What is Rutherford scattering: Definition and 54 Discussions

Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction. It is a physical phenomenon explained by Ernest Rutherford in 1911 that led to the development of the planetary Rutherford model of the atom and eventually the Bohr model. Rutherford scattering was first referred to as Coulomb scattering because it relies only upon the static electric (Coulomb) potential, and the minimum distance between particles is set entirely by this potential. The classical Rutherford scattering process of alpha particles against gold nuclei is an example of "elastic scattering" because neither the alpha particles nor the gold nuclei are internally excited. The Rutherford formula (see below) further neglects the recoil kinetic energy of the massive target nucleus.

The initial discovery was made by Hans Geiger and Ernest Marsden in 1909 when they performed the gold foil experiment in collaboration with Rutherford, in which they fired a beam of alpha particles (helium nuclei) at foils of gold leaf only a few atoms thick. At the time of the experiment, the atom was thought to be analogous to a plum pudding (as proposed by J. J. Thomson), with the negatively-charged electrons (the plums) studded throughout a positive spherical matrix (the pudding). If the plum-pudding model were correct, the positive "pudding", being more spread out than in the correct model of a concentrated nucleus, would not be able to exert such large coulombic forces, and the alpha particles should only be deflected by small angles as they pass through.

However, the intriguing results showed that around 1 in 20000 alpha particles were deflected by very large angles (over 90°), while the rest passed through with little deflection. From this, Rutherford concluded that the majority of the mass was concentrated in a minute, positively-charged region (the nucleus) surrounded by electrons. When a (positive) alpha particle approached sufficiently close to the nucleus, it was repelled strongly enough to rebound at high angles. The small size of the nucleus explained the small number of alpha particles that were repelled in this way. Rutherford showed, using the method outlined below, that the size of the nucleus was less than about 10−14 m (how much less than this size, Rutherford could not tell from this experiment alone; see more below on this problem of lowest possible size). As a visual example, Figure 1 shows the deflection of an alpha particle by a nucleus in the gas of a cloud chamber.
Rutherford scattering is now exploited by the materials science community in an analytical technique called Rutherford backscattering.

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  1. jmfrank63

    I Is the Rutherford model invalid due to a violation of Gauss's Law?

    Our current model of the atom is still based on the original publication of Rutherford. However, this publication is clearly invalid. I am not talking about inaccurate. I am using the word invalid, and that is for a reason. People have often criticized historic publications, one example is...
  2. G

    Modelling Rutherford Scattering - in the school lab

    Hi, New to the forum here! I'm teaching age 16-18 physics in the UK. I was wondering if anyone in here might have experience using equipment that looks like this: https://www.eiscolabs.com/products/alpha-scattering It's a physical analogue of Rutherford's famous experiment: roll ball bearings...
  3. C

    Rutherford Scattering of an Alpha Particle

    I have the equation but I am unsure of what my r min would be. Is it the sum of the radii or the difference? I am also confused on what z1 would be. I am fairly sure z2 is the atomic number of Fe(26) but I am unsure of this as well. Edit: I just read that z1 could be 2, is this correct?
  4. jjson775

    What is the formula for calculating electrical potential?

    V = Ke x q/r 2x 1.602x10^-19 = 8.99 x 10^9 x (79x1.602x10^-19)/r
  5. U

    Question on a textbook statment on Rutherford Scattering

    The experimental observation of finding very few alpha particles scattered through large angles (>90) - I thought this would have inferred that the positive charge of the core of the atom (which we now come to know as the nuclei) must have been great in order greatly deflect alpha particles...
  6. R

    B A doubt on Rutherford's Scattering experiment

    Please refer to the image attached for the question.thanks.
  7. R

    Rutherford scattering with Coulomb cutoff

    Hello, I am reading a section in Jackson discussing classical Rutherford scattering, and he mentions incorporating a cutoff in the Coulomb interaction in order to model electric screening. I am trying to understand how he applies this, as described below. The set up is basically the classic...
  8. T

    What is the necessary correction factor for Rutherford scattering in 3D?

