Rutherford Scattering: Inverse Relationship Explained

[Mr Bean]

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

Thanks.

 

[Bob S]

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

 

[adil0311]

hii.. i would like to know why alpha particles are more suited for this experiment than beta particles?

thxx :)

 

[Bob S]

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

 

[adil0311]

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

 

[Bob S]

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

 

[adil0311]

that was great! Thanks a lot!:)