A neutron with a mass of 1.67x10^-27 kg traveling east with a kinetic energy of 2.00x10^-21J collides perfectly elastically with helium nucleus with a mass 6.68x10^-27 kg that is initially at rest. After the collision, the neutron has a kinetic energy 1.80x10^-21J. What angle was the neutron deflected during the collision?
To determine the angle at which the neutron was deflected during the collision, we can use the principles of conservation of momentum and conservation of kinetic energy.
Let's analyze the scenario step by step:
1. Determine the initial and final velocities of the neutron and helium nucleus:
- The neutron has an initial kinetic energy of 2.00x10^-21 J and a final kinetic energy of 1.80x10^-21 J.
- We can use the formula for kinetic energy to find the initial and final velocities for the neutron.
- The formula for kinetic energy is KE = 0.5 * mass * velocity^2.
- Plugging in the values, we can solve for the initial and final velocities of the neutron.
2. Apply the conservation of momentum:
- Momentum is conserved in a perfectly elastic collision, meaning the total momentum before and after the collision is the same.
- The momentum of an object can be calculated by multiplying the mass of the object by its velocity.
- Since the helium nucleus is initially at rest, its momentum is zero.
- Set up an equation with the initial momentum of the neutron equal to the final momentum of the neutron plus the final momentum of the helium nucleus.
- Solve the equation for the final velocity of the helium nucleus.
3. Use trigonometry to find the angle of deflection:
- Once the final velocities of the neutron and helium nucleus are known, we can calculate the angle of deflection.
- The angle of deflection can be determined by the difference in direction between the initial and final velocities of the neutron.
- Use the formula for the angle between two vectors to find the angle of deflection.
By following these steps, we can get the numerical value of the angle at which the neutron was deflected during the collision.