Concepts Of Physics MCQ Edition [Volume 2]PhysicsThe Nucleus
In the decay ⁶⁴ Cu ⁶⁴ Ni + e⁺ + , the maximum kinetic energy carried by the positron is observed to be 0.650 MeV . Determine the momentum of the neutrino in kg m s ⁻¹ if it is emitted alongside a positron having a kinetic energy of 0.150 MeV . Use the relation applicable to a photon.
Options
- A1.33 10⁻²² kg m s ⁻¹
- B3.47 10⁻²² kg m s ⁻¹
- C8.00 10⁻²³ kg m s ⁻¹
- D2.67 10⁻²² kg m s ⁻¹
Correct answer
D. 2.67 10⁻²² kg m s ⁻¹
Step-by-step solution
The total disintegration energy ( Q -value) is shared between the positron and the neutrino, neglecting the recoil of the daughter nucleus. Q = K_ (e⁺) = 0.650 MeV When the positron has a kinetic energy K_ e⁺ = 0.150 MeV , the energy of the neutrino is: E_ = Q - K_ e⁺ = 0.650 MeV - 0.150 MeV = 0.500 MeV Converting this energy to Joules: E_ = 0.500 10⁶ 1.6 10⁻¹⁹ J = 8.0 10⁻¹⁴ J For a neutrino, the relationship between energy and momentum is the same as that for a photon, E_ = p_ c . p_ = E_ c = 8.0 10⁻¹⁴ 3 10⁸ kg m