Question

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

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 velocity to m/s

Given velocity \(v = 105\ mph\). Since \(1\ mile = 1.6093\ km=1609.3\ m\) and \(1\ hour = 3600\ s\). Then \(v = 105\times\frac{1609.3}{3600}\ m/s\approx46.96\ m/s\)

Step3: Use de - Broglie wavelength formula

The de - Broglie wavelength formula is \(\lambda=\frac{h}{mv}\), where \(h = 6.626\times10^{-34}\ J\cdot s\) (Planck's constant). Substitute \(m = 0.0117\ kg\) and \(v\approx46.96\ m/s\) into the formula: \(\lambda=\frac{6.626\times 10^{-34}}{0.0117\times46.96}\)

$$
LATEXBLOCK0
$$

Answer:

\(1.21\times 10^{-33}\ m\)