210Po is used as a source of 5.2 [MeV] alpha particles in a Rutherford experiment. The alpha particles are directed at a gold foil of thickness 2µm (2 x 10^6 meters) at a rate of 100000 particles per minute. The scattered particles are detected on a screen of area 1cm^2 at a distance of 12cm. Use the Rutherford formula to predict the number of alpha particles observed in 10 minutes at q= 15 degree, 30 degree and 45 degree.
Use the following data for your calculations:
N = 10^6 number of particles incident in 10 minutes
rho = 19.3 [g/cm^3] density of gold
m(Au) = 197u mass of gold atom
t = 2* 10^-6 [m] thickness of foil
Z = 79 atomic number of gold
Hint: Note that the number density n of gold is rho/m(Au) and ke^2 =1.44[MeV*fm]
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Rutherford Scattering formula :
N(θ) = NintZ2k2e4 .
where : N(θ) = Number of particles striking per unit area of the detector
Ni = Number of incident alpha particles
n = Atoms per unit volume in the target
t = Thickness of the target
Z = Atomic number of the target
k = Coulomb's constant
e = ...
The expert examines the Rutherford experiment. A step by step solution provided.