A uranium nucleus (initially m(u) = 238 u) sits at rest in empty space. Suddenly

Question

A uranium nucleus (initially m(u) = 238 u) sits at rest in empty space. Suddenly it decays, becoming a thorium nucleus [m(Th)=234 u], and ejecting a small part of its mass as an alpha-particle [m(a)= 4 u] with velocity v(a). Fill in the following blanks

a. The thorium nucleus recoils with velocity v(Th). V(Th) equals _____ times v(a).

b. The kinetic energies of the outgoing particles are K(a) and K(Th). K(a) equals _____ times K(Th).

[Express the following anser algebraically, as a multiple of v(a) if necessary]:

c. What is the velocity of the center-of-mass of the tow outgoing particles? v(cm)= _______

Explanation / Answer

a. Conservation of momentum:

   m1u1 + m2u2 = m1v1 + m2v2

   0 = 234*V(Th) + 4*V(a)

Thus, V(Th) = -4/234 * V(a) = -0.017 times V(Th)

b. K(a) = 0.5*4*V(a)^2

    K(Th) = 0.5*234*0.017^2*V(a)^2

Thus, K(a) / K(Th) = 4 / (234*0.017*0.017) = 59.15

c. Velocity of centre of mass doesn't change. Thus, it will still be ZERO

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