A nucleus, initially at rest, decays radioactivly, leaving a residual nucleus. In the process, it emits two paricles horizontally: an electron with momentum 9.0 x 10^-21 kg m/s [E] and a neutrino with momentum 4.8 x 10^-21 kg m/s [S]. In what direction does the residual nucleus move? What is the magnitude of its momentum?

To determine the direction in which the residual nucleus moves, we can use the principle of conservation of momentum. Since the initial momentum of the system (nucleus + particles) is zero (as it was initially at rest), the final momentum of the system must also be zero.

Let's assign directions to the momenta of the particles for ease of calculations:

- Electron momentum (e): 9.0 x 10^-21 kg m/s [E]
- Neutrino momentum (v): 4.8 x 10^-21 kg m/s [S]

Since the electron momentum is in the positive E direction and the neutrino momentum is in the negative S direction, the momenta add up to zero. Therefore, the magnitude of the residual nucleus's momentum should be equal to the sum of the magnitudes of the electron and neutrino momenta, and its direction will be in the opposite direction of the electron momentum.

Magnitude of residual nucleus's momentum = |e| + |v|
= 9.0 x 10^-21 kg m/s + 4.8 x 10^-21 kg m/s
= 13.8 x 10^-21 kg m/s

Direction of the residual nucleus's momentum = Opposite direction of the electron momentum (E)

Therefore, the residual nucleus moves in the "E" direction, and the magnitude of its momentum is 13.8 x 10^-21 kg m/s.

To determine the direction of the residual nucleus's movement, we need to use the law of conservation of momentum. According to this law, the initial momentum of a system is equal to the final momentum of the system.

We have two particles emitted horizontally: an electron and a neutrino. Let's label them as "E" and "S" respectively.

The initial momentum of the system is zero since the nucleus is at rest. Therefore, the final momentum of the system should also be zero. This means that the momenta of the emitted particles should cancel each other out.

Given the momentum of the electron, E = 9.0 x 10^-21 kg m/s [E], and the momentum of the neutrino, S = 4.8 x 10^-21 kg m/s [S], we can conclude that the residual nucleus must move in the opposite direction to cancel out the momentum of the emitted particles.

Therefore, the residual nucleus moves in the direction opposite to the emission of the particles.

Now, let's calculate the magnitude of the momentum of the residual nucleus.

Since the initial momentum is zero, the magnitude of the final momentum will be the sum of the magnitudes of the momenta of the emitted particles.

The magnitude of the final momentum (P) is given by:

P = √(E^2 + S^2)

Substituting the given values:

P = √((9.0 x 10^-21)^2 + (4.8 x 10^-21)^2)

P = √(81 x 10^-42 + 23.04 x 10^-42)

P = √(104.04 x 10^-42)

P = 10.2 x 10^-21 kg m/s

Therefore, the magnitude of the momentum of the residual nucleus is 10.2 x 10^-21 kg m/s.

add the two momentum vectors, then the negative of it is the momentum of the nucleus.