How Is Momentum Conserved in a Two-Dimensional Radioactive Decay?

[Procrastinate]

A radioactive nucleus of mass 5 × 10^–26 kg is at rest and emits two neutrons,
each of mass 1.6 × 10^–27 kg, at right angles to each other. If both have speeds of
360 m s^–1, calculate the recoil speed of the nucleus.


I named calculated the neutrons and named them p₁ and p₂.
Since p₁ = p₂
Therefore the momentum of both equals 1.8x10^-26

Using Pythagoras, I worked out the overall momentum to be 2.55x10^-26

I then used the formula m₁v₁ = m₂v₂ and worked out the velocity to be 509-510ms^-1; I didn't bother working out the angle because that was already the wrong answer. The real answer is 17.39ms^-1.

What have I done wrong? Thanks in advance.

 

[rl.bhat]

Therefore the momentum of both equals 1.8x10-26

Using Pythagoras, I worked out the overall momentum to be 2.55x10-26
Check these two calculations. They are wrong.

 

[Procrastinate]

Therefore the momentum of both equals 1.8x10-26

Using Pythagoras, I worked out the overall momentum to be 2.55x10-26
Check these two calculations. They are wrong.

It turns out I just got mixed up with the numbers and exponents. Thanks.

Is my formula for this correct by the way (I'll count the two neutrons as one mass)?

m₁u₁ + m₂u₂ = m₂v₂ + m₂v₂

 

[rl.bhat]

It turns out I just got mixed up with the numbers and exponents. Thanks.

Is my formula for this correct by the way (I'll count the two neutrons as one mass)?

m₁u₁ + m₂u₂ = m₂v₂ + m₂v₂

The formula is correct. The left hand side is zero. After emission the mass of the nucleus is reduced by two times the mass of the neutrons.