AP Physics 2 Exam Question: Consider a nuclear reaction in which a proton (p) collides with a uranium-235 nucleus (U-235) and produces an element X and three neutrons (n). The nuclear reaction can be represented as:

p + U-235 --> X + 3n

1. Assuming a total momentum of zero before and after the reaction, calculate the mass of the element X produced if the proton has a mass of 1.0073 atomic mass units (amu), the uranium-235 nucleus has a mass of 235.0439 amu, and the neutron has a mass of 1.0087 amu.

Answer with Step-by-Step Explanation: To solve this problem, we need to use the principle of conservation of momentum and conservation of mass.

1. Conservation of momentum: Since the total momentum before and after the reaction is zero, we can write the equation as:

(momentump + momentumU-235) = momentumX + 3(momentumn)

Since the proton and neutrons are initially at rest and the total momentum in the reaction should be zero, we can simplify the equation to:

momentumU-235 = momentumX + 3(momentumn)

2. Conservation of mass: The mass of a particle is directly related to its momentum. The equation relating momentum and mass is given by:

momentum = mass × velocity

Since the proton and neutrons are initially at rest, their momentum is simply equal to their mass.

Let's set up the equation for the conservation of mass:

(massp + massU-235) = massX + 3(massn)

Since we know the mass of the proton (1.0073 amu) and the neutron (1.0087 amu), we can substitute these values into the equation:

(1.0073 amu + 235.0439 amu) = massX + 3(1.0087 amu)

Now, let's solve for the mass of the element X.

235.0512 amu = massX + 3.0261 amu

massX = 235.0512 amu - 3.0261 amu

massX = 232.0251 amu

Answer: The mass of the element X produced in the nuclear reaction is approximately 232.0251 atomic mass units (amu).