Statement 1: If a proton and an `alpha`-particle enter a uniform magnetic field perpendicularly with the same speed, the time period of revolution of `alpha`-particle is double than that of proton.
Statement 2: In a magnetic field, the period of revolution of a charged particle is directly proportional to the mass of the particle and inversely proprotional to the charge of particle.

Explanation

To solve the problem, we need to analyze the motion of a proton and an alpha particle in a uniform magnetic field. We will use the formula for the time period of a charged particle moving in a magnetic field.

### Step-by-Step Solution:

1. **Understanding the Particles**:
- A proton has a mass \( m \) and a charge \( q = +e \).
- An alpha particle consists of 2 protons and 2 neutrons, so its mass is \( M = 4m \) and its charge is \( Q = 2e \).

2. **Time Period Formula**:
The time period \( T \) of a charged particle moving in a magnetic field is given by the formula:
\[ T = \frac{2\pi m}{qB} \]
where \( m \) is the mass of the particle, \( q \) is the charge of the particle, and \( B \) is the magnetic field strength.

3. **Calculating Time Period for Proton**:
For the proton:
\[ T_p = \frac{2\pi m}{eB} \]

4. **Calculating Time Period for Alpha Particle**:
For the alpha particle:
\[ T_{\alpha} = \frac{2\pi (4m)}{2eB} = \frac{8\pi m}{2eB} = \frac{4\pi m}{eB} \]

5. **Comparing Time Periods**:
Now we will compare the time periods:
\[ \frac{T_p}{T_{\alpha}} = \frac{\frac{2\pi m}{eB}}{\frac{4\pi m}{eB}} = \frac{2\pi m}{eB} \cdot \frac{eB}{4\pi m} = \frac{2}{4} = \frac{1}{2} \]
This means:
\[ T_{\alpha} = 2T_p \]
Therefore, the time period of revolution of the alpha particle is indeed double that of the proton.

6. **Conclusion**:
- Statement 1 is correct: The time period of revolution of the alpha particle is double that of the proton.
- Statement 2 is also correct: The period of revolution of a charged particle is directly proportional to the mass and inversely proportional to the charge.

### Final Answer:
Both statements are correct, and Statement 2 provides the correct explanation for Statement 1.

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