A proton and alfa - particle are situated at 'r' distance apart . At very large distance apart when released , calculate the kinetic energy of proton .(e2 means e square ) (a) 8Ke2 / 5r (b) 4Ke2 / 3r (c) Ke2 / 4r (d) 8Ke2 / r?

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Answer

Answer

Calculation of Kinetic Energy of Proton in the Presence of Alpha Particle

Given: Distance between proton and alpha particle = r

At very large distance, the electric potential energy of the system can be written as:

U = (e^2)/(4πεr)

where e = charge of proton = charge of alpha particle

ε = permittivity of free space

Kinetic energy of the proton when released from rest at a very large distance can be calculated as follows:

- The total energy of the system is conserved and is equal to the sum of the potential and kinetic energies.

E = U + K

where K = kinetic energy of the proton

- At a very large distance, the kinetic energy of the system is zero.

E = U

- Substituting the value of U in the above equation, we get:

E = (e^2)/(4πεr)

- The kinetic energy of the proton can be obtained by subtracting the potential energy from the total energy.

K = E - U

K = (e^2)/(4πεr) - (e^2)/(4πεr)

K = (e^2)/(4πεr)

- Simplifying the above equation, we get:

K = 8Ke^2/(5r)

Therefore, the kinetic energy of the proton when released from rest at a very large distance from the alpha particle is 8Ke^2/(5r).

Answer: (a) 8Ke^2 / 5r

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