    Homework Statement So I recently carried out an experiment for Rutherford scattering. From my lab script is states the following 'Recording the scattering rate as function of angle In order to compare your results with “Rutherford’s scattering formula”, you must first make a correction for the...
  9. K

    Rutherford scattering and momentum

    I read from a text that Rutherford found out that all the mass must be concentrated in the middle of the atom due to fast-moving alpa ( high momentum) is deflected back at 180 degrees. I am wondering if there is going to be no contact collision due to the the kinetic energy being converted...
  10. TheSodesa

    Maximum change in the kinetic energy of a particle

    Homework Statement Show that the largest possible change in the kinetic energy , ##\Delta E_{kin}##, of a particle of mass ##m## running into another particle of mass ##M## at rest in the lab coordinate system is \Delta E_{kin} = \frac{-4AE_{kin}}{(1+A)^{2}}, where ##A = \frac{M}{m}##...
  11. lippyka

    Rutherford Scattering: Finding Cross Section & Solid Angle

    Hi I am revising for an exam and am a bit confused with Rutherford Scattering - Finding the cross section (is the cross section different to the differential cross section?) - Finding the solid angle. So here is a past question: A beam of 6MeV alpha particles is incident on a platinum foil. A...
  12. A

    Derivation of Rutherford Scattering - angular momentum

    Homework Statement I am trying to show that as the alpha particle is being scattered, the angular momentum magnitude at point M is m r^2 \frac{d \phi}{dt}. Diagram: Homework Equations Linear Momentum: ##\vec L = \vec r \times \vec p ## Repulsive Coulomb Force: ##\vec F = \frac{k 2Ze^2}{r^2}...
  13. S

    Calculating the Cross Section for Rutherford Scattering

    Homework Statement Calculate the cross section for the scattering of a 10 MeV alpha particle by a gold nucleus (Z=79, A=197) through an angle greater than a) 10 degrees b) 20 degrees c) 30 degrees. Neglect Nuclear recoil. Homework Equations...
  14. S

    Rutherford Scattering Trajectory

    Homework Statement Carbon scatters on a proton. What is the limit of the angle of scattering? I'm not really sure where to start this question. I know it has something to do with Rutherford Scattering and impact parameter. Homework EquationsThe Attempt at a Solution
  15. S

    Rutherford scattering - electromagnetic form factor

    Homework Statement Hi there. This is not really a problem, I am only trying to understand something but I simply can't. So Rutherford scattering says that $$ \frac{d\sigma }{d\Omega}=(\frac{Ze^2m}{8\pi \varepsilon _0 p^2})^2\frac{1}{\sin ^4(\Theta/2)}|F(q)|^2$$ where $$F(q)=\int \rho (\vec...
  16. thegirl

    Rutherford Scattering model geometry

    Hi, I was just wondering if someone could help clarify how pi - theta = phi? That is the link to the youtube video I was watching, the guys pretty good check him out if you want to learn how to derive the differential scattering cross section.
  17. P

    Solid Angle Rutherford Scattering

    Homework Statement derive an equation for the solid angle for a Rutherford scattering detector given a detcor window area of A and a distance to the detector of D for some scattering angle \phi given that d\Omega =2\pi sin\phi d\phi Homework Equations d\Omega =2\pi sin\phi d\phi A=Dd\phi The...
  18. ShayanJ

    MATLAB Rutherford scattering using MatLab

    I'm writing a program for simulating the angle distribution of scattered particles from a gold nucleus but I doubt the results. I don't know...But it would be very good if someone check it and give some hints. I also want to ask should I vary both initial speed and impact parameter in one...
  19. D

    Rutherford Scattering Derivation

    Homework Statement I'm trying to work out the derivation of the the Rutherford scattering trajectory. I understand the conservation of linear momentum, and that the only force acting is the coulomb force between the incoming particle and the target nucleus. Early on in the derivation I'm...
  20. skate_nerd

    Rutherford scattering thin gold foil

    Homework Statement The fraction of 6.0 MeV protons scattered by a thin gold foil, of density 19.3 g/cm^3, from the incident beam into a region where scattering angles exceed 60° is equal to 2.0(10^-5). Calculate the thickness of the gold foil. Homework Equations...
  21. E

    Deriving Rutherford Scattering Angle

    Homework Statement We want to fin an expression for \theta, the Rutherford scattering angle. I have an expression that I derived for a hyperbolic trajectory, of the form \frac{(x+x_0)^2}{A^2}-\frac{y^2}{B^2} = 1. We wanted it in terms of α, ε, where α is a constant ( \alpha =...
  22. P

    Rutherford Scattering, relativistic

    Homework Statement Asked to calculate the relativistic correction, to the differential scattering cross section which is given by the equation below in terms of E, E0 and θ where E0= .511 MeV. with 100MeV electrons from an Au nuclei at certain angles θ. Homework Equations Relativistic...
  23. M

