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A nucleus at rest undergoes \( \alpha- \) decay according to the equation, \( { }_{92}^{225} X \longrightarrow Y+\alpha \). At time \( t=0 \), the emitted \( \alpha \)-particle enters in a region of space where a uniform magnetic field \( \vec{B}=B_{0} \hat{i} \) and electric field \( \vec{E}=E_{0} \hat{i} \) exist. The \( \alpha \)-particle enters in the region with velocity \( \vec{V}=v_{0} \hat{j} \) from origin. At time \( \mathrm{t}=\sqrt{3} \times 10^{7} \frac{\mathrm{m}_{\alpha}}{\mathrm{q}_{\alpha} \mathrm{E}_{0}} \) sec., where \( \mathrm{m}_{\alpha} \) is the mass and \( \mathrm{q}_{\alpha} \) is the charge of \( \alpha \)-particle. The particle was observed to have speed twice the initial speed \( v_{0} \). Then find :
(b) the velocity of \( \alpha \)-particle at time t
Given that : \( m(Y)=221.03 \mathrm{u}, m(\mathrm{He})=4.003 \mathrm{u}, \mathrm{m}(\mathrm{n})=1.009 \mathrm{u} \), \( m(p)=1.0084 \mathrm{u} \) and \( 1 \mathrm{u}=1.67 \times 10^{-27} \mathrm{~kg}=931 \mathrm{MeV} / \mathrm{c}^{2} \)
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