Question

Beryllium-8 is an unstable isotope and decays into two α particles, which are helium nuclei with mass 6.68×10−27kg. This decay process releases 1.5×10−14J of energy. For this problem, let's assume that the mass of the Beryllium-8 nucleus is just twice the mass of an α particle and that all the energy released in the decay becomes kinetic energy of the α particles.

a) If a Beryllium-8 nucleus is at rest when it decays, what is the speed of the  α particles after they are released?

b) If the Beryllium-8 nucleus is moving in the positive x-direction with a speed of 1.0×106 m/s when it decays, what is the speed of the slower-moving α particle after it is released? Assume that the α particles move entirely in the x-direction.

c) If the Beryllium-8 nucleus is moving in the positive x-direction with a speed of 1.0×106 m/s when it decays, what is the speed of the faster-moving α particle after it is released?  Assume that the α particles move entirely in the x-direction.

Answer 1

a) The energy released in the process is 1.5*10^-14 J

Since the two daughter nuclei are of the same particle, the energy will be divided equally among the two.

So,

Using the equation

with the mass of alpha particle to be 6.68*10^-27 kg,

So,

b) Here, the initial nucleus is moving in the forward X direction. According to law of conservation of momentum, the momentum of daughter nuclei must be same as the parent nucleus.

This can be evaluated in another way.

If the particles were at rest, one alpha particle would have gone in the +x direction with a velocity got from part A and the other moves in the -x direction with the same velocity.

Now, since the particles were initially moving, the forward moving particle will get some extra velocity and the backward moving particle will lose the same velocity.

Here, the initial velocity is 1.0*10⁶ m/s

So, the effective velocity of the slower particle will be

(in the -x direction)

c) The speed of the faster moving particle is

Here, the relativistic effects are not to be considered, since it is very small and negligible.