Which of the following particles has the largest de Broglie wavelength $\lambda$ if all are moving with the same velocity $v$?

Solution

1. The de Broglie wavelength is $\lambda =\frac{h}{mv}$.
2. For a constant velocity $v$, $\lambda \propto \frac{1}{m}$.
3. Compare the masses: $m_{\text{electron}}<m_{\text{proton}}\approx m_{\text{neutron}}<m_{\text{alpha}}$.
4. The electron has the smallest mass, thus it has the largest wavelength.
5. Hence the answer is (C).