KCET · Physics · Atomic Physics
In the Rutherford's alpha scattering experiment, as the impact parameter increases, the scattering angle of the alpha particle.
- A remains the same
- B is always \(90^{\circ}\)
- C decreases
- D increases
Answer & Solution
Correct Answer
(C) decreases
Step-by-step Solution
Detailed explanation
In the Rutherford's \(\alpha\)-scattering experiment,
impact parameter \((b)\) and scattering angle \(\theta\) are related as,
\(\begin{aligned} b & =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{z e^2 \cot \frac{\theta}{2}}{\left(\frac{1}{2} m v^2\right)} \\ \Rightarrow \quad b & \propto \cot \frac{\theta}{2}\end{aligned}\)
Thus, with the increase of impact parameter \((b)\), \(\cot \frac{\theta}{2}\) increases. It is possible only when \(\theta\) will decrease.
impact parameter \((b)\) and scattering angle \(\theta\) are related as,
\(\begin{aligned} b & =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{z e^2 \cot \frac{\theta}{2}}{\left(\frac{1}{2} m v^2\right)} \\ \Rightarrow \quad b & \propto \cot \frac{\theta}{2}\end{aligned}\)
Thus, with the increase of impact parameter \((b)\), \(\cot \frac{\theta}{2}\) increases. It is possible only when \(\theta\) will decrease.
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