The radius of and `alpha`-particle moving in a circle in a constant magnetic field is half of the radius of and electron moving in circular path in the same field. The de Broglie wavelength of `alpha`-particle is n times that of the electron. Find n (an integer).

Explanation

To solve the problem, we need to analyze the motion of an alpha particle and an electron in a magnetic field and relate their properties.

### Step-by-Step Solution:

1. **Understand the Motion in a Magnetic Field**:
When a charged particle moves in a magnetic field, it experiences a magnetic force that acts as the centripetal force required for circular motion. The magnetic force \( F \) is given by:
\[
F = QVB
...