Question

# A nucleus with mass number $$220$$ initially at rest emits an $$\alpha \ particle$$. If the $$Q$$ value of the reaction is $$5.5 MeV$$, calculate the kinetic energy of the $$\alpha\ particle$$

A
4.4MeV
B
5.4MeV
C
5.6MeV
D
6.5MeV

Solution

## The correct option is B $$5.4 MeV$$$$M \rightarrow X+ \alpha$$$$E = \cfrac{p^2}{2m}$$Let Total energy = $$T$$$$T = E_{\alpha} + E_{X}$$$$M = M_{\alpha} + M_{X}$$$$M_{X}= 216$$Conservation of momentum$$p_{\alpha} = p_{X}$$$$m_{\alpha} E_{alpha} = m_XE_X$$$$E_{\alpha} = \cfrac{m_x}{M}T$$$$E_{\alpha} = \cfrac{216}{220} 5.5 = 5.4 MeV$$Physics

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