Question

what is the de broglie wavelength of a 11.7 g hummingbird flying at 105 mph? round your answer to 3 significant digits.
1 mile = 1.6093 km
note: reference the fundamental constants table for additional information.
note: reference the unit conversions for derived si units table for additional information.

Explanation:

Step1: Convert mass to kg

Given mass \(m = 11.7\ g\). Since \(1\ kg=1000\ g\), then \(m=\frac{11.7}{1000}\ kg = 0.0117\ kg\)

Step2: Convert speed from mph to m/s

Given speed \(v = 105\ mph\). First, convert miles to meters: \(1\ mile = 1.6093\ km=1609.3\ m\). Then convert hours to seconds: \(1\ hour = 3600\ s\).
\(v = 105\times\frac{1.6093\times1000}{3600}\ m/s\)
\(v=\frac{105\times1609.3}{3600}\ m/s\approx46.99\ m/s\)

Step3: Use de - Broglie formula \(\lambda=\frac{h}{mv}\)

where \(h = 6.626\times10^{-34}\ J\cdot s\) (Planck's constant)
\(\lambda=\frac{6.626\times 10^{-34}}{0.0117\times46.99}\ m\)
\(\lambda=\frac{6.626\times 10^{-34}}{0.5507}\ m\approx1.20\times10^{-33}\ m\)
Convert meters to centimeters: Since \(1\ m = 100\ cm\)
\(\lambda=1.20\times 10^{-31}\ cm\)

Answer:

\(1.20\times 10^{-31}\)