A uranium 238 nucleus, initially at rest emits n alpha particle with a speed of `1.4xx10^7m/s`. Calculate the recoil speed of the residual nucleus thorium 234. Assume that the mass of a nucleus is proportional to the mass number.

Explanation

To solve the problem, we will use the principle of conservation of linear momentum. Here are the steps to find the recoil speed of the residual nucleus (Thorium 234) after the emission of an alpha particle from Uranium 238.

### Step-by-Step Solution:

1. **Identify the Initial and Final States**:
- Initially, the Uranium 238 nucleus is at rest. Therefore, the initial momentum is zero.
- After the emission of the alpha particle, we have two objects: the emitted alpha particle and the residual Thorium 234 nucleus.

...