Question

Can you estimate the de Broglie wavelength of the Earth?

Answer 1

Estimate the Earth’s mass as \[6.0 \times 10^{24}\mathrm{kg}\] and its orbital speed as \[3.0 \times 10^{4}\mathrm{m,s^{-1}}\].

h = \[6.626 \times 10^{-34}\mathrm{J s}\]

Formula: \[\lambda = \frac{h}{p} = \frac{h}{mv}\]

\[\lambda = \frac{6.626 \times 10^{-34}\mathrm{J s}}{(6.0 \times 10^{24}\mathrm{kg})(3.0 \times 10^{4}\mathrm{m s^{-1}})}\]

\[\lambda \approx 3.7 \times 10^{-63}\mathrm{m}\]