COMEDK · Physics · 27. Dual Nature of Matter
The mass of a particle \(\mathrm{A}\) is double that of the particle \(\mathrm{B}\) and the kinetic energy of \(\mathrm{B}\) is \(\dfrac{1}{8}\)th that of A then the ratio of the de- Broglie wavelength of A to that of B is:
- A 2 : 1
- B 4 : 1
- C 1 : 4
- D 1 : 2
Answer & Solution
Correct Answer
(C) 1 : 4
Step-by-step Solution
Detailed explanation
\(\lambda = \dfrac{h}{\sqrt{2mK}}\) Given: \(m_A = 2m_B\) and \(K_B = \dfrac{1}{8}K_A \Rightarrow K_A = 8K_B\) \(\dfrac{\lambda_A}{\lambda_B} = \sqrt{\dfrac{m_B K_B}{m_A K_A}} = \sqrt{\dfrac{m_B \cdot K_B}{2m_B \cdot 8K_B}} = \sqrt{\dfrac{1}{16}} = \dfrac{1}{4}\)…
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