Question

Problem 10.23 An alpha particle (a helium nucleus, containing 2 protons and 2 neutrons) starts out with kinetic energy of 10.0 MeV (10.0 × 106 eV), and heads in the +x direction straight toward a gold nucleus (containing 79 protons and 118 neutrons). The particles are initially far apart, and the gold nucleus is initially at rest. Answer the following questions about the collision. What is the initial momentum of the alpha particle? (You may assume its speed is small compared to the speed of light).  p→α, i= < , ,  > kg·m/s What is the initial momentum of the gold nucleus?  p→Au, i= < , ,  > kg·m/s What is the final momentum of the alpha particle, long after it interacts with the gold nucleus?  p→α, f= < , ,  > kg·m/s What is the final momentum of the gold nucleus, long after it interacts with the alpha particle?  p→Au, f= < , ,  > kg·m/s What is the final kinetic energy of the alpha particle?  Kα, f= J What is the final kinetic energy of the gold nucleus?  KAu, f= J Assuming that the movement of the gold nucleus is negligible, calculate how close the alpha particle will get to the gold nucleus in this head-on collision. rclosest= m What principle did you use to calculate the distance of closest approach? The Energy Principle No principles needed, just the definition of velocity The Momentum Principle Both the Energy Principle and the Momentum Principle There is not a principle that applies to this situation The radius of the alpha particle is about 2 × 10-15 m, and the radius of the gold nucleus is about 8 × 10-15 m. At the point of closest approach, do the two particles touch each other? NoNot enough information to tellYes To choose initial conditions for the program you will write to model collisions between an alpha particle and a gold nucleus, you will need to choose an initial location, and Δ⁢t. Estimating Δ⁢t: What is the initial speed of the alpha particle?  vα, i= m/s We suggest that in your program you start the alpha particle at a distance of 1 × 10-13 m from the gold nucleus. If the alpha particle did not slow down, how long would it take to travel all the way to the location of the nucleus? time = s For an accurate calculation you need to take many steps during the time the alpha particle is near the gold nucleus. Considering your estimate above, we suggest that you use Δ⁢t= 1 × 10-23 s in your program.

Answer 1