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JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
Particle \(A\) of mass \(m_{A}=\frac{m}{2}\) moving along the \(x-\)axis with velocity \(v_{0}\) collides elastically with another particle \(B\) at rest having mass \(m _{ B }=\frac{ m }{3}\) If both particles move along the \(x-\)axis after the collision, the change \(\Delta \lambda\) in \(de-\)Broglie wavelength of particle \(A,\) in terms of its \(de-\)Broglie wavelength \(\left(\lambda_{0}\right)\) before collision is
- A \(\Delta \lambda=4 \lambda_{0}\)
- B \(\Delta \lambda=\frac{5}{2} \lambda_{0}\)
- C \(\Delta \lambda=2 \lambda_{0}\)
- D \(\Delta \lambda=\frac{3}{2} \lambda_{0}\)
Answer & Solution
Correct Answer
(A) \(\Delta \lambda=4 \lambda_{0}\)
Step-by-step Solution
Detailed explanation
Applying momentum conservation \(\frac{m}{2} \times V_{0}+\frac{m}{3} \times(0)=\frac{m}{2} V_{A}+\frac{m}{3} V_{B}\) \(=\frac{V_{0}}{2}=\frac{V_{A}}{2}+\frac{V_{B}}{3}\) \(....(1)\) since, collision is elastic \(( e =1)\)…
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