Rutherford Scattering: Inverse Relationship Explained

In summary, the target-to-detector distance has an inverse relationship with the differential cross section per sterad. Alpha particles are more suited for this experiment than beta particles because beta particles are easily deflected (scattered) by electrons in the target, while the alpha particles are deflected only by the heavy nuclei. Furthermore, there are no radioactive sources that emit betas with fixed energy (because the decay energy is shared with anti-neutrinos), while radioactive alpha emitters emit fixed energy alphas.
  • #1
Mr Bean
1
0
Can anyone explain why there is an inverse relationship between target to detector distance and scattering angle?

Thanks.
 
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  • #2
If the detector has a fixed size, then the subtended solid angle varies inversely as target-to-detector-distance squared. But dσ/dΩ is the differential cross section per sterad, and is independent of target-to-detector distance. Is this what you mean?

Bob S
 
  • #3
hii.. i would like to know why alpha particles are more suited for this experiment than beta particles?

thxx :)
 
  • #4
adil0311 said:
hii.. i would like to know why alpha particles are more suited for this experiment than beta particles?
Beta particles are very easily deflected (scattered) by electrons in the target, while the alpha particles are deflected only by the heavy nuclei. Furthermore, there are no radioactive sources that emit betas with fixed energy (because the decay energy is shared with anti-neutrinos), while radioactive alpha emitters emit fixed energy alphas.

Furthermore, the distance of closest approach of a charged particle to the nucleus is inversely proportional to the kinetic energy of the incident charged particle, and the kinetic energies of alpha particles from radioactive sources are ~ 3 or 4 times the energies of beta sources. See

http://ads.harvard.edu/cgi-bin/bbrowse?book=hsaa&page=312

Look up impact parameter and distance of closest approach in

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/rutsca2.html

Bob S
 
  • #5
Hi.. thanks loads for your reply.. much clearer now.

I was also thinking in terms of penetrating power of the beta particle since it is much less massive than the alpha particle. It could be that beta particle will not pass through the atom so easily. Does that make any sense?
PS: I am only an A level student.. my scientific language is not so much developed yet. lol.

Thanks again
Adil
 
  • #6
adil0311 said:
I was also thinking in terms of penetrating power of the beta particle since it is much less massive than the alpha particle. It could be that beta particle will not pass through the atom so easily. Does that make any sense?
The penetrating power of a charged particle is proportional to ½Mv2/Zz where ½Mv2 is the projectile kinetic energy (in MeV) and Zz are the charges of the target and projectile. The kinetic energy of alpha particles is several times larger than betas, and the alpha particle z is twice the beta z. There is also an effect due to the sign of the projectile charge.

Use online software for alpha scattering in http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/rutsca2.html

At much higher energies (over 100 MeV), electrons have proven to be very effective in mapping nuclear sizes.

Bob S
 
  • #7
that was great! Thanks a lot!:)
 

Related to Rutherford Scattering: Inverse Relationship Explained

1. What is Rutherford scattering?

Rutherford scattering is a phenomenon where positively charged particles, such as alpha particles, are deflected by the positively charged nucleus of an atom.

2. How does Rutherford scattering work?

When an alpha particle approaches an atom, it is attracted to the positively charged nucleus. As the alpha particle gets closer, it experiences a repulsive force due to the like charges. This causes the alpha particle to change direction and scatter, rather than pass straight through the atom.

3. What is the inverse relationship in Rutherford scattering?

The inverse relationship in Rutherford scattering refers to the fact that the scattering angle of the alpha particles is inversely proportional to the square root of their kinetic energy. This means that as the kinetic energy of the alpha particles increases, the scattering angle decreases.

4. Why is the inverse relationship important in Rutherford scattering?

The inverse relationship allows scientists to calculate the size and charge of the nucleus of an atom by measuring the scattering angle of the alpha particles. This was a groundbreaking discovery in the field of nuclear physics and helped to further our understanding of the structure of the atom.

5. How is Rutherford scattering used in modern science?

Rutherford scattering is still used in modern science, particularly in the field of particle physics. It is used to study the interactions of subatomic particles and to determine the properties of nuclei. It is also used in medical imaging techniques, such as positron emission tomography (PET), to produce images of the human body and diagnose medical conditions.

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