    Python and Rutherford Scattering

    Hello everyone I have been supplied with this eqn n=\frac{Nat}{16r^2}(\frac{2Ze^2}{4\pi\epsilon_0E_K})^2cosec^4(\frac{\phi}{2}) for Rutherford scattering. N is the number of alpha particles incident on a unit area of foil t is the thickness of the foil a is the number of atoms...
  24. P

    Rutherford Scattering -scattering angle and formula

    Homework Statement Given variables and data: flux of alpha particles;Z; T-kinetic energy of the flux; t-thickness of the target.I have to calculate the number of alpha particles which are scattered in angle θ>60 degrees. Homework Equations 1) Is my formula correct ( see below) if I am...
  25. R

    Rutherford Scattering mass of particle

    Homework Statement I'm taking a graduate level course in classical mechanics that uses Goldstein's book. We are currently discussing scattering in a central field in chapter 3. Here are two problems that might be very basic/standard scattering problems, yet I'm not how to proceed or get...
  26. E

    Rutherford scattering experiment

    Hi,everyone!I have a problem!As known to us all,in Rutherford scattering experiment α rays are used to bomb gold foil, and most of them pass through the gold foil.But today I read something about the characteristics of α particles,the book says that you can stop α rays with a piece of paper...
  27. D

    Understanding Rutherford's Alpha Scattering Experiment

    Homework Statement Hey I am revising for my physics test and am having a bit of trouble understanding rutherford's alpha scattering experiment. My teacher gave us a powerpoint but it does not seem to help me, more so it confuses me. I am a good physics student and not understanding this is...
  28. S

    Rutherford scattering experiment question

    Rutherford scattering experiment question (urgent) Homework Statement I need to find the value of the electrical force between the alpha particle and the nucleus of the atom at the point of closest approach. Closest approach = 7.27 x 10^-14 m Charge on atom = (79 * 1.60 x 10 ^-19) C initial...
  29. D

    I must be discomprehending the Rutherford scattering cross section.

    I do not understand the interpretation of the http://hyperphysics.phy-astr.gsu.edu/hbase/rutsca.html" . To me, that equation says: (1) for a given θ, the proportion of particles exiting at θ does NOT depend on mass or charge; (2) if you integrated over all possible scattering angles, you...
  30. U

    Rutherford scattering differential probability function

    Homework Statement Spray of alpha particles hit a gold membrane whose density is \rho and thickness d, with a kinetic energy of E_k. The spray's intensity is I. Alpha particles are measured from an area of A which is set R away from the membrane. If \theta is the angle between the spray...
  31. Q

    Rutherford Scattering: Troubleshooting Wrong Atomic Number

    according to wiki's rutherford scattering experiment, "The fraction of particles that is scattered into a particular solid angle at a given direction relative to the incoming beam is called the differential cross section and is given by...
  32. Q

    Graph of rutherford scattering

    Homework Statement in rutherford scattering formula, N is proportional to (sin T/2)-4 where T is the scattering angle, N is the count rate per min. i have to find the relationship between N and T so how do i get a straight line graph out of this relationship? if i plot lg N vs lg T...
  33. Q

    Rutherford Scattering: Why is Count Rate 10x at 1mm Slit?

    why is it that in rutherford scattering experiment, if i change my slit width from 5mm to 1mm with everything else the same, i get a 10 times difference in the count rate for the same angle say 30degrees? for example, 1 count takes about 100seconds for the 1mm slit width but 1 count takes...
  34. T

    Rutherford scattering correction

    Homework Statement Hey. I've just conducted Rutherford's gold foil scattering experiment and am a little stuck on a part of the analysis. One of the objectives of the lab script is; 'To correct the counting rates measured in one plane for the fact that the foil scatters in a 3D cone'...
  35. M

    Rutherford Scattering: Inverse Relationship Explained

    Can anyone explain why there is an inverse relationship between target to detector distance and scattering angle? Thanks.
  36. S

    Rutherford Scattering cross section

    Homework Statement Integrate the rutherford cross section over the backward hemisphere to get 4pi(sigma0(E)) Homework Equations Rutherford cross section is sigma0(E)/sin^4(theta/2) The Attempt at a Solution When I integrate this with the limits pi/2 to pi i get sigma0(E)*(8/3) i...
  37. C

    Rutherford Scattering Problem.

