JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
A nucleus \(A\), with a finite de -broglie wavelength \(\lambda_A\), undergoes spontaneous fission into two nuclei \(B\) and \(C\) of equal mass. \(B\) flies in the same direction as that of \(A\), while \(C\) flies in the opposite direction with a velocity equal to half of that of \(B\). The de -Broglie wavelength \(\lambda_B\) and \(\lambda_C\) of \(B\) and \(C\) are respectively
- A \(\lambda_A\), \(2\lambda_A\)
- B \(2\lambda_A\), \(\lambda_A\)
- C \(\lambda_A\), \(\frac{\lambda_A}{2}\)
- D \(\frac{\lambda_A}{2}\), \(\lambda_A\)
Answer & Solution
Correct Answer
(D) \(\frac{\lambda_A}{2}\), \(\lambda_A\)
Step-by-step Solution
Detailed explanation
Let mass of \(B\) and \(C\) is \(m\) each. By momentum conservation \(2 m v_{0}=m v-\frac{m v}{2}\) \(\mathrm{v}=4 \mathrm{v}_{0}\) \({{\text{P}}_{\text{A}}} = 2{\text{m}}{{\text{v}}_0}\) \({{\text{p}}_{\text{B}}} = 4{\text{m}}{{\text{v}}_0}\)…
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