In radioactive decay a nucleus splits apart into charged pro

In radioactive decay a nucleus splits apart into charged products. In the case of uranium the nucleus decays into an alpha particle and a thorium nucleus. The alpha particle is just a helium nucleus (4/2 He) with a mass of 4 u and a positive charge of 2e. The thorium nucleus has a mass of 234 u and a positive charge of 90e. Just after the uranium nucleus breaks apart the system is essentially at rest and the two products are separated by 7.4 fm. What is the initial momentum of the system just after the decay? Find the speed of the alpha particle after they are a great distance apart.

Solution

A) nucleaus breaks apart due to internal forces.

hence momentum of system will be zero.

B) suppose speed of nucleus is V and speed of alpha is v.

Using momentum conservation,

0 = MV - mv

V = mv/ M = (4u v) / (234u) = 0.0171v

initial PE = kq1q2/d

PEi = (9 x 10^9 x 2 x 1.6 x 10^-19 x 90 x 1.6 x 10^-19) / (7.4 x 10^-15 )

PEi = 5.60 x 10^-12 J

initial KE = 0

and final PE = 0

using energy conservation,

5.60 x 10^-12 J = mv^2 /2 + MV^2 /2

5.60 x 10^-12 = (4u v^2 / 2) + (234u ( 0.0171v)^2 / 2)

5.60 x 10^-12 = 2.03 x 1.67 x 10^-27 x v^2

v = 4.06 x 10^7 m/s