What is the de Broglie wavelength of a hummingbird weighing 31.7 g flying at 30.0 mph?

To determine the de Broglie wavelength of the hummingbird, one must use the de Broglie wavelength formula, which is given by:

[

\lambda = \frac{h}{p}

]

where (\lambda) is the wavelength, (h) is Planck's constant ((6.626 \times 10^{-34} \text{ Js})), and (p) is the momentum of the object. The momentum (p) is calculated by multiplying the mass (m) of the hummingbird by its velocity (v):

[

p = mv

]

First, convert the mass of the hummingbird from grams to kilograms:

[

31.7 \text{ g} = 0.0317 \text{ kg}

]

Next, convert the velocity from miles per hour to meters per second. Since (1 \text{ mph} = 0.44704 \text{ m/s}), we have:

[

30.0 \text{ mph} = 30.0 \times 0.44704 \text{ m/s} \approx 13.41 \text{ m/s}

]

Now, calculating the momentum: