**Ratio of Flight Times for Proton and Alpha Particle in a Uniform Electric Field**

When a charged particle is placed in a uniform electric field, it experiences a constant force and undergoes a uniform acceleration. The time taken by the particle to travel a certain distance depends on its initial velocity, the acceleration due to the electric field, and the distance traveled.

**Equations of Motion for Charged Particles in Electric Field**

The equations of motion for a charged particle in a uniform electric field are given by:

- Velocity of the particle after time t, v = at
- Distance traveled by the particle after time t, s = 1/2 at^2
- Time taken to travel a distance s, t = √(2s/a)

where a is the acceleration of the particle due to the electric field and s is the distance traveled by the particle.

**Flight Time for Proton and Alpha Particle in Electric Field**

Let us consider a proton and an alpha particle starting from rest in a uniform electric field. The acceleration of the particles due to the electric field is given by:

- For proton, a = F/m = E*q/m_p
- For alpha particle, a = F/m = E*q/m_α

where F is the force on the particle, E is the electric field strength, q is the charge on the particle, and m_p and m_α are the masses of the proton and alpha particle, respectively.

The time taken by the particles to travel a certain distance d is given by:

- For proton, t_p = √(2d/a_p)
- For alpha particle, t_α = √(2d/a_α)

where a_p and a_α are the accelerations of the proton and alpha particle, respectively.

The ratio of flight times for the proton and alpha particle is given by:

- t_α/t_p = √(m_p/m_α)

**Explanation of Ratio of Flight Times**

From the above equation, we can see that the ratio of flight times for the proton and alpha particle depends only on their masses. Since the mass of the alpha particle is four times that of the proton, the ratio of their flight times is given by:

- t_α/t_p = √(m_p/m_α) = √(1/4) = 1/2

Therefore, the alpha particle will take half the time taken by the proton to travel the same distance in the electric field. This result is independent of the electric field strength and the distance traveled by the particles.

**Conclusion**

In conclusion, the ratio of flight times for a proton and an alpha particle starting from rest in a uniform electric field is given by the square root of the ratio of their masses. The alpha particle, being four times heavier than the proton, will take half the time taken by the proton to travel the same distance in the electric field.