2019년 1월 8일 화요일

W1.4b 산란율 계산(Counting rate Rutherford)

[커세라] 입자물리학 입문(Particle Physics: an Introduction)

1주: 물질과 힘 그리고 측정(Matter and forces, measuring and counting)
    W1.0 환영(Welcome)
    W1.1 물질(Matter)
    W1.2 힘(Forces)
        W1.2a 자연단위(Natural units)
        W1.2b 특수 상대론과 4-벡터(Special relativity and four-vector)
        W1.2c 가상입자(Virtual Particles)
    W1.3 확률과 단면(Probability and cross section)
        W1.3a 광자 빔의 감쇄(Attenuation of a photon beam)
    W1.4 러더포드 실험(Rutherford experiment)
        W1.4a 러더포드 단면(Rutherford cross section)

W1.4b 산란율 계산(Counting rate Rutherford)/동영상/영문자막/슬라이드




In the beginning of last century, Geiger and Marsden have measured the Rutherford reaction. They have counted scatters by eye. In this little video we will convince ourselves that this is indeed possible.



Geiger and Marsden took a source of polonium 210, an alpha emitter collimated to an intensity of about 1,000 particles per second, which scattered off a gold foil of 100 nm( nano-meters) thickness. And they counted the number of scatters per second by eye at angle of ten degrees at a distance of ten centimeters and over an area of about one square centimeter.




Let us first compute the properties of gold. It has a density of about 2 times 10^4 kilogram per cubic meter. Its charge is 79 and its mass is 197 atomic units which gives us a number density of about 0.6 times 10^29 nuclei per cubic meter.



Alpha particles are He-4 nuclei with charge 2 to 4 mass units and an initial intensity of 10^3 per second comes out of the collimator.



The cross section for Rutherford scattering is proportional to the product of the two charges squared inversely proportional to the incident energy squared and the sin^4 of half the scattering angle.



Using the correct conversion factors, we thus obtain a differential cross section at an angle of 10 degrees of 2 times 10^-24 square meters steradian.



This corresponds to a fraction of the initial intensity of about 1.3 per mil, which is scattered into the observed solid angle.



That is to say the count rate is about 1.3 Hz, easily observable by the naked eye.



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