Q156 / 160 · TS EAMCET 2023 (13 May Shift 1) · Physics
$\alpha$-decay of a parent nucleus $\mathrm{X}$ results in a daughter nucleus Y. If $m_x, m_y$ and $m_a$ are the masses of the parent nucleus, the daughter nucleus and the $\alpha$ - particle respectively, then the net kinetic.energy gained in the process is
- A$\left(m_x+m_a-m_y\right) c^2$
- Correct answerB$\left(m_x-m_y-m_a\right) c^2$
- C$\left(m_x+m_y+m_a\right) c^2$
- D$\left(m_x+m_y-m_a\right) c^2$
Solution
${ }_2 \mathrm{He}^4+\mathrm{X} \rightarrow \mathrm{Y}$
The net kinetic energy gained in the process
$\Delta \mathrm{E}=\left(\mathrm{m}_{\mathrm{x}}+\mathrm{m}_{\mathrm{a}}-\mathrm{m}_{\mathrm{y}}\right) \mathrm{C}^2$
Hence, the correct answer is option: 'B'.