Rutherford Scattering and relativistic effects

In summary, the kinetic energy of an alpha particle with a de Broglie wavelength equal to the diameter of the target nucleus can be calculated using the equation E = hc/λ, where E is the energy, h is the Planck's constant, c is the speed of the particle, and λ is the de Broglie wavelength.
  • #1
MrDMD83
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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 effects.
J



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  • #2
Damn dude, here's the equation you need:

[tex]E=\frac{hc}{\lambda}[/tex]
E is the energy, h is the planks constant, c (more properly v) is the speed of the particle, and lambda is the de-broglie wavelength.

E and KE are equal in this case.
 
  • #3
at a solution can be made without knowing the velocity of the particle. However, it is important to note that in a Rutherford scattering experiment, the kinetic energy of the particle is typically much higher than the rest mass energy, so relativistic effects cannot be ignored. In order to accurately calculate the kinetic energy, the relativistic energy equation, E = mc^2 / √(1 - v^2/c^2), must be used. This takes into account the mass-energy equivalence and the effects of velocity on the kinetic energy of the particle. It is also important to note that the de Broglie wavelength is given by λ = h/p, where h is Planck's constant and p is the momentum of the particle. So, in order to find the kinetic energy of the particle, the velocity and momentum of the particle must be determined using the given information.
 

1. What is Rutherford Scattering and how does it work?

Rutherford Scattering is a phenomenon that occurs when a beam of charged particles (such as alpha particles) is directed at an atomic nucleus. The particles can either pass straight through the nucleus or be deflected at various angles, depending on the size and charge of the nucleus. This scattering is caused by the electromagnetic repulsion between the positively charged particles in the beam and the positively charged protons in the nucleus.

2. How did Rutherford's experiment contribute to our understanding of the atom?

Rutherford's famous gold foil experiment, which involved directing alpha particles at a thin sheet of gold foil, provided evidence that the atom has a small, dense positively charged nucleus at its center. This discovery was a significant contribution to the development of the nuclear model of the atom and helped to disprove the previously accepted plum pudding model.

3. What are relativistic effects in Rutherford Scattering?

Relativistic effects refer to the behavior of particles moving at speeds close to the speed of light. In Rutherford Scattering, as the alpha particles approach the speed of light, their mass increases and their kinetic energy decreases. This can affect the trajectory of the particles and cause deviations from the classical predictions of Rutherford Scattering.

4. How do relativistic effects impact the results of Rutherford Scattering experiments?

Relativistic effects can cause the scattered particles to have higher energies and larger scattering angles than expected based on classical predictions. This can lead to a broader range of scattering angles and a decrease in the intensity of the scattered particles at certain angles. It is important to take these effects into account when analyzing Rutherford Scattering data.

5. What other factors can affect the results of Rutherford Scattering experiments?

In addition to relativistic effects, other factors that can impact the results of Rutherford Scattering experiments include the size, charge, and density of the target nucleus, as well as the energy and intensity of the incoming particle beam. Experimental conditions such as temperature and pressure can also play a role in the scattering process.

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