Explanation:
When an electron and an alpha particle are accelerated from rest by a potential difference of 100 V, we can use the equations of kinetic energy and potential energy to find the ratio of their momenta.

Equations:
- Kinetic energy of a particle: K.E. = (1/2)mv^2
- Potential energy of a particle: P.E. = qV

Step 1:
Calculate the kinetic energy of the electron and the alpha particle using the equation K.E. = (1/2)mv^2.

The mass of an electron is 9.11 x 10^-31 kg and the mass of an alpha particle is 6.64 x 10^-27 kg. The potential difference is 100 V.

- Kinetic energy of electron: K.E. = (1/2) x 9.11 x 10^-31 kg x (1.6 x 10^-19 J/V x 100 V)^2 = 8.22 x 10^-18 J
- Kinetic energy of alpha particle: K.E. = (1/2) x 6.64 x 10^-27 kg x (1.6 x 10^-19 J/V x 100 V)^2 = 5.94 x 10^-14 J

Step 2:
Calculate the potential energy of the electron and the alpha particle using the equation P.E. = qV.

The charge of an electron is -1.6 x 10^-19 C and the charge of an alpha particle is +3.2 x 10^-19 C. The potential difference is 100 V.

- Potential energy of electron: P.E. = -1.6 x 10^-19 C x 100 V = -1.6 x 10^-17 J
- Potential energy of alpha particle: P.E. = 3.2 x 10^-19 C x 100 V = 3.2 x 10^-17 J

Step 3:
Calculate the total energy of the electron and the alpha particle by adding their kinetic and potential energies.

- Total energy of electron: K.E. + P.E. = 8.22 x 10^-18 J - 1.6 x 10^-17 J = -7.78 x 10^-18 J
- Total energy of alpha particle: K.E. + P.E. = 5.94 x 10^-14 J + 3.2 x 10^-17 J = 5.94 x 10^-14 J

Step 4:
Calculate the momentum of the electron and the alpha particle using the equation p = √(2mE).

- Momentum of electron: p = √(2 x 9.11 x 10^-31 kg x 7.78 x 10^-18 J) = 2.59 x 10^-24 kg m/s
- Momentum of alpha particle: p = √(2 x 6.64 x 10^-27 kg x 5.94 x 10^-14 J) = 5.77 x 10^-21 kg m/s

Step 5:
Calculate the ratio of the momenta of the electron and