An electron, an \(\alpha\)-particle and a proton have the same kinetic energy. which of these has the longest de Broglie wavelength?
- a-particle
- proton
- electron
- both a-particle and proton
The Correct Option is C
Solution and Explanation
For a particle, de-Broglie wave length,
\(\lambda=\frac{h}{p}\)
Kinetic energy,
\(K=\frac{p^2}{2m}\)
Then, \(\lambda=\frac{h}{\sqrt2 mk}\propto \frac{1}{m}\)
so, Since an electron has the smallest mass, it also has the greatest de-Broglie wavelength.
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Concepts Used:
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The dual nature of matter and the dual nature of radiation were throughgoing concepts of physics. At the beginning of the 20th century, scientists untangled one of the best-kept secrets of nature – the wave-particle duplexity or the dual nature of matter and radiation.
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