Solving Mechanics Problem: Find Direction & Momentum of Recoiling Nucleus

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In summary, a nucleus undergoing spontaneous radioactive decay emits an electron and a neutrino in opposite directions. The electron has a momentum of 1.73 MeV/c and the neutrino has a momentum of 1 MeV/c. The direction and momentum of the recoiling nucleus can be determined using momentum conservation, and whether to use relativistic or classical equations depends on the accuracy required for the calculation.
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neelakash
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Homework Statement



A nucleus at rest undergoes spontaneous radioactive decayby emitting an electron of momentum 1.73 MeV/c and at right angle to to the direction of electron, a neutrino of momentum 1 MeV/c.Find the direction and momentum of the recoiling nucleus.
Here c is the velocity of light.

Homework Equations


The Attempt at a Solution



I CAN do this...but I am wondering if we are to employ the relativistic momentum concept...
Can anyone clarify?
 
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  • #2
If the momenta given in the question have been accurately determined, you don't even have to bother about whether you should use relativistic or classical equations. Both would turn up the same answer, since we make use of only momentum conservation. Now if the question were to do with something like velocity of recoil, for accuracy you should use relativistic calculations.
 
  • #3
I see...
Thank you.
 

1. What is the first step in solving a mechanics problem involving a recoiling nucleus?

The first step is to identify the given information, including the mass of the recoiling nucleus and the velocity of the emitted particle. This will help determine the initial momentum of the system.

2. How do you find the direction of the recoiling nucleus?

The direction of the recoiling nucleus can be found by using the conservation of momentum principle. The direction will be opposite to the direction of the emitted particle.

3. What is the equation for calculating momentum?

The equation for momentum is p=mv, where p is momentum, m is mass, and v is velocity. It is important to make sure that the units for mass and velocity are consistent when plugging them into the equation.

4. How does the mass of the emitted particle affect the momentum of the recoiling nucleus?

According to the conservation of momentum principle, the total momentum of a system remains constant. This means that the mass of the emitted particle will have an inverse relationship with the momentum of the recoiling nucleus. A heavier emitted particle will result in a lower momentum of the recoiling nucleus, and vice versa.

5. Can the direction and momentum of the recoiling nucleus be determined experimentally?

Yes, the direction and momentum of the recoiling nucleus can be determined experimentally by measuring the angle and velocity of the emitted particle. These values can then be used to calculate the direction and momentum of the recoiling nucleus using the conservation of momentum principle.

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