electron vs proton wavelength

Question

At same kinetic energy, which has longer de Broglie wavelength?

RankGuru · Accepted Answer

1. **Wavelength Formula**: $\lambda = \frac{h}{p} = \frac{h}{\sqrt{2mK}}$.
2. **Conditions**: Fixed kinetic energy ($K$) and constant ($h$).
3. **Dependence**: $\lambda \propto \frac{1}{\sqrt{m}}$. Wavelength is inversely proportional to the square root of the mass.
4. **Mass Comparison**: $m_{electron} \approx 9.11 	imes 10^{-31} 	ext{ kg} < m_{proton} \approx 1.67 	imes 10^{-27} 	ext{ kg}$.
5. **Deduction**: Since the electron is much lighter, it has a **longer** de Broglie wavelength than a proton if they have the same energy.

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electron vs proton wavelength

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