Question

A nucleus moving with a velocity \[\vec{v}\] emits an α-particle. Let the velocities of the α-particle and the remaining nucleus be v₁ and v₂ and their masses be m₁ and m₂. 

Options

• \[\vec{v} , \vec{v}_1 \text{ and } \vec{v}_2\] must be parallel to each other.

• None of the two of \[\vec{v} , \vec{v}_1 \text{ and } \vec{v}_2\] should be parallel to each other.

• \[\vec{v_1} + \vec{v_2}\] must be parallel to \[\vec{v}\]

• \[m_1 \vec{v_1} + m_2 \vec{v_2}\]  must be parallel to \[\vec{v}\]

Answer 1

\[m_1 \vec{v_1} + m_2 \vec{v_2}\] must be parallel to \[\vec{v}\] 
By the law of conservation of linear momentum, we can write:
\[\text{ Initial momentum } = \text{ Final momentum }\]
\[ \Rightarrow m \vec{v} = m_1 \vec{v}_1 + m_2 \vec{v}_2 \]
\[ \Rightarrow ( m_1 \vec{v}_1 + m_2 \vec{v}_2 ) \text{ must be parallel to } \vec{v}\]