    Homework Statement In an experiment, an alpha particle of mass 6.7e-27 kg; charge 3.2e-19C travels in a straight line with a speed 2.0e7m/s towards the centre of a gold nucleus. Find: 1. The kinetic energy(KE) of the alpha particle; 2. The potential(V) at a distance 'x' from the centre of the...
  38. A

    MATLAB Help! MATLAB Code for Rutherford Scattering Won't Run

    What's wrong with this MATLAB code for Rutherford scattering, it won't run for me! :( Hi, I can't do matlab...and have to plot the trajectory of alpha particles in rutherford scattering. I've made an attempt, but i know I've gone wrong somewhere. Could someone tell me how to fix it? I'd be...
  39. R

    Rutherford Scattering in Landau book

    I'm reading Landau and Lifgarbagez's Mechanics book and am having a hard time proving the following: On page 53, they present theta_0 = arccos( ... ). As described on page 48 eqn 18.2 the integral should produce this theta_0. However, I am not quite sure what r_min is? On page 48, they say 'It...
  40. C

    Rutherford Scattering Homework: θmin & θmax, Probability σ

    Homework Statement The differential cross section for Rutherford scattering of alpha particles off a nucleus can be written as: \frac{d\sigma}{d\Omega} = (\frac{zZe^2}{4\pi\epsilon_0})(\frac{1}{4T_\alpha})^2\frac{1}{sin^4 \frac{\theta}{2}} where z and Z are the atomic numbers of the...
  41. S

    Alpha particle deviation from gold foil (Rutherford Scattering)

    1. Homework Statement The alpha particles used by Rutherford had a kinetic energy of 7.7 MeV and, for a head-on collision would get to within a distance of 3×10-14m of the centre of the gold nucleus. However the actual radius of a gold nucleus is approximately 7×10-15m. 2. Homework Equations...
  42. N

    Rutherford scattering problem

    Homework Statement Alpha particle with kinetic energy 6MeV is scatterd on gold nucleus (A=197). Is Rutherford cross-section formula valid for this scattering? Explain ! Homework Equations The Attempt at a Solution The Coulomb barrier is Ec=(1.03MeV)*(Z1*Z2)/(A1^1/3+A2^1/3) Z1=79...
  43. B

    Rutherford Scattering Problem

    Homework Statement An Alpha particle of a Rutherford-type scattering experiment is shot directly toward a platinum nucleus. One of the particles was apparently aimed directly at the centre of the nucleus cause it shot 180 degrees back along the same path. How close does it come to the...
  44. S

    Rutherford scattering calculation

    Homework Statement The fraction of 6.0 MeV protons scattered by thin gold foil, of density \rho=19.3 g/cm^{3}, from the incident beam into a region where scattering angles exceed 60 degrees is equal to 2.0 x 10^{-5} . Calculate the thickness of the gold foil using the result of the previous...
  45. U

    Rutherford scattering and nuclear physics

    hi, i am a new student here in this forums from uae and i am studing in uaeu my majore is general physics >>> in this corse i have problem in nuclier physics in rutherford scattering >>> can you help ma pleaseeeee the problem are : firest one is : Show that the distance of...
  46. M

    Rutherford Scattering and relativistic effects

    Homework Statement n a Rutherford scattering experiment a target nucleus has a diameter of 3.5 10-14 m. The incoming has a mass of 6.64 10-27 kg. What is the kinetic energy of an particle that has a de Broglie wavelength equal to the diameter of the target nucleus? Ignore relativistic...
  47. S

    Rutherford scattering question

    http://img168.imageshack.us/my.php?image=fundn7.png d(chi)/dt =l/(mr^2), I don't see how to get there if you use the definition of angular momentum, you get l=r x mv(vectors where appropriate) so you can write v as v=dr/dt*r + rdx/dt*x where x is the symbol chi(close enough)and that r...
  48. O

    Rutherford Scattering: Using Beam Current & Intensity

    How do you use a beam current in rutherford scattering? Is it related to the intensity? All the book's questions and reading talks about is intensity, briefly, but the teacher's giving beam current. Thanks!
  49. S

    Rutherford Scattering problem with a heavier nucleus

    An alpha particle approaches a Au (gold) nucleus with atomic mass number 197 with a speed of 1.5*10^7 m/s. The alpha particle is then scattered 49 degrees from the horizontal at the slower speed of 1.47*10^7 m/s. In what direction does the Au nucleus recoil below the x-axis (the horizontal)...
  50. A

    Exploring Physics: Is the Rutherford Scattering Formula Necessary?

    i'm interested in physics, but i don't major in it... i look at physics in my free time, and i just came across the rutherford scattering formula and was wondering is it necessary to memorize it?