Concept:For objects moving at identical velocities, their de Broglie wavelengths depend solely on their masses in an inversely proportional relationship.
Formula:$$ \lambda = \frac{h}{mv} $$
Solution:- Since velocity \( v \) is constant for all particles, \( \lambda \propto \frac{1}{m} \).
- To find the shortest wavelength, we must identify the particle with the largest mass.
- An alpha particle consists of 2 protons and 2 neutrons (mass \( \approx 4 \text{ amu} \)), making it significantly heavier than an electron, a single proton, or a single neutron.
- Therefore, the alpha particle has the shortest wavelength.
Why other options are incorrect:An electron has the smallest mass and would thus exhibit the longest wavelength. Protons and neutrons have intermediate masses.
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