AP EAMCET · PHYSICS · Dual Nature of Matter
An \(\alpha\)-particle and a proton are accelerated from rest by the same potential, then the ratio of their de-Broglie wavelength is
- A \(2 \sqrt{2}: 1\)
- B \(1: 2 \sqrt{2}\)
- C 1 : 2
- D 2 : 1
Answer & Solution
Correct Answer
(B) \(1: 2 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
de-Broglie's wavelength, \[ \lambda=\frac{h}{p}=\frac{h}{\sqrt{2 m E}}=\frac{h}{\sqrt{2 m e V}} \] The particles are at same potential, so \[ \frac{\lambda_\alpha}{\lambda_p}=\frac{h / \sqrt{2 m_\alpha e_\alpha V}}{h / \sqrt{2 m_p e_p V}} \] Mass of \(\alpha\)-particle \(=4\)…
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