Number of Particles Scattered at 60° in an Alpha Particle Scattering Experiment

The question states that the number of particles scattered at an angle of 60° is 100 per minute in an alpha particle scattering experiment. We need to determine the number of alpha particles scattered at 90° angles.

Scattering of Alpha Particles
- Alpha particle scattering is an experiment that was conducted by Ernest Rutherford to understand the structure of the atom.
- Alpha particles, which are positively charged particles consisting of two protons and two neutrons, are fired at a thin gold foil.
- These particles are scattered as they interact with the gold atoms in the foil, and the pattern of scattering provides information about the structure of the atom.

Scattering Angle and Particle Distribution
- The scattering angle is defined as the angle between the incident alpha particle and the final scattered direction.
- The distribution of scattered particles depends on the scattering angle.
- At small scattering angles, most particles are not deflected significantly and pass through the foil with little deviation from their initial path.
- At large scattering angles, a few particles are deflected to a large extent, while most particles continue in a forward direction.

Relation between Scattering Angle and Number of Scattered Particles
- The number of particles scattered at a particular angle is inversely proportional to the square of the sine of that angle.
- Mathematically, N ∝ sin^2(θ), where N is the number of particles scattered and θ is the scattering angle.

Calculating the Number of Alpha Particles Scattered at 90°
- Given that the number of particles scattered at 60° is 100 per minute, we can use the relation N ∝ sin^2(θ) to find the number of particles scattered at 90°.
- At 60°, sin(60°) = √3/2. So, N1 ∝ (√3/2)^2 = 3/4.
- At 90°, sin(90°) = 1. So, N2 ∝ 1^2 = 1.
- We can set up a proportion: N1/N2 = (3/4)/1. Solving for N2, we find N2 = 4/3 * N1.
- Substituting the given value of N1 = 100, we get N2 = 4/3 * 100 = 400/3 ≈ 133.33.
- Therefore, the number of alpha particles scattered at 90° angles is approximately 133.33 per minute.

Answer: The number of alpha particles scattered at 90° angles is approximately 133.33 per minute.