/10000 alpha particles deflected in the alpha particle scattering experiment and therefore, the probability is 1/10000 that it will deflect (more than 90 degrees). It then goes on to say that for n layers of atoms, the probability is 1/10000n. This doesn't make sense to me. If the number of layers increases, that means the probability of deflection is getting smaller.</p> <p>Surely if there are more layers, deflection is more likely?</p> <p><a href="https://i.stack.imgur.com/BU9Yt.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/BU9Yt.png" alt="This is an image from an extract from Wikipedia on nuclear diameter"></a></p> https://physics.stackexchange.com/questions/460217/if-the-probability-that-an-alpha-will-deflect-is-1-10000-for-n-layers-is-t/460221#460221 4 Answer by BowlOfRed for If the probability that an alpha will deflect is $1/10000$, for $n$ layers, is the probability is only $1/10000n$? BowlOfRed https://physics.stackexchange.com/users/55662 2019-02-11T20:27:33Z 2019-02-11T20:27:33Z <blockquote> <p>Surely if there are more layers, deflection is more likely?</p> </blockquote> <p>If you know the probability of a single layer deflecting and you add more layers, then yes the probability of the <em>foil</em> deflecting goes up. </p> <p>We could even write something like <span class="math-container">$P_{foil} \approx P_{layer} \times \text{n}$</span></p> <p>But in the experiment, we don't know the single layer probability and we we do know the total deflection from the foil, so we change the equation: <span class="math-container">$P_{layer} \approx \frac{P_{foil}}{n}$</span></p> <p>It says that the probability of a single layer deflection goes down as the number of layers increases <em>given a constant level of detection from the foil</em></p> https://physics.stackexchange.com/questions/460217/if-the-probability-that-an-alpha-will-deflect-is-1-10000-for-n-layers-is-t/460227#460227 2 Answer by G. Smith for If the probability that an alpha will deflect is $1/10000$, for $n$ layers, is the probability is only $1/10000n$? G. Smith https://physics.stackexchange.com/users/199630 2019-02-11T20:57:25Z 2019-02-11T21:05:36Z <p>If the probability of deflection by one layer is <span class="math-container">$p$</span>, the probability of deflection by <span class="math-container">$n$</span> layers is <span class="math-container">$1-(1-p)^n$</span>. As <span class="math-container">$n$</span> goes to infinity, this goes to 1. For small <span class="math-container">$p$</span> and large <span class="math-container">$n$</span>, a good approximation is <span class="math-container">$1-e^{-pn}$</span>.</p> <p>However, for small <span class="math-container">$p$</span> and small <span class="math-container">$n$</span>, a good approximation is <span class="math-container">$pn$</span>, which is the approximation Wikipedia is using. Note that it is saying that the probability of deflection by one layer is <span class="math-container">$1/10000n$</span> and the probability of deflection by <span class="math-container">$n$</span> layers is <span class="math-container">$1/10000$</span>, not the other way around as you thought.</p>