Centripetal Acceleration

To solve this problem, we need to determine the ratio of the linear momenta acquired by an α particle and a proton when both are accelerated from rest through the same potential difference. Let's break down the steps:

Step-by-step Solution:

1. When a charged particle is accelerated through a potential difference , the work done on the particle is converted into kinetic energy. The kinetic energy gained by the particle is given by: , where is the charge of the particle.
2. The expression for kinetic energy is also given by: , where is the mass and is the velocity of the particle.
3. From the above two equations, we get:
4. The linear momentum of the particle is:
5. Now, compute the momenta for both the α particle and the proton:
   • For the α particle (He ), the charge is 2e, and the mass is approximately 4 times that of the proton. Therefore, the momentum for the α particle is:
   • For the proton, the charge is e and the mass is . Therefore, the momentum for the proton is:
6. Ratio of the linear momenta of α particle to proton:

Therefore, the ratio of linear momenta acquired by the α particle and the proton is 2√2:1.