Estimate your de Broglie wavelength (in m) when you are running. (Recall that h ~ 10−34 in SI units and 1 lb is equivalent to 0.45 kg.) For the computation, estimate how fast you can run in meters per second. (Give your mass in kg. Do not be too optimistic in your estimation. Remember the fastest runner can run 100 m in 9.58 s!)

Question

Estimate your de Broglie wavelength (in m) when you are running. (Recall that h ~ 10−34 in SI units and 1 lb is equivalent to 0.45 kg.) For the computation, estimate how fast you can run in meters per second. (Give your mass in kg. Do not be too optimistic in your estimation. Remember the fastest runner can run 100 m in 9.58 s!)

Answer 1

To estimate the de Broglie wavelength when running, we first need to estimate the speed we can run at.

Let's say the fastest runner can run 100 m in 9.58 s, so their speed would be 100 m / 9.58 s = 10.46 m/s. Let's estimate that a more average person can run at around 6 m/s.

Assuming a mass of around 70 kg (average for an adult), we have:
v = 6 m/s
m = 70 kg
h = 10^-34 m^2 kg / s

Now, we can calculate the de Broglie wavelength using the formula:
λ = h / mv

λ = (10^-34 m^2 kg / s) / (70 kg * 6 m/s)
λ ≈ 2.38 x 10^-36 m

So, the estimated de Broglie wavelength when running would be approximately 2.38 x 10^-36 meters.