Exploring Physics: Is the Rutherford Scattering Formula Necessary?

In summary, the conversation is about the Rutherford scattering formula and whether it is necessary to memorize it. The formula is not necessary to memorize, but it is important to understand the 1/(1-cos \theta)^2 dependence of the scattering cross-section. The formula also has a more useful form, the differential cross-section, which is the number of scattering events passing through an elemental area on the surface of a unit sphere centered on the scattering center.
  • #1
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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?
 
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  • #2
Don't memorize it ! :eek:

The important thing to take away from the formula is the [itex]1/(1-cos \theta)^2 [/itex] dependence of the scattering cross-section which is a signature of scattering from point-like objects.
 
  • #3
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the rutherford scattering formula is
N(cita)=(NntZ^2*e^4)/{[(8pi*epsilon)^2]*(E^2)sin^4(cita/2)} right?
because i don't see 1/[1-cos(cita)]^2...
 
  • #4
Hint: browse through a list of trig identities. :wink:
 
  • #5
so sin^4(cita/2)=[1-cos^2(cita)]/2={1-[1+cos(2cita)]/2}/2?
 
  • #6
Sorry, I didn't make this clear earlier. I was referring to the differential cross section. That's a more useful form of the scattering equation.
 
  • #7
differential cross section? what's that?
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  • #8
It's the number of scattering events that go through an elemental area on the surface of a unit sphere centered on the scattering center. In spherical co-ordinates, an area element on the unit sphere (or an element of solid angle) is given by [itex]d \Omega = sin \theta d \theta d \phi [/itex].

The differential cross-section is [itex]dN/d \Omega[/itex]
 
  • #9
ok, thank you very much! :)
 

Related to Exploring Physics: Is the Rutherford Scattering Formula Necessary?

1. What is the Rutherford Scattering Formula?

The Rutherford Scattering Formula is a mathematical equation that describes the scattering of alpha particles by a nucleus. It was developed by physicist Ernest Rutherford in 1911, and is a fundamental concept in nuclear physics.

2. How is the Rutherford Scattering Formula used in physics?

The formula is used to calculate the angle at which alpha particles will be deflected when they collide with a nucleus. This helps scientists understand the structure and composition of atoms, as well as the forces that hold them together.

3. Why is the Rutherford Scattering Formula important?

The Rutherford Scattering Formula is important because it provided evidence for the existence of a small, dense nucleus within an atom. This discovery changed our understanding of atomic structure and paved the way for further advancements in nuclear physics.

4. Are there any limitations to the Rutherford Scattering Formula?

Yes, the Rutherford Scattering Formula is only applicable to alpha particles and cannot be used to describe the scattering of other particles. It also assumes that the nucleus is a point particle and does not take into account the effects of quantum mechanics.

5. How does the Rutherford Scattering Formula relate to current research in physics?

The Rutherford Scattering Formula is still used in current research in physics, particularly in the study of nuclear structure and interactions. It has also been expanded upon and modified to account for the limitations mentioned above, making it a valuable tool in modern physics research.

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