In the Rutherford scattering experiment, the distribution of scattered particles is influenced by the angle at which they are observed. To find the difference in the number of particles observed at angles of 90 degrees and 180 degrees, we can use the principles of scattering and the relationship between the scattering angle and the intensity of the detected particles.
Understanding the Scattering Distribution
Rutherford's experiment demonstrated that alpha particles are scattered by a thin foil of gold. The scattering intensity varies with the angle due to the nature of the Coulomb force between the positively charged alpha particles and the positively charged nucleus of the gold atoms. The number of particles scattered at a given angle can be described by the formula:
Scattering Formula
The differential cross-section, which gives the number of particles scattered into a solid angle, is proportional to:
- 1/sin^4(θ) for small angles (θ)
- 1/sin^2(θ) for larger angles
For our purposes, we can simplify the analysis by noting that the number of particles detected at an angle θ is inversely related to the sine of that angle raised to a power, depending on the angle range.
Calculating the Number of Particles
Given that the number of particles observed at 10 degrees is one million per minute, we can use this as a reference point. The number of particles observed at other angles can be estimated based on the scattering distribution.
Estimating for 90 Degrees
At 90 degrees, the intensity of scattering is typically lower than at smaller angles. Using the relationship, we can approximate:
- At 90 degrees, the number of particles observed is significantly reduced compared to 10 degrees.
- For practical purposes, let’s assume the number of particles at 90 degrees is around 1/1000th of that at 10 degrees, which gives us approximately 1000 particles per minute.
Estimating for 180 Degrees
At 180 degrees, the particles are scattered back in the direction from which they came. This is often the lowest intensity due to the nature of the scattering process:
- We can estimate that the number of particles at 180 degrees is even lower, perhaps around 1/10000th of that at 10 degrees, leading to about 100 particles per minute.
Finding the Difference
Now, we can calculate the difference in the number of particles observed at 90 degrees and 180 degrees:
- Particles at 90 degrees: 1000 per minute
- Particles at 180 degrees: 100 per minute
- Difference: 1000 - 100 = 900 particles per minute
Final Thoughts
Thus, the approximate difference in the number of particles observed at angles of 90 degrees and 180 degrees is around 900 particles per minute. This illustrates how the scattering angle significantly affects the detection of particles in the Rutherford experiment, showcasing the underlying physics of nuclear interactions.
