The number of `alpha`-particless scattered per unit area N `(theta)` at scattering angle `theta` varies inversely as

Options

A. `cos^(4)((theta)/(2))`
B. `sin^(4)((theta)/(2))`
C. `tan^(4)((theta)/(2))`
D. `cot^(4)((theta)/(2))`

Answer

To solve the question regarding the number of alpha particles scattered per unit area \( N(\theta) \) at a scattering angle \( \theta \), we will follow these steps:

### Step 1: Understand the relationship
The problem states that the number of alpha particles scattered per unit area varies inversely with a certain function of the scattering angle \( \theta \).

### Step 2: Identify the relationship
From the video transcript, we find that the number of alpha particles scattered at an angle \( \theta \) is given by the relation:
\[ N(\theta) \propto \frac{1}{\sin^4\left(\frac{\theta}{2}\right)} \]

### Step 3: Write the inverse relationship
Since \( N(\theta) \) varies inversely with \( \sin^4\left(\frac{\theta}{2}\right) \), we can express this as:
\[ N(\theta) = \frac{k}{\sin^4\left(\frac{\theta}{2}\right)} \]
where \( k \) is a constant of proportionality.

### Step 4: Conclusion
Thus, the number of alpha particles scattered per unit area \( N(\theta) \) at scattering angle \( \theta \) varies inversely as \( \sin^4\left(\frac{\theta}{2}\right) \).

### Final Answer
\[ N(\theta) \propto \frac{1}{\sin^4\left(\frac{\theta}{2}\right)} \]

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