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AIIMS 2004
Exam
AIIMS
Year
2004
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

AIIMS 2004 · Physics · Center of Mass, Momentum and Collision

A nucleus of mass number A , originally at rest, emits an α...

A nucleus of mass number AA, originally at rest, emits an α\alpha-particle with speed vv. The daughter nucleus recoils with a speed

Options

  1. A2vA+4\frac{2 v}{A+4}
  2. B4vA+4\frac{4 v}{A+4}
  3. C4vA−4\frac{4 v}{A-4}
  4. D2vA−4\frac{2 v}{A-4}

Correct answer

C. 4vA−4\frac{4 v}{A-4}

Step-by-step solution

{ }^A X \quad \rightarrow{ }^{A-4} Y+\alpha^4(parentnucleus)(daughternucleus)Astheparentnucleusisatrest,thenaccordingtoconservationofmomentum.(parent nucleus) (daughter nucleus) As the parent nucleus is at rest, then according to conservation of momentum.\begin{aligned}& \Rightarrow \quad 0=m_Y v_Y+m_\alphav_\alpha\\ & \Rightarrow \quad 0=(A-4) v_Y+4 v \end{aligned}⇒vY=\Rightarrow \quad v_Y=\frac{4 v}{A-4} \text{,\text{ the }\text{ recoil }\text{ speed }\text{ of }\text{ daughter }\text{ nucleus }. }$
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