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  4. Which of the following has the longest de-Broglie wavelength if they are moving with same velocity ?

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Q. Which of the following has the longest de-Broglie wavelength if they are moving with same velocity ?

Gujarat CETGujarat CET 2007Dual Nature of Radiation and Matter

Solution:

According to de-Broglie hypothesis, the wavelength of the wave associated with particle moving with velocity v is given by
$ \lambda = \frac{ h }{ mv } $
Since, v remains the same, therefore
$ \lambda \propto \frac{ 1 }{ m } $
As $ m_\alpha > m_n > m_p > m_\beta $
$\therefore \lambda_\alpha < \lambda_n < \lambda_p < \lambda_\beta$
Therefore, $\beta$ particle has longest wavelength.