Sample 1Medium
A proton and an alpha particle, both initially at rest, are accelerated through the same potential difference. The ratio of their de Broglie wavelengths (proton : alpha) is
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The answer is B.
λ = h/√(2mqV). For the alpha particle mq = 4m × 2e = 8me, so λp/λα = √8 = 2√2.
- A.
√2 : 1 ignores the alpha particle's double charge.
- C.
1 : 2√2 inverts the ratio; the lighter proton has the longer wavelength.
- D.
2 : 1 takes only the mass ratio under the root and ignores the charge.
NCERT: Class 12 Physics, Chapter 11, Wave nature of matter