Physics

Problem

When a certain beam of neutrons has kinetic energy

36\,\text{eV}

, the de Broglie wavelength read from a plotted curve is

0.20\,\text{nm}

. Using the same curve, what wavelength should be expected when the kinetic energy is increased to

144\,\text{eV}

? a)

0.15\,\text{nm}

0.05\,\text{nm}

0.10\,\text{nm}

0.40\,\text{nm}

Intuitive explanation

The de Broglie wavelength depends on momentum, which is related to kinetic energy—but not linearly. Since $KE = \frac{p^2}{2m}$ , kinetic energy scales with the square of momentum, so wavelength $\lambda = \frac{h}{p}$ scales inversely with the square root of energy. When you increase energy by a factor of 4, momentum increases by a factor of 2, and wavelength shrinks by a factor of 2.

Intuitive explanation

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