In Rutherford scattering experiment, wha will be the ratio of impact parameter for scattering angles `theta_(1)=90^(@) and theta_(2)=120^(@)`

Options

A. 1
B. `sqrt(2)`
C. 2
D. `sqrt(3)`

Explanation

To solve the problem of finding the ratio of the impact parameters for the scattering angles \( \theta_1 = 90^\circ \) and \( \theta_2 = 120^\circ \) in the Rutherford scattering experiment, we can follow these steps:

### Step 1: Understand the relationship between impact parameter and scattering angle
The impact parameter \( B \) in the Rutherford scattering experiment is proportional to the cotangent of half the scattering angle. Mathematically, this can be expressed as:
\[ B \propto \cot\left(\frac{\theta}{2}\right) \]

### Step 2: Calculate the impact parameter for \( \theta_1 = 90^\circ \)
For \( \theta_1 = 90^\circ \):
\[ B_1 \propto \cot\left(\frac{90^\circ}{2}\right) = \cot(45^\circ) \]
Since \( \cot(45^\circ) = 1 \):
\[ B_1 \propto 1 \]

### Step 3: Calculate the impact parameter for \( \theta_2 = 120^\circ \)
For \( \theta_2 = 120^\circ \):
\[ B_2 \propto \cot\left(\frac{120^\circ}{2}\right) = \cot(60^\circ) \]
Since \( \cot(60^\circ) = \frac{1}{\sqrt{3}} \):
\[ B_2 \propto \frac{1}{\sqrt{3}} \]

### Step 4: Find the ratio of the impact parameters
Now, we need to find the ratio \( \frac{B_1}{B_2} \):
\[ \frac{B_1}{B_2} = \frac{1}{\frac{1}{\sqrt{3}}} = \sqrt{3} \]

### Conclusion
The ratio of the impact parameters for the scattering angles \( \theta_1 = 90^\circ \) and \( \theta_2 = 120^\circ \) is:
\[ \frac{B_1}{B_2} = \sqrt{3} \]

### Final Answer
Thus, the answer is \( \sqrt{3} \).

---