Which of the following particles has the longest de Broglie wavelength if they all move with the same velocity $v$?

Solution

1. The de Broglie wavelength is given by the formula $\lambda =\frac{h}{mv}$, where $h$ is Planck's constant, $m$ is mass, and $v$ is velocity.
2. Since all particles move with the same velocity $v$, the wavelength $\lambda$ is inversely proportional to the mass $m$ of the particle.
3. Comparing the masses of the given particles, the electron has the smallest mass.
4. Because the electron has the smallest mass, it results in the largest value for $\lambda$.
5. Hence the answer is (C).