Question

Uranium 238 nucleus, initially at rest, emits an Alpha particle with the speed of 1.4*10^7 metre per second. Calculate the recoil speed of the residual nucleus Thorium 234 resume that mass of the nucleus is proportional to the mass number

Answer 1

$Mass\propto Mass$ $number$ or $mass=xA$,where $A$ is mass number

Thorium, $m_t=234x$ and mass of alpha particle, $m_a=4x$

Velocity of alpha particle is $v_a=1.4\times {10}^{7}m/s$ and that of thorium is $v_t$

Applying momentum conservation, $m_a{v}_a+m_t{v}_t=0\left(rest\right)$

so $v_t=-\frac{m_a{v}_a}{m_t}$, after putting values of masses we get

$v_t=-\frac{2v_a}{117}=-2.4\times {10}^{5}m/s$

$Magnitude$ of velocity of residue nucleus i.e. Thorium nuclei is found to be $2.4\times {10}^{5}m/s$.