QUESTION $4[$Total marks: $20]$

Thorium is an element with atomic number $90.$ Thorium$-234$ is a radioactive isotope,

which decays by emitting a particle with a kinetic energy of $0\mathrm{.}27$ MeV and a half$-$life

of $24$ days.

A group of atoms of this isotope is accelerated to a speed of $108$ m$/$s$.$

$4($a$)$ What is the kinetic energy of a $234$Th nucleus? $[5$ Marks$]$

$4($b$)$ What is the velocity of a particle in the frame of the thorium nucleii, if it is emitted

with a velocity in the same direction as the thorium nucleii? $[5$ Marks$]4($c$)$ In the same case, what is the velocity of the particle in the laboratory frame? $[5$

Marks$]$

$4($d$)$ If a particle was emitted in the direction normal to the path of the nucleii, what

speed will it have in the laboratory frame? $[5$ Marks$]$