Homework #20 Problem 9.55 4 of 5 > Constants | Periodic Table Part A A radioacti

Question

Homework #20 Problem 9.55 4 of 5 > Constants | Periodic Table Part A A radioactive nucleus at rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have momenta of 9.45x1023 kg m/s and 6.80x1023 kg m/s respectively Determine the magnitude of the momentum of the second (recoiling) nucleus. | pnucleus- m's SubmitRec Request Answer Part B Determine the direction of the momentum of the second (recoiling) nucleus. Assume that the neutrino and the electron move along -z and -y axes respectively i counterclockwise from the + axis. SubmitRec Request Answer

Explanation / Answer

Since the original momentum was 0, the final momentum must be 0. Therefore, the momentum of the second nucleus must equal the opposite of the sum of the momenta of the electron and the neutrino.

If we choose coordinates so that:
- electron momentum =9.45*10-23 i
- neutrino momentum = 6.8*10-23 j
the second nucleus has momentum:
p = 10-23 (9.45i + 6.8j)

Since

sqrt(9.452 + 6.82)*10-23

= 11.64*10-23 ,


Since both x and y components of momentum are negative, the direction of recoiling nucleas will be in first quadrant:

the tangent of the angle is 6.8/9.45

=0.719

so the angle from the x axis must be: + Arctan(0.719)

= 35.73 degrees.

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