Question

A uranium-238 nucleus,initially at rest,emits an alpha particle with a speed of $1.4\times {10}^7$ $m/s$.Calculate the recoil speed of the residual nucleus thorium-234.Assume that the mass of a nucleus is proportional to the mass number.+

Answer 1

As uranium 238 nucleus emits,$\alpha$-particle with a speed of $1.4\times {10}^7$ $m/s$.

Let $v_2$ be the speed of the residual nucleus throium 234.

$\therefore m_1{v}_1=m_2{v}_2$

$\Rightarrow 4\times 1.4\times {10}^7=234\times v_2$

$v_2=\frac{4\times 1.4\times {10}^7}{234}$

$=2.4\times {10}^5\frac{m}{sec}$