I don't know how to go about this question. We only have an initial velocity and no final velocity, distance or time.
A proton is fired from far away toward the nucleus of a mercury atom. Mercury is element number 80, and the diameter of the nucleus is 14.0 fm. The proton is fired at a speed of 3.20×107 m/s. When it passes the nucleus, how close will the proton be to the surface of the nucleus? Assume the nucleus remains at rest.
well, you have a + 80 e charge fired at a +1 e charge
they repel each other
How close will the proton get to the 80 protons?
when the kinetic energy of the oncoming proton is used up climbing the potential hill of the 80 protons. it stops and backs away
Ke = (1/2) m v^2
potential of test charge q' at distance r from q is
U = 9*10^9 q q' / r
q = 80 e
q' = e
so
9*10^9 (80 e^2) /r = (1/2) m v^2
e = 1.6 * 10^-19
m = proton mass = 1.7 *10^-27
v given = 3.2*10^7
so solve for r
hope r is bigger than d/2 = 7 *10^-15
so subtract 7*10^-15 from your r to get altitude from the surface
To solve this problem, we can use the principles of projectile motion and conservation of energy. Here's how you can go about answering the question:
1. Determine the initial kinetic energy of the proton:
- The kinetic energy formula is given by KE = (1/2)mv^2, where m is the mass and v is the velocity.
- Since the mass of a proton is about 1.67 x 10^-27 kg, and the velocity is given as 3.20 x 10^7 m/s, you can calculate the initial kinetic energy.
2. Apply conservation of energy:
- As the proton moves towards the nucleus, its kinetic energy will be converted to potential energy.
- At the closest approach, all the initial kinetic energy of the proton will be converted into potential energy.
- The potential energy formula is given by PE = G(m1m2)/r, where G is the gravitational constant, m1 and m2 are the masses, and r is the distance between them.
- In this case, we can consider the proton-nucleus interaction as a gravitational interaction, so we can use the gravitational potential energy formula.
3. Calculate the distance between the proton and the nucleus at closest approach:
- Set the potential energy equal to the initial kinetic energy and solve for the distance (r).
- Rearrange the equation and substitute the values:
G(m1m2)/r = (1/2)mv^2.
- Simplify the equation and solve for r.
4. Determine the minimum distance:
- The minimum distance is the radius of the nucleus minus half its diameter.
- Use the given diameter of the nucleus (14.0 fm) to calculate the radius and subtract half of it from the previously calculated distance (r) to get the minimum distance.
By following these steps, you should be able to find how close the proton will be to the surface of the nucleus when it passes by.