NEETPhysicsDual Nature of Matter
A stationary radioactive nucleus of mass M undergoes alpha decay, emitting an alpha particle of mass m . What is the ratio of the de-Broglie wavelength of the emitted alpha particle to that of the recoiling daughter nucleus?
Options
- AM-m : m
- B1 : 1
- C(M-m) : m
- Dm : (M-m)
Correct answer
B. 1 : 1
Step-by-step solution
According to the law of conservation of linear momentum, the initial momentum of the stationary nucleus is zero. Therefore, the final momentum of the system must also be zero. Let p _ be the momentum of the emitted alpha particle and p _ recoil be the momentum of the recoiling daughter nucleus. Applying momentum conservation: p _ + p _ recoil = 0 | p _ | = | p _ recoil | The de-Broglie wavelength of a particle is given by the relation = h p , where p is the magnitude of its momentum. Since the magnitudes of the mom