In an experiment done by scattering 5.5 MeV α particles on a thin gold foil, students find that 10,000 α particles are scattered at an angle greater than 90 degrees.
How many α particles will be scattered between 60 degrees and 80 degrees?
To determine the number of α particles scattered between 60 and 80 degrees, we need to use the Rutherford scattering formula, which relates the number of scattered particles as a function of scattering angle and other parameters.
The number of α particles scattered at a given angle θ is given by:
N(θ) = N₀ * (I / 4πε₀)² * (Z₁ * Z₂ * e² / 2E)² * (1 / sin²(θ / 2))²
Where:
- N(θ) is the number of scattered α particles at angle θ.
- N₀ is the total number of α particles incident on the gold foil.
- I is the intensity of the incident α particle beam.
- ε₀ is the vacuum permittivity.
- Z₁ and Z₂ are the charges of the incident α particles and gold atoms, respectively.
- e is the elementary charge.
- E is the kinetic energy of the incident α particles.
Given the information provided, we know:
- N₀ = 10,000 (total number of scattered α particles)
- θ₁ > 90 degrees
To calculate the number of α particles scattered between 60 and 80 degrees, we need to integrate the Rutherford scattering formula over the desired range of angles:
N(60 - 80) = ∫[60°:80°] N(θ) dθ
Unfortunately, since we do not have specific values for the intensity of the α particle beam, the charges of the particles and gold atoms, and the kinetic energy of the α particles, we cannot provide an exact numerical answer. However, if you have those parameters, you can calculate the number of α particles scattered between 60 and 80 degrees using the Rutherford scattering formula.