For an electron and a proton that have the same (a) kinetic energy. (b) momentum, or (c) speed, which particle has the shorter de Broglie wavelength?

Explanation

To solve the question regarding the de Broglie wavelength of an electron and a proton under different conditions, we will analyze each case step by step.

### Step 1: Same Kinetic Energy
1. **Formula for de Broglie wavelength**: The de Broglie wavelength (\( \lambda \)) is given by the formula:
\[ \lambda = \frac{h}{p} \]
where \( h \) is Planck's constant and \( p \) is the momentum of the particle.
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