AP EAMCET · PHYSICS · Dual Nature of Matter
The ratio of de Broglie wavelengths associated with thermal neutrons at temperatures \(127^{\circ} \mathrm{C}\) and \(352^{\circ} \mathrm{C}\) is
- A \(5: 3\)
- B \(3: 2\)
- C \(3: 4\)
- D \(5: 4\)
Answer & Solution
Correct Answer
(D) \(5: 4\)
Step-by-step Solution
Detailed explanation
\(T_1 = 127 + 273 = 400 \, \mathrm{K}\) \(T_2 = 352 + 273 = 625 \, \mathrm{K}\) \(\lambda \propto \frac{1}{\sqrt{T}}\) \(\frac{\lambda_1}{\lambda_2} = \sqrt{\frac{T_2}{T_1}} = \sqrt{\frac{625}{400}}\) \(\frac{\lambda_1}{\lambda_2} = \sqrt{\frac{25}{16}} = \frac{5}{4}\)
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