Electrons- conservation of energy - electric potential

[mussgo]

An Electron is Projected An electron is projected with an initial speed of 2.4 x10^5 m/s directly toward a proton that is fixed in place. If the electron is initially a great distance from the proton, at what distance from the proton is the speed of the electron instantaneously equal to twice the initial value?


im having a lot of trouble with this problem i don't even know how to approach it can anyone pls help me to get started u..u

 

[Dick]

The sum of the kinetic energy (1/2)mv^2 of the electron plus it's potential energy in the field of the proton k*(-e)*(e)/r is a constant (note potential energy is negative!). At large r essentially all of the energy is kinetic. Find that. Now find the energy when v is doubled. At what value of r does the total energy balance?

 

[Moetasim]

I can provide some guidance on how to approach this problem. The first step is to understand the concepts of conservation of energy and electric potential in relation to the movement of electrons and protons.

Conservation of energy states that energy cannot be created or destroyed, it can only be transferred or converted from one form to another. In this case, the initial kinetic energy of the electron (due to its speed) will be converted into electric potential energy as it approaches the fixed proton.

Electric potential is the amount of energy required to move a unit charge from one point to another in an electric field. In this case, the electric potential is due to the attraction between the positively charged proton and negatively charged electron.

To solve this problem, we can use the conservation of energy equation:

Initial kinetic energy = final electric potential energy

We know the initial kinetic energy of the electron (due to its initial speed) and we can calculate the final electric potential energy at any distance from the proton using the equation:

Electric potential energy = (charge of electron x charge of proton)/distance between them

Now, we need to find the distance at which the speed of the electron is twice its initial value. This can be done by setting the final kinetic energy (due to the electric potential) equal to twice the initial kinetic energy. This will give us the distance at which the speed of the electron is twice its initial value.

I hope this helps you get started on solving the problem. Remember to always use the relevant equations and concepts to guide your approach.