Step-by-step explanation:
To find how close the proton will come to the alpha particle before coming to a stop, you can use the principles of electrostatics and conservation of energy.
First, you'll need to calculate the initial kinetic energy of the proton:
Initial Kinetic Energy = (1/2) * mass of proton * (velocity of proton)^2
The mass of a proton is approximately 1.67 x 10^-27 kg, and the velocity is 3.64 x 10^6 m/s. Calculate the initial kinetic energy.
Next, you can calculate the potential energy between the proton and the alpha particle using the formula for electrostatic potential energy:
Electric Potential Energy (U) = (k * |q1 * q2|) / r
Where:
- k is the electrostatic constant (approximately 8.99 x 10^9 N m^2/C^2)
- q1 and q2 are the charges of the proton and alpha particle, respectively
- r is the distance between them
q1 (charge of proton) = 1.6 x 10^-19 C
q2 (charge of alpha particle) = 2 * 1.6 x 10^-19 C (since an alpha particle consists of 2 protons and 2 neutrons)
Now, you can calculate the potential energy when the proton is at a distance "r" from the alpha particle. Set this potential energy equal to the initial kinetic energy of the proton and solve for "r":
Initial Kinetic Energy = Electric Potential Energy
(1/2) * mass of proton * (velocity of proton)^2 = (k * |q1 * q2|) / r
Now, solve for "r" to find how close the proton will come to the alpha particle before coming to a stop.