Ratio of the velocities acquired by alpha particle and proton when accelerated through the same potential difference

When an alpha particle and proton are accelerated through the same potential difference, their velocities acquired can be determined using the formula:

v = √(2qV/m)

where v is the velocity acquired, q is the charge of the particle, V is the potential difference, and m is the mass of the particle.

The ratio of the velocities acquired by alpha particle and proton can be determined as follows:

1. Determine the charges and masses of the particles
- Alpha particle: q = +2e, m = 4u
- Proton: q = +e, m = 1u

2. Calculate the velocities acquired by each particle
- Alpha particle: v_alpha = √(2(2e)(V)/4u) = √(eV/2u)
- Proton: v_proton = √(2eV/u)

3. Determine the ratio of the velocities acquired
- v_alpha/v_proton = (√(eV/2u))/(√(2eV/u))
- v_alpha/v_proton = (√(eV/2u))/(√(2eV/u)) x (√(2u)/(√2u))
- v_alpha/v_proton = (√(eV/2u))/(√(2eV))
- v_alpha/v_proton = √(u/4)

Therefore, the ratio of the velocities acquired by alpha particle and proton when accelerated through the same potential difference is √(u/4), which is approximately 0.5. This means that the alpha particle acquires a velocity that is about twice that of the proton when accelerated through the same potential difference.